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Designing Cost-Effective Reliable Networks From a Risk Analysis Perspective: A Case Study for a Hospital Campus

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Design and Implementation of a Hospital System Network Design (Project #7)

• Use Cisco Packet Tracer to design and implement the network solution.
• Use a hierarchical model providing redundancy in the network.
• Both HQ and Branch routers are expected to be connected using a serial connection.
• As mentioned earlier, for network cost-effectiveness, each site is expected to have one core router, two multilayer switches, and several access switches connecting each department.
• Each department is required to have a wireless network for the users.
• Every department in HQ is estimated to have around 60 users while in Branch is estimated to be 30 users.
• Each department should be in a different VLAN and a different subnetwork.
• Provided a base network of 192.168.100.0, and carry out subnetting to allocate the correct number of IP addresses to each department.
• The company network is connected to the static, public IP addresses (Internet Protocol) 195.136.17.0/30, 195.136.17.4/30, 195.136.17.8/30, and 195.136.17.12/30 connected to the two Internet providers.
• Configure basic device settings such as hostnames, console password, enable password, banner messages, and disable IP domain lookup.
• Devices in all the departments are required to communicate with each other with the respective multilayer switch configured for inter-VLAN routing.
• The Multilayer switches are expected to carry out both routing and switching functionalities and thus will be assigned IP addresses.
• All devices in the network are expected to obtain an IP address dynamically from the dedicated DHCP servers located in the server room.
• Devices in the server room are to be allocated IP addresses statically.
• Use OSPF as the routing protocol to advertise routes both on the routers and multilayer switches.
• Configure default static routing to enable routers and multilayer switches to forward any traffic that does not match routing table entries. Use next-hop IP addresses.
• Configure SSH in all the routers and layer three switches for remote login.
• Configure port-security for the server site department switch to allow only one device to connect to a switch port, use sticky method to obtain mac-address and violation mode shutdown.
• Configure the extended ACL rule together with site-to-site VPN (IPSec VPN) to create a tunnel and encrypt communication between HQ and the Branch network.
• Configure PAT to use the respective outbound router interface IPv4 address, and implement the necessary ACL rule.
• Test Communication, ensure everything configured is working as expected.
• Creating a network topology using Cisco Packet Tracer.
• Hierarchical Network Design.
• Connecting Networking devices with Correct cabling.
• Configuring Basic device settings.
• Creating VLANs and assigning ports VLAN numbers.
• Subnetting and IP Addressing.
• Configuring Inter-VLAN Routing on the Multilayer switches (Switch Virtual Interface).
• Configuring Dedicated DHCP Server device to provide dynamic IP allocation.
• Configuring SSH for secure Remote access.
• Configuring OSPF as the routing protocol.
• Configuring NAT Overload(Port Address Translation PAT).
• Configuring Site-to-Site IPsec VPN.
• Configuring standard and extended Access Control Lists ACL.
• Configuring switchport security or Port-Security on the switches.
• Configuring WLAN or wireless network (Cisco Access Point).
• Host Device Configurations.
• Configuring ISP routers.
• Test and Verifying Network Communication.

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Allegheny Health Network Wexford Hospital  High-Quality, Value-Driven Health Care Closer to Home 

Wexford, Pennsylvania, USA 

The Challenge

Allegheny Health Network enlisted HKS to expand its outpatient campus by designing an inpatient hospital that brings the same high level of care of its urban hubs to the Wexford suburb north of Pittsburgh. The existing outpatient pavilion was built in the center of its site and surrounded on three sides by surface parking lots, leaving a small area with steep topography, tight setbacks and height limitations for expansion. 

In addition to a strong focus on responsible design and sustainability, the design team took a value-based design approach centered on eight guiding principles: thinking ahead, enhanced brand, connected to community, focused care, coordinated care, caregiver satisfaction, improved user experience and flexibility.  

The Design Solution

To satisfy setback limitations and height restrictions, the hospital’s patient tower extends beyond the podium, creating a large overhang above the main entrance of the hospital with a dedicated loop for sheltered pick-up and drop-off.  

AHN Wexford Hospital offers an abundance of care, including women and infant care, labor and delivery, advance cardiac care, neurosurgery, orthopedics, oncology, 24-hour emergency care and neonatal and adult intensive care. Bedside access to patient electronic health records, telemedicine and remote monitoring increases both the quality and efficiency of care. 

Various terraces provide natural areas of respite for both patients and hospital staff, and the main lobby, dining rooms, conference rooms, waiting rooms, employee lounges and patient rooms are all situated around green spaces. A green roof reduces the heat island effect by decreasing the local ambient temperature and reduces energy loads within the building and collects rainwater. Native plants reduce the amount of water needed for irrigation, and creative storm water management systems mitigate runoff. Solar heat gain through the structure’s unitized glazed aluminum wall system helps offset the energy needed to reheat the building.  

The Design Impact

Wexford Hospital expands AHN’s brand and brings high-quality care closer to residents of Wexford, Pennsylvania. Its labor and delivery unit is the first in northern Allegheny County with a Level II neonatal intensive care unit and high-risk obstetrical services.  

Extensive prefabrication and unitization throughout the hospital reduced construction time and costs. The overhang of the tower is the world’s first Vierendeel Truss to use SidePlate technology, resulting in the use of 31% less steel and onsite labor.  

Project Features

• 295,000 square feet (27,406 square meters) 
• 160 private inpatient rooms 
• Prefabricated curtain wall, operating room ceilings and corridor MEP utility racks 
• First Level II neonatal intensive care unit and high-risk obstetrics in northern Allegheny County 
• Green roof 
• Cafe and conference center 
• 2023 AIA Healthcare Design Award 
• 2023 Healthcare Design Showcase Awards honorable mention 
• 2022 Human Experience Guardian of Excellence Award, Patient Experience 
• 2022 ENR MidAtlantic Health Care Best Project 

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Greg Luongo

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Shannon Kraus

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Case Study ACMC Hospital Routing Protocol Design

This case study is a continuation of the ACMC Hospital case study introduced in Chapter 2.

Case Study General Instructions

Use the scenarios, information, and parameters provided at each task of the ongoing case study. If you encounter ambiguities, make reasonable assumptions and proceed. For all tasks, use the initial customer scenario and build on the solutions provided thus far. You can use any and all documentation, books, white papers, and so on.

In each step, you act as a network design consultant. Make creative proposals to accomplish the customer's business needs. Justify your ideas when they differ from the provided solutions. Use any design strategies you feel are appropriate. The final goal of each case study is a paper solution.

Appendix A, "Answers to Review Questions and Case Studies," provides a solution for each step based on assumptions made. There is no claim that the provided solution is the best or only solution. Your solution might be more appropriate for the assumptions you made. The provided solution helps you understand the author's reasoning and allows you to compare and contrast your solution.

In this case study you determine the routing protocol design for the ACMC hospital network. Complete the following steps:

Step 1 Determine a suitable routing protocol or protocols for the ACMC network, and design the protocol hierarchy.

Step 2 What summary routes could be configured in this network?

Continue reading here: Review Questions Imn

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The AIA/AAH Case Study Library was officially published online in late 2016 with the goal of “bridging the gap” between research and practice . The original goals of the Case Study effort by the Research Initiatives Committee was the following:

• Gathering and/or creating case studies to share with the Healthcare Industry
• Utilizing the AIA/AAH Health Care Design Awards as a “peer-reviewed” source for case studies
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• Creating a AIA/AAH Case Study Repository or Library for sharing the case studies

It is the AIA/AAH Research Initiatives Committee’s vision that a more focused and formal approach to collegial sharing of Design Award Winning Project information will help us all do better work. By creating enough project case studies for a qualitative and comparative BASELINE in the Library which will help develop scalable metrics that in turn will provide the industry with some best practice “Rules of Thumb” and “Benchmarking” analyses on our projects which may eventually lead to and encourage additional and more rigorous research opportunities (such as POEs, etc.).

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The typical Case Study highlights the key design intentions of the project and shows photographic images to help identify design features that address those intentions. Each case study also identifies the project, the team, and the overall building gross square footage and completion date, as well as floor by floor interdepartmental Net to Gross Square Footages and Net to Gross Factors are identified . It will also identify minimum and maximum travel distances for patient and staff travel within key departments. Key Clinical Spaces are also identified in terms of typical and average range of net square footages . Finally, as an AIA Academy of Architecture for Health Design Award recipient, the Jury Comments are also included to help explain the award-winning features .

In addition to adding more award-winning Case Studies every year, the Research Initiatives Committee took a deeper dive in 2018 into “benchmarking” Acute Care nursing units and patient rooms using two of the larger hospital Case Studies - Palomar Medical Center and Rush University Medical Center. The purpose of this deeper dive was, and is, to produce a subset repository within the Case Study Library of Nursing Unit and Patient Room typologies using a consistent and rigorous format for more detailed departmental and key clinical space comparison and “benchmarking.”

Examining a series of inpatient facilities in a consistent Case Study format is beneficial in informing a data base repository; and identifying “best practices” and “rules of thumb” case study comparisons are a pre-requisite to a performance-based design approach.

The Case Studies below are in alphabetical order. Each has been categorized and tagged with the following keywords:

1. Acute Care (Hospitals)      - Medical/Surgical      - Children's 2. Ambulatory Care      - Clinics      - Surgicenters      - Cancer Care      - Specialty Care      - Freestanding ERs 3. Pediatric Care 4. Specialty Care 5. Research Facilities 6. Acute Care - Clinical Departments      - Emergency Departments      - Surgery and Interventional Departments      - Medical/Surgical Bed Units      - Critical Care Bed Units      - Radiology/Imaging Departments The first file provides a graphical index of how projects fall into the various categories above.

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Collaborative hospital supply chain network design problem under uncertainty

• Published: 05 July 2022
• Volume 22 , pages 4607–4640, ( 2022 )

Cite this article

• Khouloud Dorgham   ORCID: orcid.org/0000-0002-5720-5723 1 ,
• Issam Nouaouri 1 ,
• Jean-Christophe Nicolas 1 &
• Gilles Goncalves 1  

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Since 2016, hospitals in France have met to form Territorial Hospital Groups (THGs) in order to modernize their health care system. The main challenge is to allow an efficient logistics organization to adopt the new collaborative structure of the supply chain. In our work, we approach the concept of logistics pooling as a form of collaboration between hospitals in THGs. The aim is to pool and rationalize the storage of products in warehouses and optimize their distribution to care units while reducing logistics costs (transportation, storage, workforce, etc.). Besides, due to the unavailability and the incompleteness of data in real-world situations, several parameters embedded in supply chains could be imprecise or even uncertain. In this paper, a Fuzzy chance-constrained programming approach is developed based on possibility theory to solve a network design problem in a multi-supplier, multi-warehouse, and multi-commodity supply chain. The problem is designed as a minimum-cost flow graph and a linear programming optimization model is developed considering fuzzy demand. The objective is to meet the customers’ demand and nd the best allocation of products to warehouses. Different instances were generated based on realistic data from an existing territorial hospital group, and several tests were developed to reveal the benefits of collaboration and uncertainty handling.

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1 Introduction

A supply chain refers to a coordinated series of processes to manage system entities involved in procurement, manufacturing, warehousing, and transportation activities. These entities are highly interdependent to improve the performance of the supply chain with minimum costs. Creating both a responsive and cost-effective supply chain is critically difficult and represents a real challenge for companies. Especially when different problems may occur (i.e. warehouse management errors or lack of effective coordination), they can lead to increase inventory costs and decrease profits. To face these challenges, the logistics network design problem is considered a major strategic decision issue in supply chain management, due to its substantial influence on the efficiency of the entire supply chain process.

Over the recent past years, the hospital sector becomes an area of interest for many researchers in the literature due to its conflict with new different challenges and issues (demographic, budgetary, political, etc.). Several research studies have focused on the organization of flows (Chen et al. 2013 ) and the management of resources and tasks (Toba et al. 2008 ) to improve the performance of the global hospital supply chain (Tamir et al. 2017 ). Today, public hospitals have to initiate a reflection on their functioning and their organization and propose an efficient management strategy of the healthcare system to optimize the resources mobilized and rationalize all its activities (Pillay 2008 ). Before 2016, hospitals tend to manage their logistics process (reception, storage, preparation, distribution) autonomously. Hence, each healthcare establishment admits a logistics process specific to its needs and its functioning which becomes more and more difficult to be managed following the increase of patients number in hospitals. Especially, when they are frequently demanding in terms of service rates, responsiveness, and flexibility as was the case with COVID-19 when thousands of new daily admissions were recorded and hospitals were saturated. Hence, cooperation between hospitals was very important to ensure good management of logistics and overcome the declared health crisis. Consequently, the current hospital logistics systems require the emergence of new forms of governance and rationalization of logistics policies.

Four years ago, public hospitals in France have met officially to form THGs in the interest of reducing logistics costs through better use of their resources (managing products/material flows and distribution circuits). This new type of coordination between health establishments is among the most structuring and ambitious measures of the law on the modernization of healthcare systems. The idea is to establish a shared medical project based on cooperation and coordination between hospitals composing the THG. Among the main advantages of this territorial approach is to improve the quality of public hospital service, rationalize storage means (limitation and/or specialization of THG warehouses) and optimize the distribution system. Therefore, THGs represent an accelerator of the joint work of medical, technical, administrative, and logistics teams. The efforts began with the regrouping of purchasing function between public hospitals as part of “ PHARE ” program (Hospital purchases—Ministry of Solidarity and Health 2011) to generate “smart savings”, while arriving at the logistics process and mainly the storage and distribution functions. As it has been proven in the field of industry, university communities, etc., a collaboration strategy will be advantageous and it will strengthen the economic and social efficiency of healthcare organizations through an overall cost reduction, supplier integration, and optimization of logistics employment. Thus, to model this collaboration, knowledge about logistics functions is essential to ensure the proper functioning of the hospital supply chain.

A hospital logistics chain is identified by a set of actors and logistics processes where commodities are distributed from the supplier (origin) to the storage plant (warehouse) and then prepared to be transferred (shipping) to care units (destination). In more realistic supply chain models, the environment’s parameters (e.g. customer demands and transportation costs) may change and deterministic optimization reaches its limits (Bai and Liu 2016 ). Therefore, all strategic, tactical, and operational decisions should be made under uncertainty. Mainly, to deal with uncertain parameters, stochastic approaches have been developed, and precise information about the probability functions of these variables is needed. Besides, for a lack of historical data, we cannot elaborate probabilistic scenarios. Therefore, fuzzy linear programming could be a good solution for such a problem to handle imprecise and uncertain information (Werners and Drawe 2003 ).

In the present paper, we propose a multi-commodity, multi-supplier, and multi-warehouse optimization model to deal with two echelon network design problems within THG. On the one hand, the objective is to study the economic impact of horizontal collaboration on the total logistics cost generated and on the other hand, to cope with uncertainty in hospital demand through the development of a fuzzy chance-constrained programming approach based on possibility theory. The efficiency of the proposed model is tested and a comparison between the fuzzy chance-constrained programming and the weighted average method is carried out to demonstrate the robustness of the proposed approach. The remainder of this paper is organized as follows: in Sect. 2 we present a literature review on logistics pooling strategy and chance-constrained programming approach to tackle uncertainties in different real-world applications. Section 3 presents a description of the proposed problem and its mathematical formulation. In Sect. 4 , a description of the fuzzy programming approach is presented. Generation of instances and discussion of experimental results is done in Sect. 5 . Finally, Sect. 6 presents a conclusion with some future research studies.

