Patrick Schittekat

A metaheuristic for the school bus routing problem with bus stop selection

Existing literature on routing of school buses has focused mainly on building intricate models that attempt to capture as many real-life constraints and objectives as possible. In contrast, the focus of this paper is on understanding the joint problem of bus route generation and bus stop selection – two important sub-problems – in its most basic form. To this end, this paper defines the school bus routing problem (SBRP) as a variant of the vehicle routing problem in which three simultaneous decisions have to be made: (1) determine the set of stops to visit, (2) determine for each student which stop (s)he should walk to, and (3) determine routes that lie along the chosen stops, so that the total traveled distance is minimized. An MIP model of this basic problem is developed.

A mathematical formulation for a school bus routing problem

The school bus routing problem discussed in this paper, is similar to the standard vehicle routing problem, but has several interesting additional features. In the standard VRP all stops to visit are given. In our school bus routing problem, we assume that a set of potential stops is given, as well as a set of students that can walk to one or more of these potential stops. The school buses used to pick up the students and transport them to their schools have a finite capacity. The goal of this routing problem is to select a subset of stops that would actually be visited by the buses, determine which stop each student should walk to and develop a set of tours that minimize the total distance travelled by all buses. We develop an integer programming formulation for this problem, as well as a problem instance generator. We then show how the problem can be solved using a commercial integer programming solver and discuss some of our results on small instances

OR Practice---Supporting 3PL Decisions in the Automotive Industry by Generating Diverse Solutions to a Large-Scale Location-Routing Problem

For the distribution of spare parts to car dealers, many automotive companies use a transport network of intermediate hubs or transport platforms, operated by a set of third-party logistics (3PL) partners. The optimization of this network, particularly the selection of 3PL providers and corresponding transport platforms, is a complex decision that needs to be supported by appropriate software tools. In this paper, we develop such a tool, implement it, and show its results on a real-life case study provided by Toyota. The tool is currently in active use at Toyota to study and improve the distribution of spare parts in Germany. Using a tabu search metaheuristic, the developed tool essentially solves a large location-routing problem, but has several innovative features to increase its usefulness. First, the tool generates a set of high-quality but structurally different solutions, rather than a single one. This increases Toyotas negotiating power, increases its ability to analyze its current transport network against possible alternatives, and allows it to quickly switch between different transport networks if unexpected events occur. Second, a commercial vehicle-routing solver is integrated into the tool, to allow for a far more realistic modeling of the vehicle-routing decision.

“Multiple Neighbourhood” Search in Commercial VRP Packages: Evolving Towards Self-Adaptive Methods

All commercial packages for vehicle routing that the authors are aware of use a (meta)heuristic search procedure with several different neighbourhood structures. This paper attempts to answer the question why this is the case. As we will show, “multiple neighbourhood” search (MNS) is able to overcome the myopic behaviour of using only a single neigbourhood and is therefore more powerful. Also, MNS can be considered to be a very adaptable metaheuristic, which makes it especially suitable for the practical problems encountered in real life. We also point out that there is a need for the MNS applications used in commercial packages to evolve towards more self-adaptive systems.

Statistical analysis of distance-based path relinking for the capacitated vehicle routing problem

In this paper we develop an intelligent path relinking procedure for the capacitated vehicle routing problem, based on the relocate distance. This procedure transforms an incumbent solution into a guiding solution in a minimal number of relocate moves. In each step of the path relinking procedure, one customer is removed from the solution and re-inserted in another position. The path relinking procedure is integrated in a grasp (greedy randomized adaptive search procedure) and vnd (variable neighborhood descent) framework and thoroughly tested. This analysis shows that the path relinking procedure is not able to improve the performance of a simple grasp+vnd metaheuristic, but some interesting conclusions can nonetheless be drawn. A second contribution of this paper is an analysis of the computational results based on sound statistical techniques. Such an analysis can be useful for the field of metaheuristics, where computational results are generally analyzed in an ad hoc way and often with dubious statistical validity.