Exact solution of workload consistent vehicle routing problem with priority distribution and demand uncertainty

Abstract

This study attempts to solve a workload consistent vehicle routing problem with priority distribution and demand uncertainty. Workload consistency requires the difference in working time allocated to drivers each day within a planning horizon to be limited to a fixed range. Partial split delivery, multi-trips, and uncertain demand are also considered. To address both transportation costs and priority-based distribution concerns, hierarchical objectives are adopted with the primary objective of minimizing travel costs and the secondary objective of maximizing distribution rewards. An exact algorithm based on set-partitioning formulation and robust column-and-cut generation is proposed to solve the problem, where a lower bound and an upper bound are used to derive some feasible columns, and these candidate columns are used in solving the set-partitioning formulation to obtain the optimal solution. Simultaneous decisions on visit sequence and distribution amount under conditions of demand uncertainty exacerbate the difficulty of solving the pricing subproblem. Therefore, we design a robust labelling algorithm involving a robust feasible extension check and an optimal distribution pattern computation to address this difficulty. The upper bound is obtained by a clustering-routing-assignment heuristics. Numerical experiments indicate that the proposed exact method can effectively solve medium-and partially large-scale instances, and the results have good robustness.