2 Literature review

Supply Chain Network Design (SCND) can be defined as an integrated decision-making process dealing with different activities (procurement, manufacturing, warehousing, and transportation) to manage system entities and resources involved in distributing products/services from suppliers to end-users (Lin and Wang 2011 ). Many actors involved in a supply chain may have conict in interests. The main objective when designing a supply chain network is to reduce these conicts and increase the total revenue and/or decrease the total costs (Rabbani et al. 2018 ). A great deal of research in the scientific literature has been done to propose solutions and decision-support methods for problems related to the SCND. Mainly, collaboration strategies, embedded in SCND problems, are strongly studied by the research committee in recent years. In this section, the logistics pooling strategy, which represents a kind of collaboration between supply chain actors, will be reviewed. Later, methods and approaches to tackle uncertain environments will be discussed.

2.1 Logistics pooling strategy in supply chain network

Studies in the SCND modeling area related to warehousing and transportation/distribution networks could be classified into traditional or collaborative SCND. Therefore, sometimes traditional SCND approaches are not sufficiently effective, especially when there are problems related to the logistics units. Hence the need for developing more efficient logistics strategies, such as collaborative models where different structures cooperate to optimize their logistics processes. According to Moutaoukil et al. ( 2013 ), collaborative SCND consists to share logistics means and resources to minimize costs and increase profits, it could be either at the vertical or the horizontal level. The first category concerns partners who belong to the same logistics chain that operate at different levels of the supply network. Unlike the second type, which concerns partners of the same level (providers, manufacturers, distributors, etc.) who do not belong to the same logistics network. After solid and sustainable collaborative approaches, the logistics pooling strategy was born in the 1990s at the initiative of large distributors to increase trucks’ filling rate and delivery frequency. Since the 2000s, the pooling strategy is becoming widely developed in the literature (Mrabti et al. 2019 ) and it is considered as a horizontal collaborative approach (Moutaoukil et al. 2013 ) used to achieve economies of scale in different real-world domains.

A large number of mathematical models have been proposed for the design, planning, or optimization of the pooled supply chain. Some of these models considered one-echelon supply chain, especially in collaborative hub network problems proposed for the first time by Vermunt ( 1999 ). This work has been enhanced in 2005 by Groothedde et al. ( 2005 ), authors proposed a heuristic to solve the many-to-many hub network problem for the distribution of consumer goods, in which economies of scale and a sufficient level of reliability were achieved thanks to the collaboration between warehouses and the pooling of products during their transport from the manufacturer to the customer. Then, the pooling of multi-echelon supply chain models becomes more developed in the literature. For example in 2002, a multi-warehouse supply chain was studied in Kim and Benjaafar ( 2002 ), where authors presented the advantages of inventory pooling in limited capacity production-inventory systems with multiple plants. In 2005, a multi-supplier, single-warehouse supply chain network was considered in Cheong et al. ( 2007 ), Tuzkaya and Önüt ( 2009 ), authors developed a linear programming model for the shared network design problem. However, in Tuzkaya and Önüt ( 2009 ), a multi-commodity aspect is treated among periodic environment that involves determining the best strategy for distributing the sub-products from suppliers to warehouses and from warehouses to manufacturers in order to maximize the profit. In the same context, (Ballot and Fontane 2010 ) developed a pooled strategy in a multi-supplier, multi-product supply chain and demonstrated that vertical supply chain optimizations can still be improved by horizontal collaboration with real data from French retail chains. Besides, the authors were interested in the environmental aspect and ignore the economic side. Therefore, Pan’s study ( 2010 ) dealt with the problem with the aim of massifying flows to increase the filling rate of vehicles and evaluated the economic and environmental indicators within mathematical modeling in Integer Linear Programming.

Other researchers in the literature have used simulation techniques to deal with logistics pooling. The majority of works used simulation to compare different pooling scenarios and indicated the best one to follow. As it was presented in Pooley and Stenger ( 1992 ), the authors proposed a simulation approach to evaluate a logistic transportation consolidation strategy within a food manufacturing business. In 2009, authors in Wanke and Saliby ( 2009 ) developed a simulation tool to determine the impact of inventory centralization and regular transshipment inventory-pooling models, on holding and distribution costs and service levels. Two years later, authors Leitner et al. ( 2011 ), used simulation to apply pooling for projects in the automotive sector in Romania and Spain in order to optimize cost structures. Also, authors Moutaoukil et al. ( 2013 ); Mrabti et al. ( 2019 ) used several scenarios to compare the performance of a traditional logistics network against a pooling supply chain with a horizontal collaborative logistic strategy by evaluating the economic indicators (transport cost, loading cost, unloading cost, and vehicle filling rate). Recently, in Nicolas et al. ( 2018 ), authors presented a simulation approach to provide decision support within THGs. The developed framework helps hospitals to rationalize and pool the warehouses and their associated logistics flows. It allows decision-makers to choose and compare pooling scenarios of products within a THG based on a set of criteria chosen by hospital partners. However, designing and testing pooling scenarios to find a quasi-optimal pooling strategy can be time-consuming. Furthermore, strategic decisions must often deal with data uncertainties about future demand.

2.2 Chance-constrained programming approach

All the above literature considered logistics pooling strategy in SCND problem under deterministic conditions, where customer’s demands and logistics costs were treated as a well-known parameter. However, in a real-world environment, SCND problem is full of unpredictable and stochastic elements. Therefore, it appears essential to consider uncertainty in order to build a robust solution, especially, over a long-term decision horizon. According to Zhao et al. ( 2018 ) uncertainty can be modeled by several approaches. For example, as a good classification, Sahinidis ( 2004 ) categorizes and reviews the main optimization approaches under uncertainty into two groups: (1) stochastic optimization (recourse models, robust stochastic programming, probabilistic models) and (2) fuzzy optimization. In stochastic optimization, there are broadly three types of stochastic programming approaches: expected value models, chance-constrained programming, and dependent chance programming (Liu and Liu 2009 ). We focus on our research study on chance-constrained programming (CCP) that was first proposed in Charnes and Cooper ( 1959 ) to solve optimization problems under various uncertain situations and to ensure that the decisions meet a set of constraints with certain levels. Its main feature is to restrict the feasible region so that the confidence level of the solution is high, see Li et al. ( 2008 ). The chance-constrained programming model has been applied widely in different subject areas, such as in energy management problems (Huang et al. 2016 ; Liu et al. 2016 ), transportation (Li et al. 2017 ; Zhao et al. 2018 ), inventory management (Jurado et al. 2016 ) (Meng and Rong 2015 ), biofuel supply chain (Quddus et al. 2018 ), and even in humanitarian relief network design (Elçi and Noyan 2018 ).

Despite the presence of stochastic methods in many real-world applications, sometimes, they are difficult to be developed. Precise information about the probability distributions of stochastic parameters is needed (Werners and Drawe 2003 ), while this is not usually possible because historical data of those parameters are sometimes unavailable. Therefore, in such a situation, an appropriate approach is required. Since the appearance of fuzzy theory (Zadeh 1965 , 1974 , 1978 ), the incorporation of fuzziness in the field of combinatorial optimization becomes a challenging problem in terms of modeling and solution. Following the idea of chance-constrained programming with stochastic parameters, in fuzzy decision systems, we assume that the fuzzy constraints will hold with at least a certain degree of possibility called confidence level (Liu 1998 ). Therefore, several research studies have discussed the integration of chance-constrained programming within a fuzzy possibilistic framework and proposed different approaches to transforming the original chance constraints into a crisp equivalents model by employing possibility theory.

For example, in supply chain transportation problems, authors (Werners and Drawe 2003 ) treat the capacitated vehicle routing problem under fuzzy demand and proposed a fuzzy multi-criteria modeling approach based on a mixed-integer linear mathematical programming model. The approach presented to handle the fuzzy constraints is similar to chance-constrained programming in stochastic optimization, and the triangular form representation is proposed to represent fuzzy numbers. In 2014, Mousavi et al. ( 2014 ) addressed the location and routing problem in the cross-docking distribution networks. To tackle uncertain parameters (costs, vehicle capacity, time, etc.), the authors proposed a hybrid solution approach by combining fuzzy possibilistic programming and chance-constrained programming and represented uncertain parameters as fuzzy membership functions in the constraints. In supply chain inventory management, a traditional inventory control model with two objectives, minimizing costs and risk level, was developed in Nayebi et al. ( 2012 ). Different fuzzy parameters are incorporated in the mathematical model such as the available budgetary and presented as a triangular fuzzy number. For the defuzzification of fuzzy constraints, a fuzzy chance-constrained programming approach is proposed. In the healthcare domain, authors in Fazli-Khalaf et al. ( 2019 ) proposed a possibilistic chance-constrained programming model for designing a blood supply chain network in emergencies. Most of the main parameters of the mathematical model (demands, transportation time, capacity, costs, etc.) are tainted with uncertainty. Therefore, possibility and necessity measures are applied to cope with uncertain parameters in both objective function and constraints. Recently, in the reverse logistics domain, Ghahremani-Nahr et al. ( 2019 ) developed a mathematical programming model for the closed-loop supply chain and proposed a fuzzy formulation to address the effects of uncertainty parameters (customer demand, raw material costs, transportation costs, shortage cost, and availability of return goods and material). The authors used the trapezoidal fuzzy distribution to show the basic fuzzy programming model and the necessity measure to convert fuzzy chance constraints into their equivalent crisp ones. More recently, at the operational level, a fuzzy programming model for the truck-to-door assignment problem has been proposed to tackle the imprecise transfer times inside collaborative cross-docks (ESSGHAIER et al. 2021 ).

In summary, according to the reviewed literature, we noticed that several studies have approved the advantages of horizontal collaboration at different levels of decision-making (strategical, tactical, and operational) and application areas. However, to the best of our knowledge, none of the existing research works has modeled or studied the impact of horizontal collaboration and pooling strategy in the hospital sector and notably within territory hospital groups, since it is a new concept to consider in the healthcare domain. Studies presented in Sect. 2.1 , as almost all studies conducted on collaboration strategy, have been performed assuming perfect knowledge about the problem. Variations in available resources, workload, or possible disruptions in the logistical process have been often neglected. Moreover, to the best of our knowledge, no work combines collaboration and uncertainty handling when dealing with hospital supply chain optimization within THG. An overview of the reviewed papers is presented in Table 1 .

With the obligation to join territorial hospital groups, the logistics process within hospitals becomes more and more challenging and difficult to be controlled. Solving this problem requires perfect coordination of several operations (receiving, sorting, and shipping products) taking into account different parameters such as hospital demands or unit costs. Hence, a good logistical system greatly influences the whole hospital’s performance. It may considerably enhance the efficiency of the health care service, improve delivery quality, and reduce costs and delays incurred in a hospital supply chain. This provides us with a strong motivation to study in this active research area, especially when dealing with uncertain environments. In addition to collaboration strategy, uncertainty handling in supply chains is one of the latest trends in the literature. Today, several companies have opted for managing unforeseen changes to meet customer requirements and confront economic, environmental, and social challenges. Unlike stochastic optimization, the fuzzy chance-constrained programming approach was not previously considered for collaborative supply chain and could be a well-recognized method that relies on profound mathematical concepts such as the expected value of fuzzy numbers in the objective function and possibility and necessity measures in the constraints. In practice, by using fuzzy logic we can tackle imprecise and uncertain variables, and this represents our second motivation to study, especially in the healthcare domain, where unforeseen changes can frequently occur following recurrent epidemics or pandemics.

The major contributions of this paper are highlighted as follows : (i) introducing a new optimization model to deal with horizontal collaboration within territorial hospital groups and organizing the allocation of products between shared plants to offer an optimal pooling scenario for the decision-maker (ii) studying its economic impact under the assumption of a fully known environment by considering different logistical costs such as; full-time-equivalent costs, ordering costs, purchasing costs, holding costs and transportation, and then (iii) taking into account uncertainty in demands by developing a fuzzy chance constrained programming approach to merge the advantages of fuzzy set theory and chance-constrained optimization.

3 Problem description and mathematical formulation

Supply chain management aims to make organizations more responsive and efficient for the overall optimization of both costs and service levels. This has given rise to many reflections on the development of new collaboration strategies to create more synergies between the supply chain actors and to reduce the costs in the logistics chain. Among these collaboration strategies, we are interested in logistics pooling which is considered as a collaboration between actors of logistics chains through the sharing of resources and decisions.

In the healthcare domain, logistics pooling remains an understudied concept. Besides, it has been deployed in France’s health-care system, since 2016, where hospitals are obliged to join territorial hospital groups to enable different establishments to rationalize, pool, and optimize the storage of products in their warehouses (stores, pharmacies) and optimize their distribution to care units. The objective is to find an optimal allocation of product flows and to set up a pooling scenario that groups these flows in suitable warehouses through transport and warehousing. Depending on local needs and pre-existing cooperation, territorial hospital groups vary mainly according to their establishment’s parties, their budget, and the territories served. Generally, a THG is made up of several establishments of different sizes located in a given geographical area characterized by their density and their surface. In our study, the hospital supply chain is presented as a layered network with | S | suppliers who provide commodities to | W | warehouses (stores or pharmacy) where | P | products sub-family (food, cleaning materials, textiles, medicines, etc.) could be stored before being distributed for consumption. Currently, the logistics management policy is illustrated in Fig.  1 , where each hospital should manage its supply chain process (reception, storage, deconsolidation, preparation, distribution) and meet the needs of its units (care, catering, laundry, etc.) autonomously. Therefore, warehouses have historically been created for each establishment, knowing that every warehouse has its managing strategy that characterizes its purchasing, procurement, and storage activities and it is dedicated to serving only the set of care units belonging to the same establishment. Consequently, to acquire a product, this logistics process should be iterated independently within each hospital, which requires a lot of human and financial resources.

Autonomous logistics organization (without pooling)

Due to the important costs that could be generated, our objective is to improve the current situation by developing a logistics pooling strategy between hospitals and specifying which products sub-families will be interesting to be shared, between which hospitals? and in which warehouses?

Thus, we deploy the concept of shared warehouses and we consider that each warehouse could supply plants of different establishments for one or more product sub-families, as it is shown in Fig.  2 . This new method of logistical organization allows the different actors of the supply chain to consolidate their stocks and pool their transport (upstream and/or downstream of the shared warehouse) by reducing synchronization constraints and maintaining high delivery frequencies.

Hospital supply chain within logistics pooling

To model the warehouse organization, we consider that each warehouse could have a dual function; a storage activity through the S -warehouses to hold the stock of one or more product sub-families for long period, and/or a cross-docking activity through C -warehouses to distribute products from the arrival docks to the departure docks, without going through the stock. Knowing that each warehouse could be simultaneously considered as S -warehouse for one or more products and as a C -warehouse for others. The structure of the proposed supply chain network can be transformed into a minimum-cost flow graph, as it is illustrated in Fig.  3 , where the first level represents suppliers, the second level represents the warehouses considering that each warehouse can be represented by two nodes if it is at once a C -warehouse and S -warehouse and, the last level represents the units care. The pooling scenario is carried out in two stages, (1) the placement of certain products sub-families on one or more S -warehouses and (2) their distribution from these plants to one or more C -warehouses of other establishments. Therefore, the pooling of products sub-family will lead to a disruption of tasks for the flow considered between S -warehouses and C -warehouses. At the S -warehouse level, the distribution of the usual tasks will be now reduced only to the deconsolidation, storage, and preparation, reception and distribution will be reserved for the cross-docking.

Flow graph modeling of the hospital supply chain within logistics pooling

The goals are to select warehouses with the best managing strategy and to determine the optimal product quantity that should be delivered from suppliers while minimizing the overall logistics costs such as the Full-Time Equivalent cost (FTE) that represents the workload of employees, transportation costs which denotes expenses related to distributing products from S -warehouses to cross-docks, purchasing cost related to the products’ prices, ordering cost concerns the preparation of supplier’s order, and lastly, the holding cost related to the inventory storage. Different constraints should be respected; the product demands must be satisfied and the maximum storage capacity of warehouses should not be exceeded. The following assumptions are assumed in this research to model the THGs supply chain network:

Suppliers have unlimited delivery capacity.

A given product can be distributed by one or more suppliers at different prices.

