Operations Management of Food Recovery ProgramsPublic Deposited
Food recovery programs (FRPs) divert potential waste at grocery stores so that it can be distributed to people who do not have enough food. FRPs are administered by food banks, nonprofit organizations dedicated to the alleviation of hunger. The primary purpose of FRP is to collect donations. Eventually, the food is distributed to other nonprofit organizations (referred to as “agencies”) which in turn provide it to families and individuals. A few food banks include agencies on FRP routes, a practice that is becoming more common. This innovation presents opportunities and challenges: the presence of agencies allows the food bank to reduce the required vehicle capacity and more quickly distribute perishable food, but donations are random, so it is difficult to provide consistent service to the agencies. In this dissertation, we study three closely related models of FRP operations.The one-commodity pickup and delivery allocation problem (1-PDA) models allocation decisions for a given FRP route. The objective of the 1-PDA is to minimize the required vehicle capacity. We develop a simple three-step algorithm, the MILB algorithm, that obtains an optimal solution to the 1-PDA. We augment the 1-PDA with agency selection and node sequencing decisions to formulate the selective 1-PDTSP with stochastic supply as a mixed-integer linear program (MILP). It is possible to solve the problem with a MILP solver, but the solution time is prohibitive for many realistic instances. Therefore, we propose a heuristic procedure, the capacity reuse insertion heuristic (CRIH), based on inserting agencies into existing FRP routes. In a case study based on data provided by Northern Illinois Food Bank, we obtain insights regarding agency selection and node sequencing for FRP. We also demonstrate that CRIH provides near-optimal solutions. To model FRP operations at food banks where routing is inflexible and the food obtained from FRP is crucial to agency operations, we generalize the 1-PDA to model the one-commodity pickup and delivery allocation problem for agency-supporting FRP (the 1-PDA-as). The 1-PDA-as differs from the 1-PDA by including parameters that specify additional service requirements at donors and agencies. The objective of the 1-PDA-as is to maximize total donations collected for a given route. By applying several reformulations, we develop an optimal solution procedure for the 1-PDA-as that relies on solving a series of linear programs; however, this solution procedure cannot be applied to many realistic instances due to issues of numerical precision. Therefore, we propose a heuristic solution procedure based on the MILB algorithm. In a case study, we obtain insights about node parameters and node sequencing. We also demonstrate that the heuristic generates near-optimal solutions.