Location‐Routing with Conflicting Objectives: Coordinating eBeam Phytosanitary Treatment and Distribution of Mexican Import Commodities

We study a generalized location‐routing problem in which the key decisions are made by supply chain partners with conflicting objectives. The context of our problem is the irradiation by electron beam (eBeam) of fresh produce imported from Mexico to reduce the threat of insects and pests to the U.S. agriculture. Because too few irradiation facilities exist to serve the current demand, we focus on two parties to be coordinated: the eBeam Services Provider, who will choose the facilities’ locations and capacities, and the Distributor, who will determine routes for transporting fruits from Mexico to commercial hubs in the United States via these facilities. We demonstrate the value of cooperation and how that cooperation can be achieved and enforced for a supply chain that must coordinate the independent companies by the strategic decisions of facility location and capacity construction, as opposed to the more common coordination by capacity allocation or pricing. The parties’ interactions are modeled as a sequential game with perfect information. Specifically, we formulate the sequential and cooperative decision‐making problems as mixed‐integer programs, analyze the computational complexity of the problems, and conduct extensive computational experiments. Additionally, we detail three schemes by which the parties can engage in profitable and enforceable cooperation. These methods progressively increase each party’s commitment as trust is built and profits rise. Total cooperation increases overall profit by an average of 8.6%. Further, a stochastic program that uses sample average approximation is applied to demonstrate the results’ robustness to nature’s supply variations while maximizing the supply chain’s overall profit.