assignment theory in operations research

Assignment Problem: Meaning, Methods and Variations | Operations Research

After reading this article you will learn about:- 1. Meaning of Assignment Problem 2. Definition of Assignment Problem 3. Mathematical Formulation 4. Hungarian Method 5. Variations.

Meaning of Assignment Problem:

An assignment problem is a particular case of transportation problem where the objective is to assign a number of resources to an equal number of activities so as to minimise total cost or maximize total profit of allocation.

The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different.

Thus, the problem is “How should the assignments be made so as to optimize the given objective”. Some of the problem where the assignment technique may be useful are assignment of workers to machines, salesman to different sales areas.

Definition of Assignment Problem:

ADVERTISEMENTS:

Suppose there are n jobs to be performed and n persons are available for doing these jobs. Assume that each person can do each job at a term, though with varying degree of efficiency, let c ij be the cost if the i-th person is assigned to the j-th job. The problem is to find an assignment (which job should be assigned to which person one on-one basis) So that the total cost of performing all jobs is minimum, problem of this kind are known as assignment problem.

The assignment problem can be stated in the form of n x n cost matrix C real members as given in the following table:

Check it out now on O’Reilly

Dive in for free with a 10-day trial of the O’Reilly learning platform—then explore all the other resources our members count on to build skills and solve problems every day.

How to Solve the Assignment Problem: A Complete Guide

Table of Contents

Assignment problem is a special type of linear programming problem that deals with assigning a number of resources to an equal number of tasks in the most efficient way. The goal is to minimize the total cost of assignments while ensuring that each task is assigned to only one resource and each resource is assigned to only one task. In this blog, we will discuss the solution of the assignment problem using the Hungarian method, which is a popular algorithm for solving the problem.

Understanding the Assignment Problem

Before we dive into the solution, it is important to understand the problem itself. In the assignment problem, we have a matrix of costs, where each row represents a resource and each column represents a task. The objective is to assign each resource to a task in such a way that the total cost of assignments is minimized. However, there are certain constraints that need to be satisfied – each resource can be assigned to only one task and each task can be assigned to only one resource.

Solving the Assignment Problem

There are various methods for solving the assignment problem, including the Hungarian method, the brute force method, and the auction algorithm. Here, we will focus on the steps involved in solving the assignment problem using the Hungarian method, which is the most commonly used and efficient method.

Step 1: Set up the cost matrix

The first step in solving the assignment problem is to set up the cost matrix, which represents the cost of assigning a task to an agent. The matrix should be square and have the same number of rows and columns as the number of tasks and agents, respectively.

Step 2: Subtract the smallest element from each row and column

To simplify the calculations, we need to reduce the size of the cost matrix by subtracting the smallest element from each row and column. This step is called matrix reduction.

Step 3: Cover all zeros with the minimum number of lines

The next step is to cover all zeros in the matrix with the minimum number of horizontal and vertical lines. This step is called matrix covering.

Step 4: Test for optimality and adjust the matrix

To test for optimality, we need to calculate the minimum number of lines required to cover all zeros in the matrix. If the number of lines equals the number of rows or columns, the solution is optimal. If not, we need to adjust the matrix and repeat steps 3 and 4 until we get an optimal solution.

Step 5: Assign the tasks to the agents

The final step is to assign the tasks to the agents based on the optimal solution obtained in step 4. This will give us the most cost-effective or profit-maximizing assignment.

Solution of the Assignment Problem using the Hungarian Method

The Hungarian method is an algorithm that uses a step-by-step approach to find the optimal assignment. The algorithm consists of the following steps:

• Subtract the smallest entry in each row from all the entries of the row.
• Subtract the smallest entry in each column from all the entries of the column.
• Draw the minimum number of lines to cover all zeros in the matrix. If the number of lines drawn is equal to the number of rows, we have an optimal solution. If not, go to step 4.
• Determine the smallest entry not covered by any line. Subtract it from all uncovered entries and add it to all entries covered by two lines. Go to step 3.

The above steps are repeated until an optimal solution is obtained. The optimal solution will have all zeros covered by the minimum number of lines. The assignments can be made by selecting the rows and columns with a single zero in the final matrix.

Applications of the Assignment Problem

The assignment problem has various applications in different fields, including computer science, economics, logistics, and management. In this section, we will provide some examples of how the assignment problem is used in real-life situations.

