Generating multi depot vehicle scheduling problems with known optimal tours

Abstract

Validation of heuristics that aim to solve efficiently vehicle scheduling problems is usually done by generating random datasets and comparing one approach versus another. How far from the optimal solution are their results is usually not known, especially for larger workloads. The Multiple-Depot Vehicle Scheduling Problem (MDVSP) is a well-known and important optimization problem that aims to assign a set of trips to a fleet of vehicles provided by several depots in order to minimize the total cost of empty travel and waiting. Addressing the need to test different heuristics on various problem types, our paper introduces several generation algorithms that create random MDVSP instances, of any size, with known optimum. In order to evaluate the results, we have used both an exact MDVSP solver and a fast heuristic, analyzing the correctness and the runtime performance. Empirical testing indicates that these instances are still difficult to solve which means that they could provide a valuable tool for measuring the scalability of various MDVSP heuristics.