Progress in solving large scale multi-depot multi-vehicle-type bus scheduling problems with integer programming

This paper discusses solution methods of multi-depot, multi-vehicle-type bus scheduling problems (MDVSP), involving multiple depots for vehicles and different vehicle types for timetabled trips. All models are from real-life applications. Key elements of the application are a mixed-integer model based on time-space-based networks for MDVSP modeling and a customized version of the mathematical optimization system MOPS to solve the very large mixed integer optimization models. The modeling approach was already described in several other publications. This paper focuses on the solution methods critical to solve the very large integer optimization models. We discuss aspects to solve the initial LP and the selection of the starting heuristic. Real life applications with over one million integer variables and about 160000 constraints were solved by the optimizer MOPS. A key role plays also the architecture of new Windows workstations with Intel 64 bit processors. We present numerical results on some large scale models and a brief comparison to another state-of-the-art mathematical programming system. The presented research results have been developed in cooperation with the Decision Support & OR Lab of the university Paderborn which was responsible for the development of the MDVSP-model and the application software.