Applications in Computer Science

The assignment problem can be used in computer science to allocate resources to different tasks, such as allocating memory to processes or assigning threads to processors.

Applications in Economics

The assignment problem can be used in economics to allocate resources to different agents, such as allocating workers to jobs or assigning projects to contractors.

Applications in Logistics

The assignment problem can be used in logistics to allocate resources to different activities, such as allocating vehicles to routes or assigning warehouses to customers.

Applications in Management

The assignment problem can be used in management to allocate resources to different projects, such as allocating employees to tasks or assigning budgets to departments.

Let’s consider the following scenario: a manager needs to assign three employees to three different tasks. Each employee has different skills, and each task requires specific skills. The manager wants to minimize the total time it takes to complete all the tasks. The skills and the time required for each task are given in the table below:

The assignment problem is to determine which employee should be assigned to which task to minimize the total time required. To solve this problem, we can use the Hungarian method, which we discussed in the previous blog.

Using the Hungarian method, we first subtract the smallest entry in each row from all the entries of the row:

Next, we subtract the smallest entry in each column from all the entries of the column:

We draw the minimum number of lines to cover all the zeros in the matrix, which in this case is three:

Since the number of lines is equal to the number of rows, we have an optimal solution. The assignments can be made by selecting the rows and columns with a single zero in the final matrix. In this case, the optimal assignments are:

• Emp 1 to Task 3
• Emp 2 to Task 2
• Emp 3 to Task 1

This assignment results in a total time of 9 units.

I hope this example helps you better understand the assignment problem and how to solve it using the Hungarian method.

Solving the assignment problem may seem daunting, but with the right approach, it can be a straightforward process. By following the steps outlined in this guide, you can confidently tackle any assignment problem that comes your way.

How useful was this post?

Click on a star to rate it!

Average rating 0 / 5. Vote count: 0

No votes so far! Be the first to rate this post.

We are sorry that this post was not useful for you! 😔

Let us improve this post!

Tell us how we can improve this post?

Operations Research

1 Operations Research-An Overview

• History of O.R.
• Approach, Techniques and Tools
• Phases and Processes of O.R. Study
• Typical Applications of O.R
• Limitations of Operations Research
• Models in Operations Research
• O.R. in real world

2 Linear Programming: Formulation and Graphical Method

• General formulation of Linear Programming Problem
• Optimisation Models
• Basics of Graphic Method
• Important steps to draw graph
• Multiple, Unbounded Solution and Infeasible Problems
• Solving Linear Programming Graphically Using Computer
• Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

• Principle of Simplex Method
• Computational aspect of Simplex Method
• Simplex Method with several Decision Variables
• Two Phase and M-method
• Multiple Solution, Unbounded Solution and Infeasible Problem
• Sensitivity Analysis
• Dual Linear Programming Problem

4 Transportation Problem

• Basic Feasible Solution of a Transportation Problem
• Modified Distribution Method
• Stepping Stone Method
• Unbalanced Transportation Problem
• Degenerate Transportation Problem
• Transhipment Problem
• Maximisation in a Transportation Problem

5 Assignment Problem

• Solution of the Assignment Problem
• Unbalanced Assignment Problem
• Problem with some Infeasible Assignments
• Maximisation in an Assignment Problem
• Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

• Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

• Concepts of goal programming
• Goal programming model formulation
• Graphical method of goal programming
• The simplex method of goal programming
• Using Excel Solver to Solve Goal Programming Models
• Application areas of goal programming

8 Integer Programming

• Some Integer Programming Formulation Techniques
• Binary Representation of General Integer Variables
• Unimodularity
• Cutting Plane Method
• Branch and Bound Method
• Solver Solution

9 Dynamic Programming

• Dynamic Programming Methodology: An Example
• Definitions and Notations
• Dynamic Programming Applications

10 Non-Linear Programming

• Solution of a Non-linear Programming Problem
• Convex and Concave Functions
• Kuhn-Tucker Conditions for Constrained Optimisation
• Quadratic Programming
• Separable Programming
• NLP Models with Solver

11 Introduction to game theory and its Applications

• Important terms in Game Theory
• Saddle points
• Mixed strategies: Games without saddle points
• 2 x n games
• Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