The product price proposed by a given supplier is fixed for all warehouses.

The local managing strategies applied at each warehouse (i.e. storage and procurement strategies: procurement periods, unit costs, etc.) are maintained where the pooling of products takes place.

Numbers and locations of warehouses are assumed to be fixed and known.

Notations used in the mathematical model are described as follows:

Decision variables

\(x_{p,s,w}\) : quantity of product p transported from supplier s to warehouse w .

\(y_{p,w,c}\) : quantity of product p transported from S -warehouse w to C -warehouse c .

Sets and parameters

S : set of suppliers, | S | =1..s;

W : set of S -warehouses, | W | =1..w;

C : set of cross-docks, | C | =1..c;

P : set of products, | P | = 1..p;

PC : total purchasing cost;

OC : total ordering cost;

TC : total transportation cost;

HC : total holding cost;

FC : total Full-time equivalent cost ;

\(PC_{p,s,w}\) : unit purchasing cost of products p by the warehouse w from the supplier s that includes transportation costs;

\(HC_{p,w}\) : possession rate of product p in a warehouse w ;

\(OC_{p,w}\) :unit ordering cost of product p for a warehouse w ;

\(FTE1_{p,w}\) : full-time equivalent unit cost of product p in the S -warehouse w ;

\(FTE2_{p,c}\) : full-time equivalent unit cost of product p in the C -warehouse (cross-dock) c ;

\(TC_{p,w,c}\) : unit transportation cost of product p from warehouse w to cross-docks c ;

\(C_{w}\) : maximum storage capacity of warehouse w ;

\(d_{p,c}\) : demand of product p by cross-dock c ;

\(a_{p,w}\) : unit surface occupied by product p in the warehouse w ( \(m^2\) );

t : calendar days=365;

\(PP_{p,w}\) : procurement period of product p for warehouse w ( \(PP_{p,w}\) \(\ne 0\) );

Variables/expressions

\(I_{p,w}\) : average inventory level of product p in a warehouse w :

\(IL_{p,w}\) : inventory value of products p in warehouse w :

Different economic costs that occur at all levels of the supply chain were considered to achieve economy:

Supplier/Warehouse

Purchasing cost: the purchase amount set by suppliers in order to acquire a new product.

Holding cost: related to storage expenses of inventory (insurance, depreciation of facilities, rental and maintenance of premises, etc.).

Full-time equivalent cost (FTE): represents the FTE payroll cost used by each product sub-family (Number of FTEs x FTE salary per establishment).

Ordering cost: generated during the management of orders and varies according to the number of annual purchases (personnel costs, administrative and logistical monitoring, reception and handling charges, etc.).

Warehouse/Cross-dock

Transportation cost: direct or indirect costs of all order tracking and transport activities to ensure the delivery of products to care units.

Objective function

Constraints

The objective function 8 aims to minimize the summation of five logistics costs; total ordering cost, inventory holding costs, purchasing cost, FTE cost, and finally transportation cost. Constraints 9 ensure that the unit care’s demands for each product subfamily are satisfied. Constraints 10 guarantee that the total product quantity at each warehouse should not exceed its storage capacity. Constraints 11 represent the balance among supplies, inventory, and deliveries at each warehouse and cross-dock. Finally, constraints 12 and 13 represent the types of decision variables.

To demonstrate the impact of logistics pooling, we define two different scenarios. The first one (pooling scenario) represents the collaboration between warehouses and it is illustrated by constraints 9 – 13 . The second one represents the pre-pooling scenario where sharing commodities between warehouses is restricted and it is formulated by adding constraints 14 to the previous model.

Constraints 14 prohibit the sharing of product flows between warehouses and force each warehouse to receive only the quantity of products needed by its care unit.

4 Fuzzy chance constrained programming approach

Because of the unavailability and incompleteness of data in real-world situations, especially on the long-term horizon, several critical parameters embedded in supply chains such as customer demands, costs, and future plant capacities have an imprecise nature and could be quite uncertain. Frequently, experts and decision-makers do not precisely know the value of those parameters. If exact values are suggested, these are only statistical inferences from past data (Jiménez et al. 2007 ) and their stability is doubtful. Therefore, stochastic probabilistic modeling approaches may not be the best choice for the simple reason of unreliability of historical data and unavailability of information about the probability functions of the uncertain parameters. Hence, the obligation to resort to another representation of this uncertainty.

In this paper, we consider a fuzzy chance-constrained programming approach, where the uncertain variable is modeled as a triangular form of fuzzy numbers. Based on possibility theory, we propose to solve the problem using a possibilistic programming method. Whereas, in conjunction with the theory of fuzzy subsets to treat imprecise data, the theory of possibilities, introduced by Zadeh ( 1978 ) and developed by Dubois and Prade in ( 1988 ), offers a means of managing knowledge marred by uncertainties. According to several models that have been presented in the literature to deal with imprecise data, fuzziness could be considered in the parameters of the objective function and/or constraints, or, it could be related to the flexibility degree of constraints (Inuiguchi and Ramık 2000 ). Our proposed approach could be considered as a new variant of probabilistic chance-constrained programming based on possibility theory (Liu 1998 ) to insure the defuzzification of the fuzzy model and its effective resolution.

The fact that predicting market demands is one of the most challenging issues in SCND problems regarding its fast variation (Ruoning and Zhai 2010 ), especially with short product life cycle and the growing of innovation rate, motivated us to study the problem considering that hospitals’ demand (i.e. quantities to be delivered) is not known with certainty (i.e. at the time of planning) and characterized by variable possibility distributions and a certain necessity degree. To represent fuzziness, the demand constraints 9 need to be reformulated differently and it is redefined as follows:

The fuzzy demand \(\overset{\sim }{d_{p,c}}\) has a triangular possibility distributions based on a triplet of real numbers \(\overset{\sim }{d_{p,c}}\) = ( \(\underline{d_{p,c}}, {\hat{d}}_{p,c}, \overline{d_{p,c}}\) ) with \(\underline{d_{p,c}} \le {\hat{d}}_{p,c}\le \overline{d_{p,c}}\) (Fig.  4 ). The terms \(\underline{d_{p,c}}\) , \({\hat{d}}_{p,c}\) and \(\overline{d_{p,c}}\) represent, respectively, the most optimistic value, the most possible value and the most pessimistic value (Lai and Hwang 1993 ). \(\underline{d_{p,c}}\) and \(\overline{d_{p,c}}\) have a low possibility to belong to the set of available values, but \({\hat{d}}_{p,c}\) is definitely belongs to the set.

The possibility and necessity measures, corresponding to the satisfaction of the fuzzy demand constraints, are defined by a crisp equivalent formula (Klir and Yuan 1996 ) as it is developed below. In what follows, the abbreviations \(``Pos''\) and \(``Nec''\) represent respectively possibility and necessity.

Possibility and necessity measures of triangular fuzzy number \(\overset{\sim }{d_{p,c}}\) = ( \(\underline{d_{p,c}}, {\hat{d}}_{p,c}, \overline{d_{p,c}}\) )

In fuzzy set theory, possibility and necessity measures are employed to describe the chance of fuzzy events (Yang and Iwamura 2008 ). Hence, the satisfaction of the demand constraints is perfectly determined by the degrees of these measures. The possibility value implies the feasibility degree to satisfy these constraints. Besides, the necessity value indicates the degree of certainty of the constraints. Therefore, as suggested above, constraints 16 and 17 are modeled as crisp equivalents of the fuzzy constraints 15 :

In decision-making systems, an optimistic decision-maker deals with possibility measure, unlike the pessimistic decision-maker, who opts to deal with only necessity degree (Yang and Iwamura 2008 ). In our case, we suppose that the decision-maker is eclectic, hence, we use a combination of possibility and necessity measures to deal with the problem. Constraints 16 and 17 specify that the possibility and the necessity measures linked to the satisfaction of the demand constraints must be, respectively, greater than a threshold \(\alpha\) and \(\beta\) that are chosen by the decision-maker between 0 and 1 to express his vision towards risk. The closer the possibility degree is to 0, the more the decision-maker is optimistic, thus, the closer the degree is to 1, the harder the constraints become and the problem will be more restrictive. As well as for the necessity measure, an elevated threshold implies hard constraints and a pessimistic attitude of the decision-maker. According to the choice of values for \(\alpha\) and \(\beta\) , we distinguish different possible combinations of constraints defuzzification:

\(\alpha\) = 0 and \(\beta\) = 0 With this configuration, since the measures of possibility and necessity are between 0 and 1, constraints 16 and 17 are verified whatever the values of these measurements. Therefore, the fuzzy demand constraints are always checked regardless of the value of the demand \(\overset{\sim }{d_{p,c}}\) . This combination of thresholds is the least restrictive but the riskiest situation.

0 \(< \alpha <\) 1 and \(\beta\) = 0 The possibility constraints 16 will be replaced by:

As in the previous case, with \(\beta =0\) , the necessity constraints 17 are always verified ( \(Nec (\overset{\sim }{d_{p,c}} \le y) \ge 0\) ) regardless of all \(\overset{\sim }{d_{p,c}}\) possible values. With this combination of thresholds, the fuzzy demand constraints become more restrictive comparing with the first case.

\(\alpha\) = 1 and \(\beta\) = 0 When \(\alpha\) = 1, inequalities 16 will be defined as below:

According to the necessity definition, constraints 17 are verified ( \(Nec (\overset{\sim }{d_{p,c}} \le y_{p,w,c}) \ge 0\) ) whatever the values of \(\overset{\sim }{d_{p,c}}\) . Consequently, the fuzzy demand constraints are satisfied when the quantity delivered to the warehouse is greater than the average value of demand ( \(\overset{\sim }{d_{p,c}}\) ), which represents the deterministic case.

\(\alpha\) = 1 and 0 \(< \beta<\) 1 Since the necessity constraints \(Nec(\overset{\sim }{d_{p,c}} \le y_{p,w,c}) \ne 0\) , the possibility measure constraints 16 are always verified whatever the values of \(\overset{\sim }{d_{p,c}}\) . Therefore, the satisfaction of the demand constraints implies the satisfaction of the necessity constraints 17 :

With this combination of thresholds, the fuzzy demand constraints are more difficult to be satisfied.

\(\alpha\) = 1 and \(\beta\) = 1 Constraints with regards to the necessity measure 17 will be defined as below:

Satisfying the necessity constraints involves usually the satisfaction of the possibility measure ( \({\hat{d}}_{p,c} \le y_{p,w,c}\) ). This is the most challenging situation because the delivered quantity y should be greater or equal to the upper bound \(\overline{d_{p,c}}\) .

The combination where both \(\alpha \in\) ]0,1[ and \(\beta \in\) ]0,1[ is not possible to be modeled, because by definition (Klir 1999 ):

5 Computational experiments

In this section, we present experimental results to validate the computational efficiency and effectiveness of the model and to determine the impact of logistics pooling on our economic objective function in both deterministic and fuzzy environments. Two different configurations are used, firstly we consider the pre-pooling scenario where each hospital manages its procurement process independently, then, we consider the polling scenario, where collaboration between functional units of the THG is authorized and shared warehouses are considered. We perform computational experiments on a set of randomly generated test instances based on a realistic case study. The procedure used to generate these instances is described in Sect. 5.1 , followed by a summary of computational results for pooling and pre-pooling scenarios of the deterministic approach in Sect. 5.2 . In Sect. 5.3 we investigate the efficiency and robustness of the proposed model throughout a comparison between the FCCP approach and the weighted average method to tackle imprecise/uncertain variables (Lai and Hwang 1992 ).

5.1 Characteristics of test instances

All modeling development has been done on IBM CPLEX solver v.12.5 on a PC with an Intel i5 core processor (2.90 GHz) with 8.0 GB RAM. We performed computational experiments on a set of randomly generated test instances based on realistic parameter value ranges obtained from several logistics networks of existing territorial hospital groups in France. We considered a set of 25 instances (Table 2 ) according to assumptions that strike a balance between realism and ease of generation. Instances vary according to two main dimensions: network size and cost values. The size of an instance is given by the number of suppliers (| S |) (fixed at 2 suppliers with all instances), the number of potential warehouses (| W |), and the number of products (| P |). The 25 test instances are devised into 5 main groups according to the number of warehouses/cross-docks ranging from 2 to 25. However, instances in the same group vary according to the number of products, each group holds 5 instances with commodities numbers ranging between 4 and 36 products. Continuous uniform distributions denoted by “U”, independent from each other, were considered in the random number generation of all the variables. The cost structure and parameter values are determined as illustrated in Table 3 .

5.2 Results of the deterministic approach

5.2.1 comparison between pre-pooling and pooling scenarios.

In this section, we focus on the results of the deterministic approach for pre-pooling and pooling scenarios in a fully known environment. In Table 4 , we summarize the optimal objective values as well as the CPU times for each problem instance and for both scenarios.

We can notice that computational time increases with an increase in problem size, specifically with the number of potential warehouses and products. Additionally, it is important to note that the pooling scenario is always more time-consuming than the pre-pooling configuration (an average of 87.8 s against 191.4 s in the pooling scenario). This is noticeable especially for instance 25 where the CPU time of the pre-pooling scenario is too much lower than the pooling scenario. However, computation times in both configurations are still quite acceptable in the case of all problem instances.

In addition to computational time, to compare the quality of the optimal solution obtained, we use the relative gap of the solution which gives an idea of the gain percentage achieved for each instance:

We can see that from an economic point of view, horizontal collaboration has shown better performance compared to that of the current state (without pooling). For all instances, the total cost relative to the pre-pooling scenario is higher than the one obtained after pooling. There is an average cost reduction of approximately 16.1%. Economies are at least equal to 4.3% for instance 13 and achieve 39.6% for instance 22. Realized gains confirm that after collaboration, only warehouses with optimal supply strategies are selected for the procurement process. Besides, Fig.  5 displays details about gains realized among all instances. The total economic cost minimized is composed of purchasing cost relative to suppliers, holding cost associated with inventories at warehouses, FTE cost relating to the workforce and employment, ordering cost, and finally, an additional transportation cost is generated only after pooling and represents the charges of products shipping between warehouses. We note that 13% for the FTE cost, 19% of the inventory holding cost, and 14% for ordering cost are reduced. Hence, despite the generation of the additional transportation cost that is usually absorbed by the gain realized, we conclude that the pooling solution approach is efficient and effective as it provides better quality solutions in all instances and allows cost-saving.

Comparison of logistics costs in pre-pooling and pooling scenarios

In addition to the economic indicator, different performance metrics can be used to assess the pooling strategy:

Occupancy rate (%): this performance indicator tracks the percentage of available storage space in a potential warehouse. It is obtained by dividing the total quantity stored by the total capacity among the overall warehouses.

Pooled product rate (%): this performance metric allows us to assess the percentage of products that have been shared or grouped partially / totally after collaboration. It is obtained by dividing the number of product subfamilies pooled by the total product number.

# S -warehouses: this indicator represents the number of warehouses that have kept their functions as storage and cross-dock stores after pooling among those considered only as cross-docks (i.e. the number of S -warehouses remained open after pooling).

According to Table 5 , the occupancy rate of warehouses decreases with an average improvement of 4%. Therefore, we can confirm that horizontal collaboration ensures better stock management and allows us to save more free space for other internal use. Moreover, according to the pooled product rate, more than 50% of the products’ sub-families have been pooled among the overall instances, which confirms that collaboration is usually more advantageous. Finally, based on the number of warehouses that remained open after pooling (# S -warehouses) and kept their functions as storage and cross-dock stores, for the majority of instances, we can see that there are always at least two or more warehouses that have been considered as cross-docks only. This allows us to realize gains through null storage and ordering costs at the S -warehouses level.

