Branch-and-Price Based Heuristic Algorithm for Fuzzy Multi-Depot Bus Scheduling Problem

This paper deals with fuzzy multi-depot bus scheduling (FMDBS) problem in which the objective function and constraints are defined with fuzzy attributes. Credibility relation is used to formulate the problem as an integer multicommodity flow problem. A novel combination of branch-and-price and heuristic algorithms, is proposed to efficiently solve FMDBS problem. In the proposed algorithm, the heuristic algorithm is applied to generate initial columns for the column generation method. Also, a heuristic algorithm is used to improve the generated solutions in each node of the branch-and-price tree. Two sets of benchmark examples are applied to demonstrate the efficiency of the proposed algorithm for large-scale instances. Also, the algorithm is applied to solve the classical multi-depot bus scheduling problem. The results show that the proposed algorithm decreases integrality gap and computational time in comparison with the state-of-the-art algorithms and normal branch-and-price algorithm. Finally, as a case study, the bus schedules in Tehran BRT network are generated.