• Reasons for using simulation
• Monte Carlo simulation
• Limitations of simulation
• Steps in the simulation process
• Some practical applications of simulation
• Two typical examples of hand-computed simulation
• Computer simulation

13 Queueing Models

• Characteristics of a queueing model
• Notations and Symbols
• Statistical methods in queueing
• The M/M/I System
• The M/M/C System
• The M/Ek/I System
• Decision problems in queueing

Algorithmic Optimization Techniques for Operations Research Problems

• Conference paper
• First Online: 24 February 2024
• Cite this conference paper

• Carla Silva 11 ,
• Ricardo Ribeiro   ORCID: orcid.org/0000-0003-2983-9080 12 &
• Pedro Gomes 13  

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 935))

Included in the following conference series:

• Proceedings of the Computational Methods in Systems and Software

94 Accesses

This paper provides an overview of the key concepts and approaches discussed in the field of Algorithmic Optimization Techniques. Operation re-search plays a role in addressing complex decision-making challenges across industries. This paper explores a range of algorithmic methods and optimization strategies employed to solve real-world problems efficiently and effectively.

This paper outlines the core themes covered in our research, including the classification of optimization problems, the utilization of mathematical models, and the development of algorithmic solutions. It highlights the importance of algorithm selection and design in achieving optimal solutions for diverse operations research problems.

Furthermore, this underscores the relevance of this research area enhancing decision-making processes, resource allocation, and overall efficiency in industries such as transportation, supply chain management, finance, and healthcare. The paper aims to provide readers with insights into cutting-edge algorithmic techniques, their applications, and their potential impact on addressing complex optimization challenges in operations research.

Algorithmic Optimization Techniques for Operations Research Problems serves as theoretical board for researchers, practitioners, and students seeking to understand and apply algorithmic optimization methods to tackle a wide range of operations research problems and make informed decisions in various domains.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

• Available as PDF
• Read on any device
• Instant download
• Own it forever
• Available as EPUB and PDF
• Compact, lightweight edition
• Dispatched in 3 to 5 business days
• Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications. Prentice Hall, Upper Saddle River (1993)

Google Scholar  

Bektas, T.: The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega 34 (3), 209–219 (2006)

Article   Google Scholar  

Brandeau, M.L., Sainfort, F., Pierskalla, W.P.: Operations Research and Health Care: A Handbook of Methods and Applications. Kluwer Academic Publishers, Dordrecht (2004)

Book   Google Scholar  

Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1963)

Hillier, F.S., Lieberman, G.J.: Introduction to Operations Research. McGraw-Hill, New York (2014)

Jain, A., Meeran, S.: Multi-objective optimization of supply chain networks. Comput. Chem. Eng. 27 (8–9), 1155–1174 (2003)

Nocedal, J., Wright, S.J.: Numerical Optimization. Springer, Cham (2006)

Ozcan-Top, O., McCarthy, T.: A review of optimization models for patient admission scheduling in hospitals. Health Care Manag. Sci. 20 (2), 139–162 (2017)

Papadimitriou, C.H., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Dover Publications, New York (1998)

Salhi, S.: Heuristic Algorithms for the Vehicle Routing Problem. Wiley, Hoboken (2000)

Simchi-Levi, D., Kaminsky, P., Simchi-Levi, E.: Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies. McGraw-Hill, New York (2019)

Toth, P., Vigo, D.: The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia (2002)

Acknoff, R.L.: The future of operational research is past. J. Oper. Res. Soc. 30 (2), 93–104 (1979)

Bakker, H., Fabian, D., Stefan, N.: A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice. Omega 96 , 102080 (2020)

Bertsimas, D., Dunn, J.: Optimal classification trees. Mach. Learn. 106 , 1039–1082 (2017)

Article   MathSciNet   Google Scholar  

Carrizosa, E.: Enhancing interpretability in factor analysis by means of mathematical optimization. Multivar. Behav. Res. 55 (5), 748–762 (2020)

Cazals, C., Florens, J., Simar, L.: Nonparametric frontier estimation: a robust approach. J. Econometr. 106 (1), 1–25 (2002)

Jordan, M.I., Mitchell, T.M.: Machine learning: trends, perspectives, and prospects. Science 349 (6245), 255–260 (2015)