5.2.2 Sensitivity analysis

The solution quality and the target variables generated could be affected based on changes in values of the input parameters such as hospital demand, warehouse capacity, unit logistics costs, etc. Therefore, sensitivity analysis is a way to predict how changes in coefficients of the model can affect the optimal solution obtained. In what follows, different experiments were conducted on unit transportation cost, warehouse capacity, and demand. Only one of those input parameters was varied each time, and all others remained unchanged from their previously-tested values.

As a first study, considering the importance of transportation cost ( \(TC_{p,w,c}\) ) generated during pooling, we motivated the analysis by changing the unit transportation cost upwards and downwards and evaluating the impact of its variability on the optimal solution, all the other parameters remained unchanged from their previously-tested baseline values. This study was carried out considering the most challenging instance ( instance 25). We observe that the obtained optimal solution (network structure) remains the same following the gradual increase in unit transportation cost until \(TC_{p,w,c}\) = \(TC_{p,w,c}\) +24%. However, only the total cost is impacted and it has slightly increased by 0.7%. Above 24% increase in unit transportation cost, the optimal procurement and distribution plan (optimal solution) is no longer maintained and the solver offers new solutions that further reduce costs. On the other side, by decreasing unit transportation cost even by \(100\%\) (i.e. \(TC_{p,w,c}\) = \(TC_{p,w,c}\) +100%) the solution remains the same. In this case, we can conclude that the optimal solution is insensitive to the decrease of \(TC_{p,w,c}\) .

Afterward, we focus our sensitivity analysis on the warehouse’s capacity ( \(C_{w}\) ) considering the same instance (25). Therefore, we have varied it upwards and downwards and we noticed that the optimal solution (network structure) remains the same until the warehouse’s capacity value is decreased by 28% (i.e. \(C_{w}= C_{w}-28\%\) ). Only the total objective cost generated is affected. Above \(28\%\) , the solver offers new solutions that generate a new collaborative schema. Besides, by increasing the maximum storage capacity value even with 100% the optimal solution is unchanged.

Since demands tend to be varied at the time of delivery, it is important to answer the question; at each demand value, the optimal solution remains unchanged? Therefore, we have displayed the right-hand side sensitivity analysis results of constraint 9 by using CPLEX display sensitivity command. Then, we check for each product the difference between the current demand value, and the up value that corresponds to the maximum tolerated demand increase and we calculate an average percentage for all products. The obtained results demonstrate that for all warehouses the optimal solution remains unchanged by increasing the demand value until reaching an average demand increase of 25%. Above this value, a new optimal solution will be generated and the network structure will be changed (new distribution schema). From this analysis, we can deduce that even the variation of a single demand in a single warehouse could generate changes in our optimal solution as well as in our network architecture. Thus the interest and the motivation behind our study on uncertainty in the next sections by considering the demand as a fuzzy parameter.

5.3 Results of the fuzzy approach

Given the incompleteness of data in real-world situations, we deal in this section with uncertain demand values modeled as a fuzzy number and solved as a possibilistic chance constraint programming model for both pre-pooling and pooling scenarios. Firstly, we present the changes made on instances to manage the fuzzy demands, then, we determine the influence of possibility and necessity degrees (threshold parameters: \(\alpha\) and \(\beta\) ) variation on the total cost.

5.3.1 Problem instances: fuzzy demand

We are modifying the instances generated to adapt them to SCND problem with fuzzy demand. The updates concerns only hospital demands represented by fuzzy numbers with symmetrical triangular form \(\underline{d_{p,c}}, {\hat{d}}_{p,c}, \overline{d_{p,c}}\) where \({\hat{d}}_{p,c}- \underline{d_{p,c}}= \overline{d_{p,c}}-{\hat{d}}_{p,c}\) . A new parameter labeled uncertainty rate is added to model the fuzzy demand and denoted by \(r_{uncert}\) . In real-life, we noticed that the demand can vary between 0.15 and 0.2, therefore, we decided to fix the uncertainty rate’s value at 0.15 for all our next experiments. The three components of the fuzzy demand \(\overset{\sim }{d_{p,c}}\) are determined as follows:

Normalization: \({\hat{d}}_{p,c}\) represents the initial demand in the deterministic model.

The lower bound (best scenario): \(\underline{d_{p,c}}= {\hat{d}}_{p,c}*(1- r_{uncert})\) .

The upper bound (worst scenario): \(\overline{d_{p,c}}= {\hat{d}}_{p,c}*(1+ r_{uncert})\) .

5.3.2 Configuration of thresholds \(\alpha\) and \(\beta\) of the FCCP model

Thresholds \(\alpha\) and \(\beta\) given by the decision-maker have a great influence on the fuzzy demand constraints and consequently, on the problem costs that allow a certain degree of flexibility to the constraints satisfaction. Therefore, in this section, we look for several solutions to the problem corresponding to different combinations of thresholds. The execution of the FCCP optimization approach has been performed on both uncertain collaborative and non-collaborative scenarios, considering instance 25, which has been chosen because of its challenging warehouses and products number. Besides, In order to reduce the number of simulations, we create a set of threshold combinations as follows: we increase the value of possibility degree alpha from 0 to 1 in steps of 0.1 with necessity degree beta fixed at 0. Then, when \(\alpha\) is equal to 1, we increase in the same way the \(\beta\) value from 0 to 1. Results are given in Table 6 .

Concerning the generated solution (Table 6 ), we noticed that we can confirm conclusions made in Sect. 5.2 about the deterministic model. According to the computed gap through Eq. 18 , the pooling strategy is the most advantageous scenario that produces lower costs compared with the pre-pooling configuration with an average gain of 27.7%. In addition, the variation of \(\alpha\) and \(\beta\) had a great influence on the solution quality. The best solution corresponding to the lowest total cost obtained is generated with a null necessity degree and a low possibility degree ( \(\alpha \le 0.4\) ). The worst solution is obtained when \(\alpha =1\) and \(\beta =1\) . With this threshold combination, the decision-maker considers the worst scenario with a maximal value of demand, therefore, a higher total cost is generated. This cost represents the price to pay for not being out of stock when the demand is higher than expected. For \(\alpha =1\) and \(\beta =0\) , the solution is equal to that generated by the deterministic model. We note that the combinations of thresholds \(\alpha\) and \(\beta\) represent an increasingly strict evolution of the fuzzy demand constraints. The larger their values, the stricter the fuzzy demand constraints, the greater the cost generated, and the less the risk of changes. However, a low degree’s values represent an optimistic attitude against the risk and generate a more economically advantageous solution.

5.3.3 Comparison of deterministic and fuzzy approach

Since collaboration has shown better performance in all instances (Sect. 5.2 ), we will compare the results of the deterministic approach obtained in Table 4 with the configuration of the fuzzy model in a pooling scenario. High value of \(\alpha\) and \(\beta\) ( \(\alpha =1\) and \(\beta =0.7\) ) is considered to deal with a challenging and constraining case which is close to the worst scenario ( \(\alpha =1\) and \(\beta =1\) ). As shown in Table 7 , the tests were performed on 25 instances with an uncertainty rate equal to 0.15. The CPU time increases depending on the instance size and the configuration of the scenario considered. Comparing the results in Tables 4 and 7 , we observed that the FCCP model had a slower temporal performance compared with the deterministic model (an average CPU equals to 208.8s against 191.4s in the deterministic approach). Even in an uncertain environment, the collaborative configuration is more time-consuming compared with the non-collaborative scenario (Table 6 ). In terms of solutions quality, we use the relative gap of the solution to compare the results of the fuzzy approach (Table 7 ) against the deterministic one (Table 4 ):

we notice that the collaboration between warehouses in a fuzzy environment with elevated values of thresholds allows the increase of costs compared to the deterministic configuration on all instances with an average gap equals to 1.7% in Table 7 . The obtained results confirm our observation deduced previously; the higher the threshold values, the stricter the fuzzy demand constraints, the greater the cost generated, and the less the risk of changes. Hence, gains or losses will depend on the scenario that will be considered by decision-makers.

5.4 Solution robustness

In order to test the effectiveness of our fuzzy programming approach, a comparison between the FCCP and the weighted average method (Hossain and Mahmud 2016 ; Paksoy et al. 2012 ) is considered and different comparative techniques are proposed such as TOPSIS method. The objective is to test the robustness of the solution under the two proposed fuzzy methods against unforeseen changes in demand when the pooling scenario is defined. The weighted average method is detailed in the Appendix A . The experimental results have been performed on two groups of instances with 15 and 25 plants (medium and large instances). Therefore, we re-played the optimal planned solution obtained when the demand is normalized to \(\hat{ d_{p,c}}\) identified as a reference scenario for both deterministic and fuzzy methods. Moreover, we re-execute the optimal solution for the case when the worst scenario ( \(\overline{ d_{p,c}}\) ) occurs and determine the additional costs that will be generated and how the planned solution could be significantly affected. Knowing that the additional quantity generated will not be penalized and will be integrated at the usual cost. To deal with the most constrained scenario, the thresholds \(\alpha\) , \(\beta\) and \(\gamma\) are fixed to 1 for the FCCP and the weighted average method, respectively. Table 8 presents the cost values for planned and worst case scenarios in the deterministic and uncertain configurations considering the FCCP and the weighted average method to solve the fuzzy demand.

According to the obtained results, when the worst scenario occurs, the optimal target solution for the deterministic configuration becomes irrelevant since costs increase by 3.7% on average. Then, we compute the gap between the solutions generated in each fuzzy method (FCCP and weighted average method) against that generated in the deterministic case when demand increases more than was planned (worst scenario). Although solutions of the weighted average method are more interesting when the planned scenario is considered (6184 against 6236 in FCCP), they become irrelevant and generate more additional costs compared to the FCCP when the worst scenario is considered (− 0.4% against − 1.4 in FCCP%).

To develop more decisive conclusions about both methods, we propose a multi-criteria analysis method known as TOPIS (Technique for Order of Preference by Similarity to Ideal Solution). It was developed by Ching-Lai and Kwangsun ( 1981 ) to compare a set of alternatives based on a pre-specified criterion. It can be defined as a sort method to approximate the ideal solution based on the similarity degrees of finite evaluation objects and idealized criteria (Wang and Duan 2018 ). More details about the TOPSIS algorithm could be found in Bulgurcu ( 2012 ). To develop the data matrix in Table 9 , we consider FCCP and the weighted average method as an alternative set. For the criterion set, we consider measures derived from our experimental results such as total costs in planned and worst solutions, the gap between the worst solutions in deterministic and fuzzy situations, and the total filling rate of warehouses in the worst-case scenario. Then, each criterion is normalized to be between 0 and 1 according to an appropriate formula as demonstrated in Table 10 . Next, different weights should be given for each of those criteria based on decision-maker experience, so that the total of weights must be equal to 1 and the weighted normalized matrix in Table 11 is formed by multiplying each value by their weights. We consider that the weights of all criteria are equal to 0.25. After that, we compute the distance between the target alternative and the best/worst alternative according to the euclidean distance. Finally, the ranking of the fuzzy methods (alternatives) according to their performance index value is obtained. From Table 12 , looking to the higher performance index value of the FCCP, we can further confirm that it is the best performance alternative compared to the average weighted method to be used to solve possibilistic linear programming problems.

To conclude, we can affirm that the FCCP approach confirmed its ability to absorb more risk compared with the weighted average method and consequently, its effectiveness to deal with fuzzy optimization. In general, the consideration of uncertainty has been proven by both methods to enable better handling of unplanned changes with a more stable and advantageous solution compared to the deterministic case. Notably, when dealing with bad situations and adopting a more realistic attitude (high necessity and possibility degree) to avoid considerable losses.

6 Conclusion and future work

Logistics management is essential for the proper functioning of healthcare organizations to meet the efficiency and effectiveness required by the hospitals. In this study, a horizontal collaborative strategy within territorial hospital groups was proposed. The objective is to demonstrate the performance of the pooling strategy and to propose an optimal scenario for the allocation of products to improve economically the hospital supply chain by reducing costs (order cost, transport cost, inventory keeping cost, and FTE costs) and increasing revenue. Therefore, a multi-supplier, multi-warehouse, and multi-product linear programming model is developed to organize product pooling within care units. A set of several instances, inspired from a real THG database, are randomly generated and experiments have been done on both pre-pooling and pooling scenarios. However, due to the unavailability and incompleteness of data in real-world situations, various additional costs could be incurred when an unexpected change occurs. To deal with such a situation, a fuzzy chance-constrained programming approach with uncertain demand is developed to provide risk-averse and robust solutions to the decision-maker. The robustness of the model was evaluated for the deterministic and fuzzy configurations by comparing the weighted average method using the TOPSIS method. According to the obtained results, the pooling strategy could be beneficial and involve cost saving even when dealing with fuzzy demand and unexpected events.

This work could be extended to several future studies. First, other large-scale instances could be generated and tested. Then, a multi-period optimization model could be proposed as an extension to deal with operational decisions in the supply chain. Later on, dealing with a multi-objective supply chain problem could be a good idea to incorporate other different aspects of sustainability such as environmental and social objectives in the context of horizontal collaboration.

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Acknowledgements

This work is co-financed by the “Agence Régionale de Santé (ARS)” of Hauts-de-France region and the university of Artois. The support is gratefully appreciated.

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To compare the FCCP method with the weighted average method, the pattern of symmetric triangular distribution representation is implemented to demonstrate the fuzzy demands in constraints. The main reason to employ triangular fuzzy number in this study is that it represents a good trade-off between expressiveness, simplicity, and flexibility of the fuzzy arithmetic operations (Dubois et al. 2004 ). The weighted average method is applied to convert \(\overset{\sim }{d_{p,c}}\) into a crisp number using the most and least possible values. Following the thresholds of possibility and necessity used in FCCP, a minimum acceptable membership level, \(\gamma\) , could be given by the decision maker according to his / her attitude towards risk. Therefore, the corresponding auxiliary crisp inequality of the triangular fuzzy demand can be expressed as follows:

where \(w1 + w2 + w3 = 1\) , w 1, w 2 and w 3 represent the weights of the most pessimistic, most likely and most optimistic attributes, respectively. However, according to the knowledge and the experience of decision makers, the weights of \(\underline{d_{p,c}}\) , \(\hat{d_{p,c}}\) , \(\overline{d_{p,c}}\) can be modified subjectively and adapted to different real-world situations based to the definition below:

\(w1= \frac{1-\gamma }{2}\)

\(w2= \frac{1}{2}\)

\(w3= \frac{\gamma }{2}\)

In several relevant studies (Wang and Liang 2004 ; Liang 2006 ; Paksoy et al. 2012 ; Pourjavad and Mayorga 2019 ), authors usually used a minimum acceptable membership level for all the fuzzy constraints and applied the concept of the most possible values for the deffuzification of their models. The reason of defining the above weighted average values is that the most possible values are generally the most important ones, thus, a larger weights values should be assigned (Liang 2006 ). Besides \(\overline{d_{p,c}}\) and \(\underline{d_{p,c}}\) represent the boundary solution of the fuzzy demand for each care unit since they are the too pessimistic and too optimistic values, then smaller weights can be often considered. Consequently, changes to the values of \(\gamma\) affect the values of the critical weights and the solution generated. Hence, the corresponding auxiliary crisp inequality expression of constraints 9 can be presented using the weighted average method, as following;

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Dorgham, K., Nouaouri, I., Nicolas, JC. et al. Collaborative hospital supply chain network design problem under uncertainty. Oper Res Int J 22 , 4607–4640 (2022). https://doi.org/10.1007/s12351-022-00724-y

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DOI : https://doi.org/10.1007/s12351-022-00724-y

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Exploring the networking behaviors of hospital organizations

• Fausto Di Vincenzo 1  

BMC Health Services Research volume  18 , Article number:  334 ( 2018 ) Cite this article

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Despite an extensive body of knowledge exists on network outcomes and on how hospital network structures may contribute to the creation of outcomes at different levels of analysis, less attention has been paid to understanding how and why hospital organizational networks evolve and change. The aim of this paper is to study the dynamics of networking behaviors of hospital organizations.

