Vehicle routing problem considering equity of demand satisfaction

Planning of distribution processes has been represented by vehicle routing problems (VRP), where objective functions are commonly related to the cost of routes and delivery times involved in those processes. However, other objectives, such as equity of demand satisfaction, are of particular interest in social or non-profit distribution systems. This study addresses a VRP focused on an egalitarian distribution among all demand centroids considering a heterogeneous fleet. In particular, our goal is to maximize the minimum fraction of fulfilled demand to foster the equity of demand satisfaction while minimizing the delivery times as a secondary objective. We formulate our optimization problem as a mixed-integer linear program that is intractable by using a commercial solver for large instances. Therefore, we design three variants of the biased random-key genetic algorithm, and one of them can obtain near-optimal solutions for instances up to 120 demand points and 15 routes in less than one minute of computational time. Finally, we present an analysis of the trade-off between egalitarian demand satisfaction and total delivery time for a scenario based on an economically deprived region in Mexico.