Kumar, A.M., Satyanarayana, S., Wilson, N., Zachariah, R., Harries, A.D.: Operational research capacity building in Asia: innovations, successes and challenges of a training course. Publ. Health Action 3 (2), 186-8 (2013). https://doi.org/10.5588/pha.13.0008 . PMID: 26393025; PMCID: PMC4463115

Pu, G., Wang, Y.: Survey of undergraduate or courses from IE programme: content, coverage, and gaps. J. Oper. Res. Soc., 1–20 (2023)

Vilalta-Perdomo, E., Hingley, M.: Beyond links and chains in food supply: a community OR perspective. J. Oper. Res. Soc. 69 (4), 580–588 (2018)

Koskela, L.: Why is management research irrelevant? Constr. Manag. Econ. 35 (1–2), 4–23 (2017)

O’Brien, F.A.: On the roles of OR/MS practitioners in supporting strategy. J. Oper. Res. Soc. 66 (2), 202–218 (2015)

Ackoff, R.L.: Resurrecting the future of operational research. J. Oper. Res. Soc. 30 , 189–199 (1979)

EPSRC. Review of the Research Status of Operational Research in the UK. Engineering and Physical Sciences Research Council, Swindon (2004)

Rosenhead, J.: Reflections on fifty years of operational research. J. Oper. Res. Soc. 60 (sup1), S5–S15 (2009). https://doi.org/10.1057/jors.2009.13

Kunc, M.: System Dynamics: Soft and Hard Operational Research. Springer, Cham (2017)

Download references

Author information

Authors and affiliations.

Atlântica University, UNINOVA, Lisbon, Portugal

Carla Silva

Atlântica University, CESNOVA, Minho, Portugal

Ricardo Ribeiro

Atlântica University, Barcarena, Portugal

Pedro Gomes

You can also search for this author in PubMed   Google Scholar

Corresponding author

Correspondence to Carla Silva .

Editor information

Editors and affiliations.

Faculty of Applied Informatics, Tomas Bata University in Zlin, Zlin, Czech Republic

Radek Silhavy

Petr Silhavy

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Cite this paper.

Silva, C., Ribeiro, R., Gomes, P. (2024). Algorithmic Optimization Techniques for Operations Research Problems. In: Silhavy, R., Silhavy, P. (eds) Data Analytics in System Engineering. CoMeSySo 2023. Lecture Notes in Networks and Systems, vol 935. Springer, Cham. https://doi.org/10.1007/978-3-031-54820-8_26

Download citation

DOI : https://doi.org/10.1007/978-3-031-54820-8_26

Published : 24 February 2024

Publisher Name : Springer, Cham

Print ISBN : 978-3-031-54819-2

Online ISBN : 978-3-031-54820-8

eBook Packages : Intelligent Technologies and Robotics Intelligent Technologies and Robotics (R0)

Share this paper

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

• Publish with us

Policies and ethics

• Find a journal
• Track your research

Search Icon

Events See all →

At-home anthro live.

1:00 p.m. - 1:45 p.m.

Alumni Weekend 2024

Various locations

268th Commencement

Franklin Field

Wawa Welcome America Day

10:00 a.m. - 5:00 p.m.

Penn Museum, 3260 South St.

Arts, Humanities, & Social Sciences

University-led research project seeks to streamline air travel

Megan ryerson of the weitzman school of design is part of a collaborative nasa-funded research team taming the turbulence of airport delays..

Long lines at the check-in counters, frustrated passengers stranded at airports, and the chaotic cancellation of flights due to unexpected storms or technical outages are becoming increasingly commonplace as more and more people rely on air travel, placing significant burden on decades-old infrastructure and protocols.

Responding to these growing challenges, Megan Ryerson , UPS Chair of Transportation at the University of Pennsylvania’s Weitzman School of Design and professor of city and regional planning and electrical and systems engineering at the School of Engineering and Applied Science , is part of a transformative research initiative aimed at bolstering the resilience of air travel. Funded by NASA, this project, led by a team of researchers and industry practitioners, will explore how the National Airspace System can be more adaptive to major storms, facility outages, and other technical issues that disrupt airline flight.

The project focuses on three critical thrusts aimed at transforming the National Airspace System: scenario generation; decision-making optimization; and validation, evaluation, and translation.

Scenario generation involves creating realistic simulations of potential issues such as weather disruptions and traffic congestions, allowing for proactive planning and robust contingency strategies.