Stochastic actor-based model for network dynamics was used to quantitatively examine data covering six-years of patient transfer relations among 35 hospital organizations. Specifically, the study investigated about determinants of patient transfer evolution modeling partner selection choice as a combination of multiple organizational attributes and endogenous network-based processes.

The results indicate that having overlapping specialties and treating patients with the same case-mix decrease the likelihood of observing network ties between hospitals. Also, results revealed as geographical proximity and membership of the same LHA have a positive impact on the networking behavior of hospitals organizations, there is a propensity in the network to choose larger hospitals as partners, and to transfer patients between hospitals facing similar levels of operational uncertainty.

Conclusions

Organizational attributes (overlapping specialties and case-mix), institutional factors (LHA), and geographical proximity matter in the formation and shaping of hospital networks over time. Managers can benefit from the use of these findings by clearly identifying the role and strategic positioning of their hospital with respect to the entire network. Social network analysis can yield novel information and also aid policy makers in the formation of interventions, encouraging alliances among providers as well as planning health system restructuring.

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Interest in understanding how and why hospital organizations choose collaborative partners overtime is a relatively recent issue and is related to a new strand of research that investigates these phenomena using concepts and methods from organizational sociology and network theory [ 1 , 2 , 3 , 4 , 5 ]. Networking behavior of organizations matters because they can achieve better performances, mitigate competition, learn by interaction, and develop effective ways to absorb external knowledge produced by their partners [ 6 , 7 , 8 , 9 ]. Networking matters also because organizations are connected to their environments through other organizations [ 10 ]. As a consequence, the quality, quantity and value of resources that an organization can access and the terms of availability of such heavily depend on the relations that it is able to establish with exchange partners [ 11 ].

Previous literature assumes that existing and past relations among organizations may act endogenously to induce networking [ 7 , 12 ], and how the position that an organization occupies in the web of industry relations affects the formation of networking relationships [ 13 ]. Despite an extensive body of knowledge exists on network outcomes and on how network structures may contribute to the creation of outcomes, less attention has been paid to understanding how and why organizational networks emerge, evolve, and change [ 14 ].

A quantitative exploration based on social network analysis (SNA) and specifically on stochastic actor-based model for network dynamics [ 15 , 16 , 17 ] was employed to understand networking behavior dynamics of hospital organizations, and specifically to identify the endogenous and exogenous determinants underlying the propensity of hospitals to exchange network ties. The research relies on original fieldwork and longitudinal data on patient transfer relations within a regional community of hospital organizations in Italy. Patient transfer flows reflect collaboration and the existence of underlying relationships between the hospitals involved [ 1 , 2 ]. Patient transfers between hospitals are directly observable and require high levels of coordination and communication [ 3 ]. The transfer of a patient requires the exchange of detailed clinical information which by definition, is complex due to the growth and specialization of clinical knowledge and the multiple combinations of conditions that patients can be subject to, and involves the co-construction of an understanding of the patient that needs also to consider the cognitive aspects of the actors involved in the exchange [ 18 ].

Recently, a number of studies have addressed the issues of the determinants of patient transfer between hospital organizations. In order to reduce staff uncertainty and coordinate their efforts, hospitals tend to routinize destination selection such that staff immediately contacted a “usual” transfer destination [ 19 ]. Transfer destination selection, therefore, was primarily driven at an institutional level by organizational concerns and bed supply, rather than physician choice or patient preference [ 19 ]. Remaining within the ambit of the organizational features, further studies have shown how patients are more likely to be transferred between hospitals differing in size [ 20 ], high-volume and larger hospitals are more attractive partners than small hospitals based on their greater availability of resources and infrastructures [ 21 ], resource complementarity especially in terms of technological assets and expertise matter in explaining the propensity of hospital to collaborate [ 22 ], and that patients often move from low-performance hospitals to high-performing hospitals [ 1 , 20 ]. Among the institutional variables, it was highlighted how patients are more likely to be transferred between hospital belonging to the same Local Health Authority (LHA) and having the same organizational forms (ownership-governance structure) [ 3 ]. Finally, the literature analyzed the impact of the geographical variable, highlighting how geographically proximate hospitals were somewhat more likely to share patients [ 2 , 23 ].

Despite this abundance of studies, most of them have in common the limit of being studies with a cross-sectional data setting or that have not been pushed to longitudinally analyze the evolution of patient transfer dynamics in a wide span of time. There are two researches that, however, are an exception to this limitation. The first, conducted by Lomi et al. [ 4 ], observed patient sharing events between hospitals during four consecutive years finding that quality of care, measured as 45-day risk-adjusted readmission rate, has an impact on the propensity of hospital organizations to exchange patients over time. The second, conducted by Stadtfeld et al. [ 5 ], explains assimilation and differentiation mechanisms (among which the propensity to transfer patients) between network partners over time. However, currently, no studies have already provided a longitudinal investigation of the determinants of patient transfer evolution employing stochastic actor-based model for network dynamics, and modeling partner selection choice as a combination of multiple organizational attributes and endogenous network-based processes. The present study aims to fill this gap in the literature.

Research setting

The dynamics of patient transfer relations within the entire network of hospitals providing services to patients in Abruzzo, a region in central Italy with a population of approximately 1,300,000 residents, have been analyzed. The Italian National Health Service (I-NHS) is a publicly funded health system that provides universal coverage. The government, at the central level, allocates resources to 20 Italian regions and is responsible for defining the core benefit packages and ensuring that basic coverage is provided to the entire population. Regional governments have wide autonomy in planning, allocating resources, and organizing regional level services, and are responsible for delivering health care services to their resident populations.

The Abruzzo regional health system is entrusted to six LHAs, and health care services are provided by 35 hospital organizations (22 public and 13 private). Of the 22 public hospitals, two are teaching hospitals. Public hospitals provide highly specialized hospital care and are characterized by technical, economic, and financial autonomy. Teaching hospitals are hospitals linked to universities, and provide education, research, and tertiary care. Private hospitals are partially financed by the regional healthcare service and are investor-owned organizations that provide ambulatory assistance, hospital care, and diagnostic services.

The study setting seems to be particularly appropriate for the purpose of this research. The first reason is that earlier research in this context [ 3 , 24 , 25 ] and the fieldwork show the presence of local networks of collaboration among hospitals, which mainly stem from the transfer of patients between hospitals. Patient transfer occurs when one hospital directly transfers one or more elective patients to another hospital. For example, hospitals that provide only basic services may send patients with more complicated clinical problems to another provider that offers comprehensive specialty care. Patient transfer may also be driven by ‘asymmetries’ in regional providers’ clinical resources or competences: e.g., hospitals may transfer patients to other local providers if they lack the necessary medical equipment (e.g., intensive care unit beds), expertise (e.g., staffing), or supplies. These informal networks become established and can have important implications for organizational performance [ 24 , 25 ].

The second reason is that, given the great strategic and organizational autonomy of our empirical setting, there are no significant external factors that influence the networking process for which to control. In the period considered in this study, there were no significant policy interventions that substantially altered the institutional framework, the number of providers, or the structure of the local inter-organizational network. Exception is the progressive reduction in the number of beds set by regional authorities, but this has affected proportionally all hospitals.

The third reason why this is an ideal case to study network dynamics is that Abruzzo health care system suffers from a lack of systemic planning and strategy coordination among its hospitals [ 26 ]. Unlike some other regions that have fostered inter-hospital collaboration through well-defined and formal collaboration mechanisms (e.g., “hub&spoke” models or clinical pathways for patient referrals), coordination in Abruzzo emerges mainly through patient transfer among providers [ 3 ]. Especially in regions where systemic planning and organizing of health provision is lacking, collaborative initiatives among hospitals arise and evolve endogenously [ 26 ]. These emergent “self-organizing” properties of inter-hospital networks may produce outcomes and behaviors that can be investigated by employing longitudinal models and social network analysis [ 15 ].

Data collection

The analysis draws on a range of rich data. Data on patterns of collaborative interdependencies during the period 01/01/2003–31/12/2008 among all hospitals in the region were extracted from the hospital information system database managed by the Abruzzo Region. Data on hospital activities, and information on demographics and performance, were taken from the Abruzzo Health Agency archives and yearly reports. These data are collected regularly and archived digitally by the Region for administrative purposes, and by the Health Agency for its operational and reporting activities. Archival sources are generally more precise and detailed than surveys and provided complete information on the network of hospitals: there were no missing data.

Dependent variable

Since this study is interested in understanding the dynamics of networking behavior of hospital organizations, the dependent variable is inter-hospital collaboration measured as transfers of patients [ 1 , 2 , 22 ]. Using available data on patient transfer among regional hospitals, as dependent variable, six “35 × 35” dichotomized matrices one for each of the years from 2003 to 2008 were built. The rows and columns of each matrix respectively report the hospitals that sent and admitted at least one patient between January 1 and December 31 in each of the year considered. Because matrices may vary depending on the dichotomization criteria, separated analyses were conducted to assess the effect on the results of different criteria (i.e. “greater-than” mean value, “greater-than” zero). The results obtained were qualitatively similar.

Explanatory variables

This research tested for several organizational-level variables that might influence networking behavior of hospital organizations. Specifically:

Measure of the level of complexity of the cases which are treated in a given hospital. It measures if hospitals facing with highly complex cases (for example, transplants, stroke, or hearth attacks) have different networking behavior compared to hospitals treating patients with a low degree of disease severity (for example, appendicitis, rehabilitation, etc.).

N° of common specialties

It counts the number of overlapping specialties, and indicates to what extent two hospitals are alike because they do the same thing or not. It serves to investigate whether the transfer of patients occurs between hospitals that overlap in knowledge stocks. Using available data on specialties (clinical wards) present in each hospital in the region, was built a “35 × 35” matrix. The rows and columns of the matrix respectively report the hospitals in the Region, while the cells of intersections report the number of overlapping specialties between each pair of hospitals. The matrix was computed for the year 2003 and was regarded as a constant in the statistical model as there have not been major changes in the number and types of specialties present at each hospital during the six years.

Staffed beds

A proxy of dimension, measured as the number of staffed beds [ 1 , 20 ].

LHA membership

It considers the affiliation of hospitals to the distinct LHAs in which the region is divided [ 3 ]. In a “35 × 35” matrix, the rows and columns of the matrix respectively report the hospitals in the Region, while the cells of intersections report 1 if pairs of hospitals were affiliated to the same LHA, 0 otherwise.

Performance

Measured as productivity, has been computed as the total number of admissions adjusted for case mix, divided by total number of staffed beds [ 24 ].

Geographical distance

A “35 × 35” matrix, the rows and columns of the matrix respectively report the hospitals in the Region, while the cells of intersections report the distance between each pair of hospitals expressed in km [ 23 ].

Percentage of emergency admissions

It represents unplanned emergency admissions as a percentage on the total admitted patients, as in previous studies [ 27 ]. It is commonly used as proxy of the level of uncertainty of input (i.e. patients) faced by the hospital [ 22 ].

Each variable was computed yearly, for the six-year period 2003–2008. Table  1 presents the descriptive statistics for the independent variables used in this research.

Geographical distance between hospitals, LHA membership and the number of specialties are constant over time, showing the absence of structural policies for the re-designing of the hospitals regional system. The mean of staffed beds reduces over time (such as the percentage of emergency admissions) while the case mix complexity and the productivity indicators slightly increase in the six years analyzed. Table  2 reports correlations among all the variables included in the full model.

In the estimation, the model controlled also for some structural endogenous effects named respectively outdegree, reciprocity, transitive ties, three cycles, balance, indegree-popularity, and outdegree–activity. Table  3 describes in detail each of the types of relational patterns investigated and how they should be interpreted. Only these simple and basic effects and not for the more sophisticated ones have been included in the model because they represent the most commonly used in works that exploits stochastic actor-based models [ 28 , 29 ].

Estimation technique

The R-Siena Software Package [ 15 ] allowed to conduct the exploratory analysis. The observed changes can be explained as functions of both individual and dyadic characteristics of actors and structural effects. Specific actor attributes and dyadic characteristics either favor or reduce the probability that two hospitals will transfer patients and so collaborate. For each actor and dyadic attribute, several effects have been included in the model specification. As explained by Snijders et al. [ 15 ], for continuous actor covariates (e.g., staffed beds, case mix, productivity, emergency admissions), three kinds of actor-driven mechanisms can be specified. The sender (ego) and receiver (alter) effects evaluate the tendency for organizations with higher attributive value to, respectively, send out more (higher outdegree) or receive more (higher indegree) than others. The “similarity” effect measures whether collaborative relations tend to occur more often between organizations with similar values for a given attribute. Finally, for the constant dyadic (LHA membership and overlapping specialties), the effects included in the model measure the tendency for ties between actors with the “same” value of that variable. Structural effects represent endogenous network mechanisms that also may influence the probability of interdependence between actors. For examples of introductory papers employing stochastic actor oriented models the reader can refer to Snijders, van de Bunt and Steglich [ 15 ]. For a more mathematical treatment and definition of effects in such models for network dynamics the reader can refer to Ripley et al. [ 29 ].

Table  4 reports key statistics describing the evolution of network ties in terms of density (i.e. ratio of number of collaborative ties observed yearly on the total number of possible ties), average degree (i.e. average number of collaborative partners for each node), and total number of ties. With the exception of the year 2006, density and number of ties increased slightly from 11% in 2003 to 12.2% in 2008, and from 131 in 2003 to 145 in 2008 respectively. Also, in the six-year period observed, the average number of collaborative ties increased from 3.743 to 4.143.

To explore networking behavior dynamics more in-depth, have been also considered the collaborative patterns at dyadic level over time (see Table  5 ). The column labeled 0 → 0 reports the number of pairs of hospitals that did not develop a collaborative relationship in the observed wave; the column labeled 1 → 1 indicates the number of pairs that maintained their collaborative relationships. The other two columns report the number of ties formed or dissolved from one year to the next. Consistent with the third column in Table 4 , also Table 5 shows a growing trend in tie changes: during the period of observation, 213 new collaborative ties were formed and 199 existing relationships were dissolved. The Jaccard coefficient is a measure of similarity for two sets of data, with a range from 0% to 100%. The higher is the percentage, the more similar are the two networks of hospitals. The values in Table 5 show that around 50% of ties, over time, change between subsequent observations from one year to another.

The empirical results of the stochastic actor based model estimations are presented in Table  6 . The analysis of the endogenous effects suggests that collaborative ties do not evolve randomly but instead follow specific relational patterns. The significant negative effect of outdegree and the significant positive effect of reciprocity respectively indicate a general tendency of organizations against outgoing collaborative ties and the propensity overtime to reciprocate received collaborative ties. The significance of these two basic measures is crucial in stochastic actor-based model for network dynamics as they provide robustness to the entire model [ 15 ]. A lack of their significance would imply that the phenomenon object of investigation (i.e. the propensity to exhibit collaborative ties) is not statistically relevant. In addition, the network presents overtime a general tendency toward transitive ties, meaning as collaborative ties tend to be established with partners of direct partners. This is in line with the study results of Madhavan, Gnyawali and He [ 30 ] on triads formation in cooperative networks. The remaining endogenous effects are not statistically significant.

The coefficient of N° of common specialties is negative and significant. This implies that there is a negative relationship between the similarity in terms of overlapping specialties and the propensity of organizations to collaborate. Higher levels of overlapping specialties have a negative impact on networking behavior of hospital organizations, reducing their propensity to exchange collaborative ties.

The variable case-mix (similarity) is negatively and significantly correlated with the dependent variable, meaning that network ties are more likely to be observed among organizations with different values in this index. Geographical distance is negative and significant. This implies that there is a geographical proximity effect [ 2 ], namely that as the distance decreases the propensity of hospital organizations to collaborate increases.

