Modeling for the equitable and effective distribution of donated food under capacity constraints

Abstract

Mathematical models are presented and analyzed to facilitate a food bank's equitable and effective distribution of donated food among a population at risk for hunger. Typically exceeding the donated supply, demand is proportional to the poverty population within the food bank's service area. The food bank seeks to ensure a perfectly equitable distribution of food; i.e., each county in the service area should receive a food allocation that is exactly proportional to the county's demand such that no county is at a disadvantage compared to any other county. This objective often conflicts with the goal of maximizing effectiveness by minimizing the amount of undistributed food. Deterministic network-flow models are developed to minimize the amount of undistributed food while maintaining a user-specified upper bound on the absolute deviation of each county from a perfectly equitable distribution. An extension of this model identifies optimal policies for the allocation of additional receiving capacity to counties in the service area. A numerical study using data from a large North Carolina food bank illustrates the uses of the models. A probabilistic sensitivity analysis reveals the effect on the models' optimal solutions arising from uncertainty in the receiving capacities of the counties in the service area.

Keywords:

• Food distribution
• equity
• fairness
• effectiveness
• food bank
• capacitated network flow problems
• resource allocation
• humanitarian logistics
• food supply chain
• food insecurity

Acknowledgements

We thank the FBCENC, specifically, Charlie Hale, Vice President of IT & Operations at FBCENC, and Earline E. Middleton, Vice President of Agency Services and Programs at FBCENC, for their help and support.

Funding

This research has been supported by the National Science Foundation with the grants CMMI-1000018 and CMMI-1000828. The opinions expressed in the article represent those of the authors and not necessarily those of the National Science Foundation.

Additional information

Notes on contributors

Irem Sengul Orgut

Irem Sengul Orgut received her Ph.D. in Industrial Engineering with a minor in Statistics in 2015 from the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. She now works at Lenovo as the Corporate Quality Statistics Project Manager where she uses Big Data and Analytics tools to improve customer engagement. Prior to starting her doctoral studies, she received her B.S. degrees in Industrial Engineering and Mechanical Engineering from Bogazici University, Istanbul, Turkey, in 2010. Her research interests include stochastic modeling of complex supply chains with multiple objectives and conflicting decision makers with application focus on long-term humanitarian issues and public health problems. She received various awards for her teaching and research. She served as the president of the INFORMS Student Chapter at NCSU and is a member of IIE and INFORMS. Her web address is https://iremsengul.wordpress.com/.

Julie Ivy

Julie Simmons Ivy is an Associate Professor and Fitts Faculty Fellow in Health Systems Engineering in the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. She received her B.S. and Ph.D. in Industrial and Operations Engineering from the University of Michigan. She also received her M.S. in Industrial and Systems from Georgia Tech. Her research interests are mathematical modeling of stochastic dynamic systems with emphasis on statistics and decision analysis as applied to health care, public health, and humanitarian logistics. She is a member of INFORMS, IIE, and the Health Systems Engineering Alliance (HSEA) Board of Directors.

Reha Uzsoy

Reha Uzsoy is Clifton A. Anderson Distinguished Professor in the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. He holds B.S. degrees in Industrial Engineering and Mathematics and an M.S. in Industrial Engineering from Bogazici University, Istanbul, Turkey. He received his Ph.D. in Industrial and Systems Engineering in 1990 from the University of Florida. His teaching and research interests are in production planning and supply chain management. Before coming to the United States he worked as a production engineer with Arcelik AS, a major appliance manufacturer in Istanbul, Turkey. He has also been a visiting researcher at Intel Corporation and IC Delco. He was named a Fellow of the Institute of Industrial Engineers in 2005 and Outstanding Young Industrial Engineer in Education in 1997 and has received awards for both undergraduate and graduate teaching.

James R. Wilson

James R. Wilson is a Professor in the Edward P. Fitts Department of Industrial and Systems Engineering at North Carolina State University. His current research interests are focused on probabilistic and statistical issues in the design and analysis of simulation experiments, with special emphasis on applications in health care and production. He is a member of ACM, ASA, and ASEE and he is a Fellow of IIE and INFORMS. His web address is www.ise.ncsu.edu/jwilson.