The decision-making optimization portion uses advanced predictive models and operational research to provide recommendations for air traffic managers, ensuring that responses to any given scenario are effective and efficient.

And finally, the validation, evaluation, and translation focus ensures the practical application of research outcomes. It involves testing the proposed solutions in simulated environments and real-world settings to evaluate their impact and effectiveness, followed by formulating guidelines that can be implemented by stakeholders such as airport authorities, port authorities, the Federal Aviation Administration (FAA), and airlines.

The project, slated to begin in August, ironically came about during a discussion spurred by a major delay.

Turbulence at the TRB

Last year, on a chilly early January morning in Washington, D.C., Ryerson was attending the annual Transportation Research Board (TRB) conference.

Attendance ranges well into the thousands, Ryerson says, and it is a great way to connect and learn about what is going on in the field. “It’s the most special conference because it's a real motley crew of who’s who in transportation; there are a lot of Department of Transportation folks, a lot of practitioners, students, and your most seasoned professors,” she says.

As the conference was winding down, “the Federal Aviation Administration experienced a significant outage in their Notice to Air Missions system (NOTAM), a critical piece of infrastructure that communicates necessary flight safety information to pilots," Ryerson says, “and, as you could imagine, passengers and airports were in disarray and flights were grounded across the nation.”

The following morning, amid the unfolding chaos, Ryerson had planned a breakfast with Dave Lovell, a professor at the University of Maryland and her longtime collaborator in air transportation optimization. As they headed to their meeting, “my phone buzzed relentlessly with updates and messages from my colleagues trapped at airports, texting me in disbelief at the extent of this disruption.”

Sitting down for breakfast at a café near the conference venue, the atmosphere was charged with a palpable sense of urgency, Ryerson says. “The catch-up session between me and Dave quickly turned into a NOTAM deep dive,” she says, “and, with our expertise in air transportation, we saw this event not as an isolated incident but as a symptom of the broader vulnerabilities within the air transportation system.”

They discussed how such disruptions were becoming more frequent and severe, exacerbated by factors like climate change and technological failures, and the conversation turned into a catalyst as the two looked into a way to bolster the resilience of air transportation. They aimed to develop strategies that could mitigate the effects of such disruptions and decided to formalize their discussions into a white paper focusing on resilience strategies and they planned to assemble a “dream team.”

This team would later include Max Li, a former student of Ryerson’s from Penn who is now an assistant professor of aerospace engineering at the University of Michigan; Patty Clark, as the former chief aviation strategic officer at the Port Authority of New York and New Jersey, with extensive experience monitoring and solving delay problems at major airports in the New York area; and Mark Hansen, a professor of civil engineering at the University of California, Berkeley, who had been Ryerson's Ph.D. advisor.

With the groundwork laid, Ryerson and her colleagues began reaching out to other potential collaborators and community colleges, involving them in crafting a full proposal to submit to NASA.

Expanded operations

By mid-2023, Ryerson and the team were ready to submit a comprehensive proposal. They targeted a specific NASA call for projects under the University Leadership Initiative and saw this as a unique opportunity to highlight the work of community colleges by including several neighboring institutions in their proposal.

“Education, outreach, and workforce development are a huge component of this project,” says Li, who will be serving as a faculty co-director in public outreach and supporting initiatives for spreading awareness of opportunities to learn more about the aerospace industry. “We’re here to highlight the broader roles that support the people we see when we hop on planes. From aircraft mechanics and engineers to airline and airport management there are programs from our partnered institutions that will help the next generation’s workforce join the bigger ecosystem here.”

Ryerson says that their work towards bolstering resilience within air transportation contributes to equity in mobility. “For many, paying that airfare is a big expense,” she says, we want to ensure “that, if the flight is cancelled because things happen, there are provisions in place to get you to your destination in a way that won’t negatively impact you or your finances.”

The nuts and bolts

Ryerson explains that the provisions she and her team seek to tie in some existing frameworks airlines use to remedy such problems, such as inter-airline agreements. “These are essentially deals that airlines may make with each other when they have to deal with stranded passenger during a disruption,” she says. “One airline will buy tickets from a competitor airline to accommodate passengers to make sure they can get stranded, disrupted passengers where they need to be.”

