Advanced OR and AI Methods in Transportation BRANCH-AND-PRICE FOR INTEGRATED MULTI-DEPOT VEHICLE AND CREW SCHEDULING PROBLEM

We propose a branch-and-price algorithm to solve the integrated multidepot vehicle and crew scheduling problem. An integer mathematical formulation that combines a multicommodity network flow model with a set partionning model is presented. We solve the corresponding linear relaxation using a column generation scheme. Two branching strategies are tested over benchmark instances available in the Internet. Computational results show the effectiveness of our approach. 1. The Integrated Vehicle and Crew Scheduling Problem The vehicle and the crew scheduling problems are important combinatorial optimization problems that arise in the planning process of mass transit companies. Usually, vehicles are scheduled before the crews. During the vehicle scheduling process one has to optimally link timetabled trips producing vehicle blocks, so that each vehicle block forms a feasible schedule for a vehicle. If vehicles are located at different depots, one has to simultaneously construct the vehicle blocks and assign them to the depots. Then, the problem is NP-Hard. On the crew scheduling problem one has to ensure that a set of crews covers the set of vehicle blocks at minimum cost. Each vehicle block is split into pieces of work, sequences of timetabled trips and deadhead trips, where a change of driver is not allowed. A crew duty is a combination of pieces of work that respects several constraints such as maximum and minimum spread, maximum working time without a break, break duration and a maximum number of changeovers. The vehicle blocks characteristics influence the resulting crew duties and the crew duty set may lead to changes on the original vehicle blocks. 1 Universidade Técnica de Lisboa, Instituto Superior de Agronomia, Centro de Investigação Operacional, Tapada da Ajuda,1349-017 Lisboa, Portugal, [email protected] 2 Universidade de Lisboa, Faculdade de Ciências, DEIO, Centro de Investigação Operacional, Bloco C6, piso 4, Cidade Universitária, 1749-016 Lisboa, Portugal, [email protected] 3 Universidade de Lisboa, Faculdade de Ciências, DI, Centro de Investigação Operacional, Bloco C6, piso 3, Cidade Universitária, 1749-016 Lisboa, Portugal, [email protected]