In line with previous studies [ 22 , 27 ], the results show that input uncertainty matter in explaining how hospital organizations choose their collaborative patterns. The variable Emergency admissions (similarity) is positive and significant, revealing a propensity to transfer patients between hospitals facing similar levels of operational uncertainty.

With reference to the proxy of size, staffed beds (alter) is positive and significant, showing a tendency in the network to choose larger hospitals as partners to which transfer patients [ 20 ].

The proxy used to measure whether similarities or differentials in performance levels (ie productivity) induce the networking behavior of hospitals organizations is not significant. It follows that if on the one hand it is widely recognized in literature that higher levels of collaboration produce a positive impact on organizational performance [ 24 ], on the other hand - at least in this specific case study - the opposite relationship is not true and therefore performance doesn’t matters in explaining partner selection.

Finally, the variable LHA is positive and significant, meaning that collaborative ties are more likely to develop between hospital organizations belonging to the same LHA.

Understanding the factors that stimulate or hinder networking behavior of organizations is a matter of significant theoretical interest and has remained high on the list of priorities of researchers interested in network relations [ 14 ]. Using stochastic actor-based model for network dynamics [ 15 , 16 , 17 , 29 ], the purpose of this paper was to model partner selection choice as a combination of individual organizational attributes and endogenous network-based processes. The opportunity was provided by the availability of very rich data and the identification of an ideal empirical context within a regional community of hospital organizations in Italy.

The networking behavior of hospital organizations was observed through the study of patient flows, since the previous literature has amply demonstrated to us how this represents a valid proxy reflecting collaboration and the existence of underlying relationships between the hospitals involved in patient transfers, because of the high levels of coordination and communication that patient transfer requires [ 1 , 2 , 22 , 25 ]. Although recently numerous studies have addressed the issue of patient transfer and investigated its determinants, this research topic was still uncovered as regards the study of evolutionary dynamics and factors that over time can induce or prevent ties formation among hospital organizations.

This research found that high levels of overlapping specialties reduce the propensity to exchange collaborative ties. This seems to suggest that perceiving another hospital organization as similar (in terms of dependence on the same resources, i.e. inputs represented by the patients), in this context seems to increase the competition between similar organizations and consequently inhibits the formation of network ties. Indeed, when two hospitals have many overlapping specialties, it implies that they are vey similar, they take care of the same diseases and treat the same type of patients, and thus may perceive each other as potential competitors [ 22 ]. Also this research found that, over time, network ties are more likely to be observed among hospital organizations that face with different case-mix. This seems to suggest that networking behavior is driven by clinical knowledge stock owned by a given hospital. Hospitals can suffer for the lack of high specialized physicians and nurses skilled to work in the intensive care unit, coronary care unit, stroke unit or operating surgery rooms equipped for transplantation, so they send patients to hospitals which could offer appropriate care related to patients’ pathologies [ 18 ]. In addition to the case-mix, the analysis also reveals a tendency in the network to choose larger hospitals as partners to which transfer patients, probably due to the fact that larger hospitals are more equipped in terms of resources and technologies [ 1 , 20 ].

The results of the empirical analysis show that, over time, collaborative ties are more likely to develop between hospital organizations belonging to the same LHA. This can be interpreted in line with what was found by Veinot et al. [ 19 ], i.e. patient transfer is not considered by hospitals only as a solution to contingent one-off problems, rather it happens in a structured and localized social context where hospital organizations tend to routinize destination selection in order to coordinate their efforts and conserve their cognitive resources for patient care. The significance of the geographical dimension shows how the search for partners is also guided by proximity. This result, therefore, confirms what found by Mascia and colleagues [ 23 ] and extends the validity of their findings longitudinally to a wider time frame.

The last explanatory variable is operational uncertainty, that manifests when internal organizational activities are difficult to plan, or planned activities are difficult to execute, and it comes from unpredictable variation in internal operating conditions, which require change in original plans and routines, and the revision of resource allocation decisions. Although it is well known in the literature that health care organizations respond to uncertainty by creating ties [ 22 , 27 ], this study adds that within the network there is a propensity over time to choose as collaborative partner hospitals facing similar levels of operational uncertainty. Future studies will have to clarify the motivations and theoretical mechanisms that explain this criterion in the choice of the partner organization.

Finally, results found that the formation of network ties between organizations is explained by peculiar forms of structural (or local) configurations, composed of subsets of two or three network actors and the possible ties among them [ 30 ]. These dyadic and triadic micro-processes have been measured statistically to provide evidence on how endogenous local forces drive the formation (and evolution) of network ties. Among the dyadic configurations, outdegree (the overall tendency of organizations to exhibit outgoing collaborative ties) and reciprocity (the overall tendency of organizations to exhibit reciprocal ties) are significant and confirm the non-static nature of the network investigated. Among the triadic configurations, only transitive ties (the tendency toward transitive closure, where collaborative ties are established with partners of partners) are significant in explaining how networks ties evolve over time [ 22 , 28 ].

To reduce the risk of over-interpreting the results, it is useful to reflect on the main limitations of this research, which provide opportunities for future research. First, one specific relation, i.e. patient transfer among hospitals, was analyzed. Although inter-hospital collaboration is widely used in the literature [ 3 ], it is possible that hospitals also collaborate in other ways including exchanges of doctors, cross training of medical staff, and technology transfer. Future studies should pay attention to the multiplexity that inter-organizational collaboration is likely to involve. Second, our findings are based on data for a six-year period from hospitals in a single region of Italy and may reflect issues specific to the local context or the time period. Further research is encouraged on the dynamics of collaboration, in order to extend the application of longitudinal models for social network analyses to other settings, and to check whether our findings can be generalized.

This study provides new insights by addressing the application of longitudinal models for social network analysis, which so far have received scant attention in health care. Delivery of hospital services is highly influenced by the formation of collaborative networks between providers. Hospital managers and policymakers are invited to use network analytic techniques that allow them to be informed about the current collaborative network. Also, through the use of these tools they can obtain novel information and understand better the effects of these networks, supporting the formation of structured agreements between hospitals, and allowing to draw proper patient flow at the regional level.

Health care networks are strongly self-organizing and emergent in nature, independent from (or even negatively influenced by) management and policymakers’ interventions (absence of interventions). It is therefore recommended to the latters of carefully define organizational characteristics (such as number of specialties, case-mix, size), institutional factors (LHAs) and geographical proximity as they count in determining the formation and shaping over time of hospital networks.

Abbreviations

Italian National Health Service

Local health authority

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Acknowledgements

The author is grateful to Francesca Masciarelli and Daniele Mascia for their comments and feedback on an earlier version of the manuscript, and to Valentina Evangelista for her support collecting data and providing empirical analysis. Precious support for data gathering has been provided also by the Abruzzo Agency of Public Health. A previous version was presented at the 2016 Academy of Management Annual Meeting, Anaheim (California), USA, Health Care Management Division, taking advantage from the suggestions provided by the audience.

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Di Vincenzo, F. Exploring the networking behaviors of hospital organizations. BMC Health Serv Res 18 , 334 (2018). https://doi.org/10.1186/s12913-018-3144-4

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A Case Study of a Whole System Approach to Improvement in an Acute Hospital Setting

Marie e. ward.

1 Centre for Innovative Human Systems, School of Psychology, Trinity College, The University of Dublin, D02 PN40 Dublin, Ireland; [email protected]

Ailish Daly

2 Beacon Hospital, Sandyford, D18 AK68 Dublin, Ireland; [email protected]

Martin McNamara

3 UCD Centre for Interdisciplinary Research, Education & Innovation in Health Systems, School of Nursing, Midwifery & Health Systems, UCD Health Sciences Centre, University College Dublin, D04 V1W8 Dublin, Ireland; [email protected] (M.M.); [email protected] (S.P.T.)

Suzanne Garvey

Sean paul teeling.

4 Centre for Person-Centred Practice Research Division of Nursing, School of Health Sciences, Queen Margaret University, Queen Margaret University Drive, Musselburgh EH21 6UU, UK

Associated Data

Not applicable.

Changes in healthcare tend to be project-based with whole system change, which acknowledges the interconnectedness of socio-technical factors, not the norm. This paper attempts to address the question of whole system change posed by the special issue and brings together other research presented in this special issue. A case study approach was adopted to understand the deployment of a whole system change in the acute hospital setting along four dimensions of a socio-technical systems framework: culture, system functioning, action, and sense-making. The case study demonstrates evidence of whole system improvement. The approach to change was co-designed by staff and management, projects involving staff from all specialities and levels of seniority were linked to each other and to the strategic objectives of the organisation, and learnings from first-generation projects have been passed to second and third-generation process improvements. The socio-technical systems framework was used retrospectively to assess the system change but could also be used prospectively to help healthcare organisations develop approaches to whole system improvement.

1. Introduction

The Patient Safety and Quality Improvement (QI) movements in healthcare have been slow to achieve momentum in improving outcomes [ 1 ]. Braithwaite et al. (2018) estimate that in healthcare organisations, nearly two-thirds of initiatives experience implementation failure [ 2 ]. Changes in healthcare tend to be project-based with whole system change, which acknowledges the interconnectedness of socio-technical factors, not the norm. In addition, it can be difficult both to sustain change beyond the project lifecycle as well as to generalise change to a broader level [ 3 ].

Lean Six Sigma is a powerful methodology that reduces waste and variation in an organisation and ultimately minimises operating costs, optimises productivity, and maximises customer satisfaction [ 4 ]. LSS is the merger of two methods used in process improvements. Lean originated in Toyota car production factories and focuses on refining and improving processes as well as eliminating non-value-added (NVA) activities [ 5 ]. Six Sigma was introduced by Motorola to optimise its manufacturing processes by reducing their variability through the rigorous application of process metrics collection and statistical analysis [ 6 , 7 ]. Since the early 2000s, LSS thinking has been adapted into healthcare with the goal of improving patient safety, quality of care, efficiency, patient satisfaction, and performance [ 8 ].

Healthcare providers worldwide, both publicly and privately funded, are faced with similar challenges of caring for an ageing population with a limited pool of financial and personnel resources. Consequently, the need to seek improved efficiencies while continuing to provide safe and high-quality services has become more and more acute [ 9 ]. LSS has been implemented in many healthcare organisations, with impacts achieved across many clinical and administrative pathways and processes [ 10 , 11 ]. While there are positive associations between LSS adoption and performance indicators in individual case studies [ 12 , 13 , 14 , 15 ], overall evidence on the success of LSS is mixed. Considerable time and effort need to be spent on implementation for LSS to be associated with gains in hospital performance. The degree to which this investment is made depends on the system maturity, leadership commitment, daily management system use, and training [ 16 , 17 ]. There is also increasing recognition of the importance of improving both patient and staff experience of healthcare [ 18 , 19 ] and moving to person-centred approaches in healthcare [ 20 ]. Political and policy stakeholders have widely advocated that person-centred care should be at the heart of the health system [ 21 , 22 , 23 , 24 ]. Person-centredness refers to embedded practices within a specific type of culture that enable and facilitate the delivery of person-centred care [ 25 , 26 ]. Person-centred cultures are deemed necessary for the delivery of person-centred care [ 26 ]. Person-centred care has an explicit focus on ensuring that the client or patient is at the centre of care delivery [ 25 , 27 ] and is concerned with every person involved in the patient’s care, including staff members and patients and their families/carers [ 20 , 27 ].

Implementation science as a field aims to help understand the factors surrounding the uptake of evidence-based practice into healthcare [ 28 ]. A central tenet of implementation science is that implementation strategies will be most successful when they align with healthcare systems’ existing culture, infrastructure, and practices [ 29 ]. Context has thus emerged as a key construct in understanding challenges to healthcare improvement [ 30 ]. Inconsistencies exist, however, in defining context [ 31 ] and in understanding the complexity of context in healthcare [ 32 ].

When talking about the healthcare system as a whole system, it is important to refer to a method for describing such a system that addresses its complexity and provides an analysis that gives leverage over the mechanisms of system change. McDonald et al.’s 2021 [ 33 ] work presented in this special issue makes a cogent argument for the importance of taking a socio-technical systems (STS) approach to whole system understanding and change. STS analysis involves studying the dynamic interconnectedness of elements of the system at different levels, such as team, processes, and information and knowledge. They propose a model called the CUBE for STS analysis that focuses on four domains:

1.1. Culture

Culture represents the pattern of shared basic assumptions and (what is often) a partial shared understanding of the STS and incorporates Schein’s [ 34 , 35 ] and Pigeon and O’Leary’s [ 36 , 37 ] work on culture.

1.2. System Functioning

System functioning represents how the system actually works and incorporates both formal elements (work-as-imagined), i.e., Policies, Procedures, Protocols, and Guidelines (PPPGs) as well as informal elements (work-as-done or the sequence of activities that normally takes place) [ 38 ] and incorporates Perrow’s functional focus on complexity and coupling [ 34 ].

1.3. Action

Action represents how we act within the system, incorporates Turner and Pidgeon’s work on the flows of information, knowledge and understanding, and anything that happens in the system that is recordable or measurable [ 37 ]; this can be analysed at different levels, such as individual actions, team performance against a standard, activity sequences, or key outcome, process, and balancing measures in relation to system performance [ 35 ].

1.4. Sense-Making

Sense-making represents how we understand and make sense of our world and incorporates Weick’s work on how individuals operating within the system make sense of it, often through practical action [ 39 ].

These dimensions of the CUBE are further broken down in terms of four types of relation: Goals (linked to objectives and outcomes), Process (sequential relations), Social Relations (reciprocal relations of working with and reporting to), and Information and Knowledge (exchanges of meaning that link people and processes). Figure 1 represents the CUBE.

Pictorial representation of the CUBE.

This case study reports on the system-wide implementation of LSS in conjunction with person-centred care principles in a large acute private hospital setting. The organisation’s mission is to provide exceptional patient care in an environment where quality, respect, caring, and compassion are central. This mission is based on organisational values of dignity, excellence, collegiality, and communication. In 2014, the organisation set out on a journey of expansion and growth. It was recognised that if this was to be achieved while holding the highest standards in quality and safety of patient care all staff would need to be involved and play a role. At that time, the organisation had achieved accreditation by the Joint Commission International and to maintain this was a key organisational goal [ 40 ].

This case study sets out to address the question ‘Was the deployment of LSS and person-centred care in this hospital a change on a whole system level?’. The CUBE will be employed as a descriptive and analytic framework to help answer this question.

The CUBE framework is firstly used here to outline some of the important considerations prior to the commencement of the change programme.

1.5. Culture

There was a recognition of the importance of culture from the outset. Retention and development of a highly-skilled staff body with significant organisational knowledge would be crucial to the journey of expansion. A key organisational priority became adopting a person-centred approach with the principles of collaboration, inclusiveness, and participation (CIP) underpinning process improvement in the hospital [ 20 ].

1.6. System

The following strategic objectives were set in 2014: to ensure excellence in quality and safety of patient care through compliance with the six International Patient Safety Goals as outlined by Joint Commission International [ 35 ]; to use Information Technology to enhance Safer Patient Care; to improve Patient Flow, and to improve Care of the High-Risk Patient. With the setting of these strategic objectives, it was recognised that all improvement work needed to come under one approach and be aligned to these strategic objectives as set out in the Hospital Leadership Goals 2014 [ 41 ]. This has been a criticism of QI in healthcare with the term ‘projectitis’ referring to an excessive focus on small projects that are not aligned to the strategic goals of the organisation or each other [ 42 ].

1.7. Action

Not all action in healthcare is suitable for easy measurement. A key focus of the hospital’s efforts, however, would be the ability to measure current performance and to know when a change is an improvement [ 43 , 44 ]. Another priority would be to give healthcare teams information and knowledge on how they were performing so that they would make sense of their own processes and improvement [ 38 , 45 ].