There are nuances, though, because companies want to make a profit, she says. “So strange things start to happen in this space. Like airline ‘X’ severing an inter-airline agreement with ‘Y,’ not selling to Y during an outage because X comes out looking a whole lot better if Y fails to deliver during a bad period.”

Ryerson also cites how airlines have years-long leases on gates at airports and that one airline may decide to block access to a gate from a competitor’s plane that needs to use it, which means “if your plane has to land at a gate that’s not permitted for use, and that’s the only one that’s open, you may just sit on the tarmac until a common-use gate opens up. Since there aren’t many common-use gates at most airports, that could be a long wait.”

Ryerson emphasizes the importance of predictive analytics and simulation-based preparedness in managing these inter-airline dynamics more effectively, and the team is taking the lessons learned to generate the next set of protocols.

Li's contributions to the proposal sheds light on the use of machine learning models to forecast air traffic scenarios and develop contingencies for each of the major stakeholders.

“For situation A, we’re going to have plan 1, plan 2, plan 3, and so on, and we’re going to make sure that these contingencies are tailored to whoever we’re talking to. For airlines, we adapt one set of models because their objectives are different than even another competitor airline. You could have different competing objectives and neither of these airlines’ objectives are necessarily aligned with that of the airport, which may not be aligned with that of the FAA. So, this is what makes the problem tricky because there are multiple stakeholders with multiple objectives, but that's what also makes it exciting from a mathematical perspective,” Li says.

“But you can make all the models you want and try predictions till you turn blue, but that means close to nothing if you don’t have a keen understanding of how situations on the ground tend to pan out, which is where Patty and her decades of experience at the airport have and continue to provide valuable insights,” Li says.

Connecting more than flights

Li and Ryerson note how Clark has helped them broaden their research beyond wheels-up to wheels-down to account for variables that often go unseen in the literature.

“Patty Clark is a brilliant leader in air transportation. Since the early days of my career, she has been teaching me about how the air transportation system truly runs and introducing all of us to parties involved from the Port Authority to get their perspectives. Patty is completely focused on passenger mobility and passenger customer service in air transportation,” Ryerson says.

“The Port Authority always took the position to make sure passengers are taken care of before and after they land, so in working with Mark, Megan, and more recently, Max, I had shared as much valuable information about the considerations staff make when things don’t go as planned,” Clark says. “If a plane is delayed, we need to assess the availability of services in and around the airport like concessions, taxis, rental cars, trains; we need to make sure there are personnel who can handle the cargo, unexpected baggage, or passengers with special needs, and so these are all considerations that may cascade if they’re not accounted for.”

Clark says she also works to keep the focus on the broader goals of air travel, citing President Harry S. Truman’s address at the grand opening of Idlewild Airport, now known as John F. Kennedy International Airport, in which he emphasized the importance of air travel in promoting international understanding and cooperation.

“He spoke about air travel not just as a means of transportation but as a gateway to peace and mutual respect among nations,” Clark says. “This vision of air travel as a bridge between cultures and communities is something that resonates deeply with our team's objectives.”

Clark explains that this historical perspective provides a framework for the team’s efforts today in improving the resilience and efficiency of air travel. “It’s not just about getting passengers from point A to point B. It’s about ensuring that air travel remains a reliable and accessible service that fosters connectivity and understanding across the globe,” she says.

Class of 2025 relishes time together at Hey Day

Picturing artistic pursuits

Hundreds of undergraduates take classes in the fine arts each semester, among them painting and drawing, ceramics and sculpture, printmaking and animation, photography and videography. The courses, through the School of Arts & Sciences and the Stuart Weitzman School of Design, give students the opportunity to immerse themselves in an art form in a collaborative way.

Campus & Community

Penn celebrates operation and benefits of largest solar power project in Pennsylvania

Solar production has begun at the Great Cove I and II facilities in central Pennsylvania, the equivalent of powering 70% of the electricity demand from Penn’s academic campus and health system in the Philadelphia area.

Education, Business, & Law

Investing in future teachers and educational leaders

The Empowerment Through Education Scholarship Program at Penn’s Graduate School of Education is helping to prepare and retain teachers and educational leaders.

‘The Illuminated Body’ fuses color, light, and sound

A new Arthur Ross Gallery exhibition of work by artist Barbara Earl Thomas features cut-paper portraits reminiscent of stained glass and an immersive installation constructed with intricately cut material lit from behind.