Partial Dominance in Branch-Price-and-Cut for the Basic Multicompartment Vehicle-Routing Problem

We consider the exact solution of the basic version of the multiple-compartment vehicle-routing problem, which consists of clustering customers into groups, routing a vehicle for each group, and packing the demand of each visited customer into one of the vehicle’s compartments. Compartments have a fixed size, and there are no incompatibilities between the transported items or between items and compartments. The objective is to minimize the total length of all vehicle routes such that all customers are visited. We study the shortest-path subproblem that arises when solving the problem with a branch-price-and-cut algorithm exactly. For this subproblem, we compare a standard dynamic-programming labeling approach with a new one that uses a partial dominance. The algorithm with standard labeling already struggles with relatively small instances, whereas the one with partial dominance can cope with much larger instances. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This research was supported by the Deutsche Forschungsgemeinschaft [Grant IR 122/10-1 of Project 418727865]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.1255 .