1.8. Sense-Making

Providing staff with excellent educational and developmental opportunities would be essential to support sense-making. The desired “future state” was a better patient and staff experience supported by a culture where all staff members, from Board and Executive Management Team (EMT) to frontline staff, had a shared vision of the goals and adopted a system-wide approach to process improvement, avoiding working in silos [ 46 ]. The organisation had a strong history of supporting staff in the completion of post-graduate education and training; however, before this project, education and training opportunities had been considered based on the individual’s or possibly the department’s needs. Outputs were delivered at the individual or departmental level. A system-wide consideration of education and training needs and outputs had not previously been attempted. It would be essential that staff were educated together to achieve a system-wide approach to change and improvement.

2. Materials and Methods

2.1. case study.

A case study approach [ 47 , 48 ] was adopted here to understand the deployment of a whole system change in the acute hospital along the four dimensions of STS outlined above. A case study is an approach that is used to generate an in-depth, multi-faceted understanding of a complex issue in its real-life context [ 49 ]. This case study sets out to address the question ‘Was the deployment of LSS and person-centred care in this hospital a change on a whole system level?’. The case study analysis was informed by a number of different sources of evidence [ 47 ].

2.2. Evidence

2.2.1. internal hospital documentation.

Hospital Leadership Goals (2014)

Education and Training Working Group; agendas and minutes (2015–2021)

Education and Training Working Group; gap analysis (2015)

Lean Academy presentation to the Hospital Board of Directors (2016)

LSS projects; meeting notes, project progress tracking (2017–2021)

2.2.2. Seven Research Studies Presented in This Special Issue

Operation Note Transformation: The Application of Lean Six Sigma to Improve the Process of Documenting the Operation Note in a Private Hospital Setting [ 50 ].

Releasing Operating Room Nursing Time to Care through the Reduction of Surgical Case Preparation Time: A Lean Six Sigma Pilot Study [ 51 ].

Redesigning the Process for Scheduling Elective Orthopaedic Surgery: A Combined Lean Six Sigma and Person-Centred Approach [ 52 ].

Lean Six Sigma Redesign of a Process for Healthcare Mandatory Education in Basic Life Support—A Pilot Study [ 53 ].

The Use of Lean Six Sigma for Improving Availability of and Access to Emergency Department Data to Facilitate Patient Flow [ 54 ].

Using Lean Six Sigma to Redesign the Supply Chain to the Operating Room Department of a Private Hospital to Reduce Associated Costs and Release Nursing Time to Care [ 55 ].

The Use of Lean Six Sigma Methodology in Reducing Length of Stay and Improving Patient Pathway in Anterior Cruciate Ligament Reconstruction Surgery (submitted) [ 56 ].

2.2.3. Participant Observation

One of the authors (AD) is the Director of Education, Innovation, and Rehabilitation at the hospital and has been on this whole system change journey since 2014. She has observed most of the processes concerning the deployment of LSS and person-centred care across the hospital. Another author participated in the Education and Training Working Group (SG). Another author (SPT) is one of the staff members from the Lean Academy who has also been involved since the beginning of the deployment from an academic provision perspective and has observed the system change unfold through this lens since 2017.

2.3. Synthesis

The synthesis of the evidence was facilitated by two authors (MEW and MMcN). MEW was involved in the development of the STS CUBE framework [ 33 , 57 ] and MMcN developed the university-accredited LSS curriculum to overcome system blindness [ 58 ], which was used within the hospital. MEW and MMcN supported the synthesis of the evidence by using questions from the CUBE framework combined with reflective questions from Oshry’s Organic Systems Framework (OSF) [ 59 , 60 ]. Because of the participatory nature of the involvement, it was felt important to add this reflective dimension. Oshry’s OSF provides a framework and vocabulary for describing human systems as organic wholes and allows us to understand and, potentially, influence a range of system phenomena. Oshry’s concepts enable us to see the whole as a pattern of systemic relationships (what the whole is) and as a pattern of systemic processes (what the whole does). He addresses how, as system members, we experience ourselves, our relationships with others, the systems we are a part of, other systems, and the relationships among systems, and it allows us to make more informed decisions and to take more informed actions based on these experiences. A set of questions based on the CUBE and Oshry’s OSF can be found in Table 1 and Table 2 . These questions were posed by MEW and MMcN to the other authors and answered through a process of iteratively writing up this case study. The synthesis set out to generate an answer to the question of whether or not this change could be described as being at a whole system level.

High-level questions are derived from the STSA CUBE [ 46 ].

Reflective questions derived from Oshry’s Organic Systems Framework [ 48 , 49 ].

2.4. Approach to Change

The approach to change at the time of commencement is now outlined under the domains of the CUBE.

2.4.1. Culture

Simpson et al. (2019) describe the importance of healthcare organisational culture when considering quality and patient safety in healthcare [ 49 ]. In 2014, the organisation culture was evolving from a “Power Culture” where the key to the organisation sits in the centre surrounded by widening circles of intimates and influence [ 61 ] (Handy 1999 p. 86). While such a command-and-control culture supported the successful initial drive to build and open the hospital, there was an acknowledgement that a challenge to sustaining and developing an organisation based on a “Power Culture” can be high staff turnover and staff dissatisfaction. There was a need to evolve to a culture of collaboration, inclusion, and participation, allowing the right staff power and influence to contribute to service progression and ultimately organisational development and expansion [ 20 ].

2.4.2. System

The strategic goals that the change was to support are outlined in Table 3 . These are aligned to the JCI accreditation program chapters. JCI accreditation had been achieved by the organisation and a key strategic goal was to maintain this accreditation.

The organisation’s strategic goals.

2.4.3. Action

Each part of the change process would address a strategic goal and would need to achieve certain pre-defined outcomes as outlined in Table 4 below.

System and action table.

2.4.4. Sense-Making

With support from the Board of Directors and the EMT, an Education and Training Working Group (ETWG) was created to identify the needs of the organisation and recommend relevant education and training programmes for implementation. The ETWG comprised a diverse set of stakeholders, all with a crucial role in developing a strategic direction for the organisation. The ETWG agreed on the importance of including all staff in opportunities to input into the design of the education programme; however, they also identified the challenge in accessing and meeting with a wide number of staff productively and effectively. Therefore, an open platform for suggestions was created through town hall meetings, departmental meetings, and performance reviews, including training needs analysis. Each ETWG member took responsibility for a staff/departmental grouping to gain their thoughts on education and training requirements as outlined in Table 5 .

Education and Training Working Group.

Engagement sessions were structured as focus groups with one-to-one sessions also facilitated when requested. The results of the stakeholder engagement sessions helped to inform the desired outcome of education and training solutions as outlined in Table 6 .

Outputs from stakeholder engagement sessions.

Participants were asked to consider focus group themes in the context of the wider organisation rather than discipline or department-specific and the context of the deliverables outlined by the hospital Board of Directors and EMT. To ensure inclusion, a representative from all departments was invited to contribute. When choosing a representative, departments were encouraged to consider staff from all grades/groupings—not specifically managers.

Based on feedback from stakeholders, the ETWG proceeded to scope potential education and training solutions with some key outcomes required in the following areas:

• the culture of quality and patient safety as a priority goal for the organisation would need to be endorsed in any education and training programme;
• to continue to deliver the best patient care, the organisation would need to constantly evolve and improve, working to best international evidence-based practice; and
• the programme would need to take account of the strategic direction of the organisation, including the use of technology to enhance patient care, optimise patient flow, and optimise care of the high-risk patient.

The ETWG identified that the gap in organisational knowledge lay not in the theory of what care to provide but the project management and process improvement skills to bring those theories to fruition. Rather than middle management/senior clinicians passing an idea to EMT to realise, the goal was to achieve a system-wide change in how projects are delivered—co-creating and realising strategies with senior and middle management and frontline staff working together [ 62 ]. Thus, education and training would need to be accessible to team members from all disciplines and all levels of seniority. To support future goals of improved inter-professional collaborative and shared decision-making, education and training that was accessible to the wider healthcare team across levels of seniority, from EMT to department managers as well as staff directly involved in the patients’ journey through the organisation, was deemed a priority [ 62 ].

To add accountability to students and the organisation, a formal academic qualification was deemed a requirement. This was to ensure that students would receive official recognition of knowledge gained and the organisation would be able to formally identify deliverables from investment in training that could be expected.

With education requirements defined ( Table 6 ), the ETWG completed a scoping review of literature of Cinahl and PUBMED databases using keywords including Process Improvement, Healthcare, and Person-Centredness. Emerging evidence of the role of LSS in wider healthcare settings was identified. Of particular note was the variation in LSS work completed in healthcare settings, including administration/patient scheduling, Emergency Department patient flow, Theatre flow, and laboratory turnaround times [ 11 , 63 , 64 , 65 , 66 ], as well as the impact of LSS in improving quality, patient safety, and employee engagement in healthcare [ 27 ]. The ETWG identified LSS as an evidence-based approach to process improvement. Its background in business and then healthcare aligned with the logistics of merging clinical and business process improvements in a private healthcare setting. The principles of LSS include recognising the complexity of healthcare, avoiding silo working, always being open to change and improvement, gathering data to create knowledge, cutting waste not care and focusing on improving the process rather than seeking person-specific improvements that matched the ethos of the organisation.

The ETWG took the evidence from the literature and sought further information regarding the impact of LSS in healthcare through visiting sites that had successfully implemented LSS to examine the “lived experience” of the organisation and their team. This took the form of a site visit to an acute hospital as well as attendance at a White Belt: “Fundamentals of Process Improvement for Healthcare” provided by the Mater Lean Academy. On assessing the literature and reflecting on the site visit, the ETWG reflected on the potential for LSS in healthcare as an education and training resource for process improvement in the organisation. The specific advantages related to accessibility. The structured delivery of LSS from White Belt: “Fundamentals of Process Improvement for Healthcare” to Green Belt: “Professional Certificate Process Improvement in Health Systems” to Black Belt: “Graduate Diploma Process Improvement in Health Systems” would enable staff at all levels to access LSS training—from a 1-day training course to a 1-year diploma.

The ETWG agreed to recommend LSS as an education programme to support process improvement in the organisation. The hospital Board of Directors supported the recommendation and an implementation plan was agreed upon. The support of the Board and EMT was a key requirement before the implementation plan and was based on the following principles:

• LSS training would be made available to all staff. Training would not be discipline or grade-specific. This was important in developing staff who ‘can’, contextualising the change across the organisation, and recognising the role of all employees [ 62 ].
• The method of delivery would be the same for all staff—thus, there was no specific delivery methodology for the EMT.
• The organisation would fully support participation in LSS education events. This included the provision of study leave and financial support for attendance at LSS training events. Thus, the improvement approach was resourced from the outset.
• Members of the EMT were committed to attending training events and acting as executive sponsors as projects emerged. This confirmed leadership commitment through walking the walk, getting involved, and supporting the project [ 50 , 51 , 52 , 53 , 54 , 55 , 56 ].

3.1. How Change Was Achieved in the Organisation

The details for how each individual project achieved its goals are written up in the accompanying papers to this case study [ 50 , 51 , 52 , 53 , 54 , 55 , 56 ]. Some examples of quality and patient safety improvement include: a reduction in the length of stay for surgeries, leading to less likelihood of acquiring a healthcare-associated infection; an increase in capacity to deliver Basic Life Support across the organisation; surgical notes transferred to electronic platforms to improve legibility and accessibility; and releasing nursing and healthcare assistants time to care for patients. Please see Table 7 for a full list of outcomes.

LSS projects delivered through collaborative, inclusive, and participative working.

The mechanisms for change at a system level are presented here using the four domains of the CUBE.

3.1.1. Culture

As can be seen in Table 7 , it is evident that the teams involved in the process improvement projects were from a wide range of backgrounds and seniority, some directly involved in the process, some giving an external perspective. Working from a common framework of the LSS methodology underpinned by a person-centred approach has allowed voices across disciplines and seniority to take an active role in project delivery. It has allowed for devolved responsibility for project delivery from the EMT level. The organisational culture shifted from a power-based culture to a task-based culture [ 61 ].

3.1.2. System

All projects supported organisational strategic goals as well as quality and patient safety priorities. Table 7 demonstrates the system-wide impact of process improvement projects delivered to date. Learnings from first-generation projects have been passed to second and third-generation process improvements ( Figure 2 ). Rather than being completed in isolation, projects are linked and outcomes are used to inform further process improvement.

Interconnection of projects supporting multiple strategic targets.

3.1.3. Action

Each of the projects described in Table 7 has resulted in concrete tangible outcomes for the organisation. For example, the Emergency Department data are circulated daily to the Emergency Department and EMT [ 54 ]. The use of LSS to redesign the delivery of Basic Life Support (BLS) training has resulted in a 50% increase in the capacity to deliver BLS [ 53 ]. Key to this was the academic qualification attached to the LSS training. The requirement to present a completed project that was nominated and supported by the hospital Board of Directors and EMT gave influence and a voice to the project groups.

3.1.4. Sense-Making

The deployment of LSS in conjunction with person-centred care commenced in the hospital in 2017. The following practical aspects of deployment were also put in place to support the above principles. All staff members were included in invites to attend training events. LSS training events were advertised through hospital-wide newsletters, email groups, team meetings, etc. Every staff member was invited to attend White Belt training. Staff from all disciplines and grades attended White Belt training together; there was no specific training for members of the EMT. This supported the hospital’s values of removing barriers between senior managers and staff directly involved in patient care as well as encouraging collaboration across teams/moving from a siloed approach to process improvement. White Belt training had to be completed before moving on to Green Belt training. Academic institution requirements were also noted. Once a staff member was assigned a place at a training event, they agreed to participate actively in the training event. To encourage collaboration, training events were arranged with team members from different departments and at different levels of seniority.

To ensure a whole system approach to improvement, each staff member applying for Green or Black Belt training was asked to submit a project charter as part of their application. Members of the EMT and quality and patient safety staff committed time to potential students to co-design project suggestions and project charters. This ensured that projects were aligned to the strategic goals and direction of the organisation. From a staff perspective, this also demonstrated the EMT and senior management commitment to their improvement project. This commitment was also demonstrated in practice. To assist with staff being released for improvement work, each application required approval from the staff member’s line manager—to ensure cover was in place for the staff member’s improvement leave as required. The first White Belt course was delivered in May 2017. Attendees included the CEO, a nurse specialist, a procurement operative, a physiotherapist, a healthcare assistant, and a patient services administrator. The ETWG had achieved a very important goal—the training event was accessible to all and had served to show that hierarchy was not going to be a barrier to improvement [ 67 ].

Following the implementation of White Belt training events, the organisation was ready to submit applications for Green Belt training commencing September 2017. For the candidates proceeding to Green Belt training, the organisation and candidates hoped that this would empower “middles” to lead process improvement by giving them the skills to integrate the needs and requirements of management with the potential and skills of the frontline staff [ 60 ]. The first Black Belt training programme was completed in November 2020, delivering advanced knowledge on LSS in healthcare. This also delivered the very significant milestone of the hospital being able to deliver White Belt training internally.

Each LSS training event resulted in specific deliverables. At the Black Belt/Green Belt level, this was the completion of process improvement projects with a tangible impact on the strategic goals of the organisation. At the White Belt level, a network of staff familiar with LSS tools was developed who could assist Black and Green Belts to achieve project goals. Every staff member in the hospital has a role to play in quality and patient safety. The accessibility of LSS to all staff created an avenue for all staff to learn and become actively involved in patient safety activities. Combining a person-centred approach and stakeholder engagement methodology, a shared purpose approach has emerged in the LSS projects to date. The project teams formed and refined the project goals and took a shared responsibility with key stakeholders to see projects through to completion.

3.2. Case Study Synthesis

The importance of taking a socio-technical systems approach to whole system change that focuses on the four domains of culture, system, action, and sense-making was stressed in the Introduction [ 33 ] as an important approach to move forward the lack of traction on quality and patient safety improvement that has afflicted healthcare over the last 20 years [ 1 , 2 ].

