A comparison of different solution approaches to the vehicle scheduling problem in a practical case

Abstract

The Vehicle Scheduling Problem (VSP) consists in assigning a set of scheduled trips to a set of vehicles, satisfying a set of constraints and optimizing an objective function. A wide literature exists for the VSP, but usually not all the practical requirements of the real cases are taken into account. In the present paper a practical case is studied, and for it a traditional method is tailored and two innovative heuristics are developed. As the problem presents a multicriteria nature, each of the three algorithms adopts a different approach to multicriteria optimization. Scalarization of the different criteria is performed by the traditional algorithm. A lexicographic approach is followed by an algorithm based on logic programming. Finally, a Pareto optimization approach is implemented by a modified genetic algorithm. All the algorithms are tested on the real problem, and two of them produce interesting practical results. Scope and purpose This paper presents the practical experience with a real case of Vehicle Scheduling Problem (VSP). The VSP is a classical optimization problem which is faced in the operational planning of public transportation systems (see for instance Dantzig and Fulkerson. Naval Research Logistics Quarterly 1954;1:217–222). It consists in assigning a set of scheduled trips to a set of available vehicles, in such a way that each trip is associated to one vehicle and a cost function is minimized. For some versions of it, such as when all vehicles are equal and share the same depot, efficient algorithms exist (see for instance Bodin et al. Computers & Operations Research 1983;10:63–212, Carraresi and Gallo. European Journal of Operational Research 1984;16:139–151); nevertheless, real-life applications often turn out to be complex, due to the particular requirements which are present in practical situations, but are hard to be modeled. Practical requirements for this problem, usually not considered in the literature, include considering several criteria, producing different alternative solutions, and getting hints on how data could be modified to improve the effectiveness of the solutions. The paper analyzes the features of the real problem and discusses different algorithmic approaches for it. It has basically two purposes. The first is to analyze, formalize and comply with the experienced requirements of the practical problem. The second consists in assessing the applicability and performance of non-conventional heuristics and of a traditional exact method.