Multiple Depot Vehicle Scheduling Research Articles

Multiple depot vehicle scheduling with controlled trip shifting

The multiple depot vehicle scheduling problem (MDVSP) has been widely studied in the context of public transit systems. Given a timetable of bus trips, it consists of finding a set of bus schedules that covers every trip exactly once while satisfying vehicle availability at each depot and minimizing the operating costs. This work considers a generalization of the MDVSP that allows slight modifications of the trip scheduled start times. By shifting some trips, one can indeed expect to cover all trips with fewer vehicles or less expensive deadheads (vehicle moves without passengers). However, reducing the operational costs in this way should not be too detrimental to the overall quality of the timetable and, therefore, the following criteria should be controlled: the number of shifted trips, the headways between the consecutive trips of a line, and the quality of some passenger connections. To solve this generalized problem, we develop a two-phase matheuristic: the first phase computes vehicle schedules with a column-generation heuristic; the second relies on a mixed integer program to find the best possible timetable considering the computed vehicle schedules. Penalties are introduced in the first phase to increase the chances of finding a better-quality timetable in the second phase. Computational tests on real-life datasets from a bus company show that the proposed matheuristic can solve the problem efficiently, yielding solutions with a significant reduction in the number of vehicles used compared to the solutions of the classical MDVSP and a limited alteration of the timetable.

New variable depth local search for multiple depot vehicle scheduling problems

The multiple depot vehicle scheduling problem (MDVSP) is a well-known and important NP-hard problem in transport scheduling. In this study, we first provide an original interpretation of the search...

Study on Optimization Model of Multiple Depot Vehicle Scheduling in Logistics Distribution of Expressway Service Area

Based on the unblocked reliability theory of the road network, combined with the characteristics of the logistics distribution of expressway service areas, the concept of network unblocked reliability on logistics distribution was put forward. Under the reliability analysis, the optimization model of multi objective, multi depot and open vehicle scheduling on logistics distribution of highway service areas was established, and the ant colony algorithm was designed. In the end an example was analyzed to validate the usability of the optimization model by comparing with saving mileage, which demonstrates the established optimization model of multiple depot vehicle scheduling is of a better practical value to guide the optimization decision making of logistics distribution network and to improve the reliability of logistics distribution of expressway service areas.

List-graph colouring for multiple depot vehicle scheduling

This article addresses a multiple depot vehicle scheduling problem (MDVSP) arising in public transportation. The general problem consists in assigning vehicles to trips while minimising the number of scheduled vehicles and the operational costs. The MDVSP considered here takes into account heterogeneous types of vehicles with complex relations among them. This special feature matches well situations encountered in practice, but makes the problem particularly difficult. We introduce a new formulation based on list-graph colouring, from which an iterative tabu search is developed for vehicle minimisation. The approach is assessed on seven real-world benchmarks and yields highly satisfactory results in terms of solution quality and computation time.

Stabilized column generation for highly degenerate multiple-depot vehicle scheduling problems

Column generation has proven to be efficient in solving the linear programming relaxation of large scale instances of the multiple-depot vehicle scheduling problem (MDVSP). However difficulties arise when the instances are highly degenerate. Recent research has been devoted to accelerate column generation while remaining within the linear programming framework. This paper presents an efficient approach to solve the linear relaxation of the MDVSP. It combines column generation, preprocessing variable fixing, and stabilization. The outcome shows the great potential of such an approach for degenerate instances.

Optimization Model for Large-Scale Bus Transit Scheduling Problems

A procedure is presented for solving real-world large-scale multiple depot vehicle scheduling (MDVS) problems considering the route time constraints (RTCs). The procedure is applied to some test problems and then to a real-world problem. The real-world problem is the transit bus scheduling problem of the mass transit administration (MTA) in Baltimore, Maryland. The RTCs are added to the MDVS problem to account for real-world operational restrictions such as fuel consumption. Formulation of the MDVS problem, the set of constraints for considering the time restriction, and a heuristic procedure for solving the MDVS problems with RTCs are discussed. Application of the proposed procedures in solving bus scheduling problems in large cities requires a reduction in size of those problems in terms of number of variables and constraints. Two techniques are proposed to decrease the size of the real-world problems. Combining these techniques results in a strategy to reduce the MTA problem size into a manageable and solvable size. The solutions to the reduced size problems are further improved by solving a series of single depot vehicle scheduling problems for each of the MTA depots. The final results from the proposed model are compared with the MTA’s January 1998 schedule. The comparison indicates that the proposed model improves on the MTA schedules in all aspects. The improvements are 7.90 percent in the number of vehicles, 4.66 percent in the operational time, and 5.77 percent in the total cost.

Vehicle Scheduling in Public Transit and Lagrangean Pricing

This paper investigates the solution of the linear programming (LP) relaxation of the multi-commodity flow formulation of the multiple-depot vehicle scheduling problems arising in public mass transit. We develop a column generation technique that makes it possible to solve the huge linear programs that come up there. The technique, which we call Lagrangean pricing, is based on two different Lagrangean relaxations. We describe in detail the basic ingredients of our approach and give computational results for large-scale test data (with up to 70 million variables) from three German public transportation companies. Because of these results, we propose Lagrangean pricing as one of the basic ingredients of an effective method to solve multiple-depot vehicle scheduling problems to proven optimality.