The results of this case study are now discussed with these four domains in mind. At the outset, the organisation required increased knowledge and skills in person-centred process improvement to help staff provide a sustainable workforce that could engage with and support organisation expansion and development. The person-centred implementation of LSS in the organisation has resulted in the emergence of a task-based culture that focuses on involving the right people with the right resources to complete improvements [ 61 ]. The unifying power of the group is in their approach to the project—a commonality in structuring the project utilising LSS tools based on the principles of collaboration, inclusion, and participation [ 27 ]. These principles allow staff who have completed Green and Black Belt training to support process improvement outside of their usual areas of work—moving away from silo-based improvement or ‘projectitis’ and to more of a system-wide approach to change. LSS graduates from one area are supporting improvement in another. This enables sharing of knowledge and skills, the building up of organisational trust, systemic learning at both a tacit [ 63 ] and explicit level, and the provision of support to system-wide improvement. Interdependencies between projects and areas are noted and a systems view emerges. Staff from patient services supported improvement projects in theatre procurement and graduates from physiotherapy supported projects in information technology/education planning. Investing time and energy to allow staff to do this can be a challenge in a busy acute hospital. By employing the principles of stakeholder engagement promoted by LSS—seeking to understand and giving voice, but also ensuring improvement sessions were well structured with identifiable deliverables, staff were happy to dedicate time to achieve the desired outcome and the organisation supported this.

Study leave was approved before Green Belt and Black Belt training and education commenced. A support network for covering staff was agreed upon. The clear message of support from the Board and EMT removed concerns regarding financial and study leave support. More challenging was facilitating stakeholder engagement/data collection sessions. Teams had to be mindful to meet their stakeholders at times and venues that suited. Additionally, hugely important was the need to reassure stakeholders that the teams sought to understand processes and challenges and seek solutions. The purpose of a LSS project was never to examine or find fault with the person—94% of the problems are caused by the system and 6% by the individual [ 68 ].

In terms of the development of a long-term sustainable team that can support hospital development and expansion, the hospital has moved through forming, storming, and norming and is currently progressing to performing [ 69 ]. D’Andrematteo (2015) [ 70 ] called for further investigation into the organisation-wide success and weakness of LSS. In this system-wide implementation of LSS underpinned by a person-centred approach, the hospital has achieved an organisation-wide approach to improvement involving staff from all specialities and levels of seniority.

Benefits and challenges involving roles within the improvement team were noted. The involvement of clinicians in healthcare improvement is central to system change [ 71 ]. There was great support from clinicians throughout—from practical support given by the Orthopaedic Consultants and Anaesthetist in implementing Day Case Anterior Cruciate Ligament surgery to the “external” process view offered by the Speech and Language Therapist to theatre procurement and stock management [ 55 ]. Each LSS project is based on the collaboration of team members from a combination of medical, nursing, HSCP, and management/administrative backgrounds [ 72 ].

Clinicians are trained to make quick decisions to address an evolving presentation in a patient. The temptation to start a process improvement with “I know the solution—we just have to …..” was something that a lot of staff had to learn to avoid. Process owners within teams also had to learn to allow others the authority to examine processes and facilitate stakeholder engagement and data collection—in some cases acknowledging that team members from outside the process were better placed to complete these activities—as they approached them with “fresh eyes”. This supports a culture where all staff members have psychological safety [ 67 ] and feel able to speak up for important issues such as quality and safety of patient care [ 68 ]. Psychological safety is an essential component of achieving JCI accreditation [ 40 ]. It helps healthcare move on a journey towards high reliability [ 1 ] and to building organisational resilience [ 73 ]. The management is also learning to distribute power and knowledge and acknowledge the expertise and insights of others. There is less emphasis on the positional role and traditional authority [ 74 , 75 ].

LSS is now the method of choice used for improving processes. LSS is also used to present improvements as part of JCI accreditation. The organisation completes JCI accreditation every three years. As part of this accreditation, the hospital reports on key performance indicators, including length of stay and readmission rates, and quality improvement projects around these indicators. Please see Table 8 .

Hospital leadership goals and key performance indicators.

From 2019, these projects have been completed using the LSS methodology. The hospital first achieved JCI accreditation in 2007 and has been re-accredited every three years since then—most recently in 2019. Continuing to achieve re-accreditation requires continuing improvement as well as a commitment to quality and safety of care, including the International Patient Safety Goals.

In addition to the projects described above and as a reflection of the maturing of a LSS culture in the organisation, the LSS methodology has now been adopted as the process improvement method of choice in the organisation. Green and Black Belt projects, as mentioned above, have led to legacy projects outside of the academic structure.

As the number of staff familiar with the LSS approach increases in the organisation, the use of various methods, tools, and strategies has become commonplace. For example, when planning a new or changed service, first thoughts are always to align with the strategic objectives of the organisation, followed by using LSS tools such as process mapping to understand how the service currently runs (AS IS mapping) and to identify how the service will run (TO BE mapping). When analysing potential risks associated with changing a process, a Failure Modes Effect Analysis (FMEA) is completed as standard—this is of particular benefit when preparing for JCI accreditation as it is a tool that JCI commonly requests as part of their accreditation of quality and safety improvement in the hospital.

The CUBE STS analysis framework as further developed in the Access Risk Knowledge (ARK) Platform addresses questions of value in terms of the projected gain and the actual gain of the change achieved [ 28 , 66 ]. In Table 7 the expected outcome and the actual outcome achieved are presented for each individual project. Improvements also occurred outside of these projected outcomes, for example, improvements related to operation notes also improved patient safety and created a template for the transference of further documents to the patient electronic record—without having to seek external consultancy advice. Value can also be seen by stakeholder satisfaction and improved patient care. Examples of stakeholder satisfaction include:

“The novelty, of actually being able to read the handwriting and understand the detail of the surgery, is brilliant!”

“It’s so easy to use”,

“With the help of the templates, I can complete my Op note in minutes”

“It’s saving me so much time!”

“Love the layout, it’s so easy to read”

Harder to estimate is overall Return on Investment (ROI). Four years into the deployment, ROI can be estimated by savings made related to improvement projects. Each of the seven studies reported on here achieved outcomes that can be quantified separately, e.g., projects involving theatre stock have led to a 91% reduction or EUR 24,769 in the value of out-of-date stock and a 45% reduction in nursing stock preparation time (releasing that nursing time to caring for patients) [ 51 , 55 ]. Projects involving patient flow, such as improving the pathway for patients attending Anterior Cruciate Ligament reconstruction, have resulted in an additional 24.6 bed days annually in the organisation [ 56 ]. This implementation was funded within the existing postgraduate education and training budget. Analysis of staff retention and progression is complicated due to many changing circumstances resulting from the COVID-19 pandemic. Of the 32 staff who have completed Lean Six Sigma practitioner training, 25 (78%) remain and are progressing to new roles in the organisation. Further analysis of the 21% of staff trained who have left the organisation is required to identify motivating factors behind the staff member’s decision to change.

Another ROI was the ability to continue White Belt training with in-house resources, meaning the cost of continuing LSS training in the organisation reduced significantly in 2020. Perhaps a mark of leadership satisfaction with the LSS programme was that rather than allocating those savings to another area, the savings were ploughed back into LSS training and education—supporting further Green Belt and Black Belt training.

4. Discussion

The case study synthesis, using the CUBE domains of culture, action, system functioning, and sense-making combined with Oshry’s OSF, has enabled us to answer the question of whether or not these elements combined to create agency for change at the organisational level of the hospital. The case study demonstrates evidence of whole system improvement; projects involving staff from all specialities and levels of seniority are linked to each other and to the strategic objectives of the organisation, and learnings from first-generation projects have been passed to second and third-generation process improvements.

The question of whole system change is difficult, however. There is little agreement in the literature on what constitutes ‘whole system’ change, which speaks to the origins of this special issue. This case study has taken the approach that the design of an effective agency of complex and socio-technical system change requires both an understanding of socio-technical systems and the engineering of their development [ 28 ] and takes some reflection on our role as actors within the system [ 47 , 48 ].

Flynn et al. (2019) [ 77 ] completed a realist evaluation to identify contexts and mechanisms that enabled and hindered implementation and had an effect on the outcome of sustainability of what was meant to be a whole system Lean intervention in a pediatric healthcare setting (CMOs). This intervention was noted as being the ‘largest Lean transformation in the world’ [ 78 ]. While Flynn et al.’s evaluation focused on the outcome of sustainability, the framework could still be used to assess whether the hospital intervention reported here did have an impact at a systems level. The CMOs from Flynn et al.’s work are thus presented here along with a response from the synthesis of evidence in this case study.

CMO1: The early stages of Lean’s implementation were funded, mandated, and top-down in nature (C), driven by an external consultancy firm that initially focused on training senior leadership (C). Frontline staff did not feel involved in Lean changes, and they felt pressured to adopt Lean (M). The Lean language used did not make sense to staff (M). Training failed to demonstrate a connection between Lean and healthcare.

In this case study, it can be seen that an approach to whole system improvement was co-designed from within the system by a team of staff (ETWG) in conjunction with the Board of Directors and EMT. A partnership approach was developed with the UCD Lean Academy who are a team of former and current healthcare workers who have adopted LSS for healthcare staff. The training used and examples given were based in the Irish healthcare settings. The UCD Lean Academy has committed to supporting healthcare teams publish their research to add to the international evidence base [ 12 , 13 , 14 , 15 , 79 ]. Materials from these cases studies were used to support the training.

CMO2: The complexity and dynamic nature of healthcare (C) were perceived as incongruent with the nature of Lean. The translation of Lean to patient care did not make sense for many staff and Lean efforts felt impersonal. Lean training failed to make the connection between Lean and healthcare clear for staff (M) and the early stages of implementation led by the consultancy company failed to customise Lean to the local context. This triggered pitfalls to the success of Lean, such as feelings of disconnection and negative perceptions of Lean (M), resulting in resistance to and a lack of support for Lean continuation (O).

In this case study, it was seen that LSS process improvements were designed and led by organisational staff from the outset with support from staff from the Lean Academy. Organisation stakeholders met with their colleagues rather than with an external consultant. This enabled a shared approach to understanding the challenges, the joint consideration of solutions, and an acknowledgement of previous efforts at improvement made in the past, rather than a suggestion of “just do it” solutions.

CMO3: Lean was implemented in areas that experience constant change (C), early stages of implementation involved multiple Lean events for training purposes (C), and frontline staff felt overwhelmed from the constant change, they were unsure what changes were due to Lean, and felt that Lean was the latest fad (M). This led to negative perceptions of Lean, resistance, and a lack of support by frontline staff (O).

As a relatively young organisation, staff are accustomed to change and progression with short lead-in times. In this case study, it was evident that rather than change being seen as a challenge, the use of LSS and data-driven solution design allowed team members to participate actively in change and take ownership and credit when solutions were found.

CMO4: The contract of the external consultancy leading Lean’s implementation ended (C), placing the continuation of Lean on internal senior leaders and unit managers (C). This led to a process of customisation of Lean to the local context through a variety of ways. This customisation of Lean and shift in implementation triggered positive and negative responses from frontline staff, unit managers, and senior leaders (M). As a result, only some Lean efforts became embedded. However, there was variation and a discrepancy between senior leaders and unit managers compared with frontline staff on perceptions of how embedded Lean efforts were (O).

In this case study, it was seen that the hospital system was committed to building up in-house expertise from the beginning via the training of White, Green, and Black Belts who would reinvest in the system and train further White Belts.

CMO5: The context of early stages of implementation (C) failed to trigger sense-making processes necessary for staff to understand Lean and potentially engage with and begin to embed Lean into their practices (O). Shared values were evident between Lean principles and staff professional values as healthcare providers. However, value congruency without clear sense-making processes resulted in a lack of adoption of Lean behaviours as part of normalised frontline practices. Sense-making processes were hindered by a failure of initial Lean training efforts to translate the principles of Lean into the context of healthcare that would resonate with staff (M). Lean language and the lack of staff involvement in Lean changes also hindered sense-making processes and feelings of engagement. This resulted in negative perceptions of Lean, a lack of buy-in, and a lack of support for the continuation of Lean from frontline staff (O).

In this case study, it can be seen that there was a focus on sense-making from the outset. One learning from the LSS deployment to date is the need to explore and understand the pain/challenge from all perspectives from the outset.

Strengths and Limitations

The strengths of taking a case study approach are that it allows us to attempt to answer complex questions by triangulating different data from different sources [ 43 ]. Internal consistency was increased by collecting data from multiple sources and by using different types and sources of data. Reliability was aided by transparency in terms of outlining the questions and processes of synthesis [ 80 ].

A criticism, however, of this study could be that only one author (MEW) was outside of the process as it was happening. However, there is also a strength in combining insider insights on change and using the rigour of a STS analytic framework such as the CUBE combined with Oshry’s Organic Systems Framework to approach the case study.

A further point to be acknowledged is that this case study reports on the system that was one hospital. This is the strength of the case study approach and helps us give importance to and answer questions on topics in their own right. However, as noted above, whole system change is complex and there may be other factors at play when we consider a ‘systems-of-systems’ approach and acknowledge the wider impact of societal, legislative, political, and other factors on that system. As Flynn et al. note in this special issue [ 81 ], there is growing traction for the need to look at what has been termed ‘learning health systems, which are dynamic ecosystems where scientific, social, technological, policy, legal, and ethical dimensions are aligned to enable continuous learning and improvement to be embedded across the system [ 82 ]. COVID-19 has also taught us a great deal about the importance of taking a ‘systems-of-systems’ approach in healthcare and there are further lessons to be learned from this [ 83 ].

5. Conclusions

There are strengths and limits to the case study approach; however, we hope here, guided by an STS approach, to add to the body of literature on what would constitute whole system improvement in healthcare. Recognising the organisation’s culture , aligning complex system functionality requirements and the ability to activate these requirements to deliver concrete outcomes, and developing a shared understanding or sense-making of future goals aligned with embedding a person-centred approach to whole system improvement have synergised in a way that credibly addresses what it takes to change a whole system. Through the growing organisation-wide knowledge of the LSS approach and methods underpinned by person-centredness [ 27 ], the hospital is creating an increasing network of those who, in Oshry’s terms, “can”, “know”, and “want” to continuously strive for improvement in the quality and safety of patient care in the organisation [ 60 ]. This case study highlights achievements to date. The organisation will continue to grow and develop process improvement with a growing network of staff to support this important work. The STSA CUBE framework and Oshry’s OS framework were used here retrospectively to assess an intervention but could also be used prospectively to help healthcare organisations develop approaches to whole system improvement. Future areas of development for this organisation and to promote the sustainability of LSS and person-centred care include: (1) assessing the impact of LSS/person-centred process improvement through a stakeholder survey as well as the recording of formal project outputs; (2) disseminating and celebrating achievements internally and externally; and (3) continuing to reinvest in training and education to ensure leaders and process improvers remain equipped with skills and knowledge in this constantly evolving field.

Acknowledgments

The authors acknowledge the support of the hospital’s Executive Management Team, Board of Directors, and Education and Training Working Group in the scoping and implementation of this project. We also thank the UCD Mater Lean Academy for the support provided during this project.

Author Contributions

Conceptualisation, M.E.W., M.M., A.D., and S.P.T. methodology, M.E.W., M.M., and A.D.; formal analysis, M.E.W., M.M., and A.D., writing—original draft preparation, A.D., M.E.W., and M.M. writing—review and editing, A.D., M.E.W., M.M., S.G., and S.P.T.; visualisation, A.D. and M.E.W.; funding acquisition, A.D. and S.G. All authors have read and agreed to the published version of the manuscript.

The research received no external funding.

Institutional Review Board Statement

This work took place as part of ongoing organisational quality improvement. Institutional Review Board approval was not required.

Informed Consent Statement

Data availability statement, conflicts of interest.

The authors declare no conflict of interest.

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