Fair Stochastic Vehicle Routing with Partial Deliveries

This paper explores the fair stochastic vehicle routing problem with partial deliveries (FSVRP-PD), a variant of the traditional vehicle routing problem with uncertain customer demands. Unlike conventional approaches that mandate full customer demand satisfaction, we relax this requirement to accommodate several real-world applications, such as humanitarian logistics and food rescue operations, where total demand often exceeds available resources. Our proposed solution approach promotes fair and equitable distribution of resources across all beneficiaries by requiring that the expected fill rate for each customer meets a predefined threshold. A solution to the FSVRP-PD constitutes a set of routes with a minimal total routing cost, where the expected minimum fill rates are met for every customer. Finding such a solution requires solving two interdependent subproblems: route planning and sequential resource allocation. To this extent, we develop an exact branch-price-and-cut algorithm capable of solving instances with up to 75 customers. Resource allocation follows Rawlsian fairness criteria that maximize the minimum service level across all customers in a route. To enhance the performance of the algorithms, particularly in pricing problems, we propose several problem-specific bounding techniques. Through numerical experiments, we demonstrate that our approach outperforms traditional routing and resource allocation policies by yielding superior cost and service equity outcomes. Funding: This work was funded by the Dutch Research Council (NWO) DAta-dRiven E-Commerce Order FULfillment (DAREFUL) Project [Grant 629.002.211]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2024.0556 .