A bi-level multi-objective programming model for bus crew and vehicle scheduling

This paper focuses on the analysis of bus crew and vehicle scheduling under the management system commonly-seen in China. With considerations of management rules in practice and related regulations in China, this study proposes a bi-level multi-objective programming model for optimizing the crew and vehicle scheduling for the operation of public bus system. The developed model first estimates the lower bound of the global minimum number of drivers and buses needed in each week. The upper-level model minimizes the difference between the solution and the estimated lower bound and determine the number of vehicles needed; and then the lower-level model tries to minimize the number of drivers needed in each day. A branch and bound solution method has been developed to solve the proposed NP-Hard model, and has been programmed to achieve the computer aided crew and vehicle scheduling. A case study based on four different timetables demonstrated that the estimated lower bounds are with 13% of the global optimization that can ben achieved by the proposed approach. The implementation of the developed method can efficiently reduce the operation cost and support the automated intelligent scheduling for the Advanced Public Transportation System.