A fair multi-commodity two-echelon distribution problem

In the context of a short and local supply chain of fresh produce in the public sector, we introduce a fair multi-commodity two-echelon distribution problem. A decision maker has to decide on the planning of the first-echelon collection trips of commodities from suppliers to distribution centers equitably and on the second-echelon delivery routes of commodities from the centers to customers. In addition to the classic objective of minimizing the total transportation cost in vehicle routing problems, the goal is to make sure that all suppliers receive an equitable service with regard to their profits. This is done by introducing fairness measures into the problem as a set of constraints. We use two widely used inequality metrics from the literature and present a novel problem-specific equity measure as well. We model the problem as a mixed-integer program using an arc-route-based formulation and suggest a matheuristic to solve the problem. Through numerical experiments, we analyze the performance of our matheuristic on a series of generated instances and on the instances of a French fresh produce supply chain from the literature. We evaluate the efficacy of the three used fairness schemes with regard to a series of key performance metrics and investigate the strengths and weaknesses of the different fairness measures. Moreover, we study the trade-off between enforcing fairness and optimizing transportation costs to come up with insights for the managers of the supply chain.