Robust optimization model of schedule design for a fixed bus route

The time control point strategy is often adopted by bus operators in China and Singapore to provide more reliable transit service. It is thus important to design a schedule, in which bus drivers should devote their efforts to catch up a scheduled arrival time at a predetermined time control point on a bus route because passengers can definitely benefit from a reliable bus route schedule. This paper first proposes a novel reliable bus route schedule design problem by taking into account the bus travel time uncertainty and the bus drivers’ schedule recovery efforts. It proceeds to develop a robust optimization model for the proposed problem, which aims to minimize the sum of the expected value of the random schedule deviation and its variability multiplied by a weighting value. A Monte Carlo simulation based solution method is subsequently designed to solve the robust optimization model. Finally, a numerical example based on a real bus route in Suzhou city of China is carried out to demonstrate the strength of the robust optimization model. We find that the optimal scheduled travel time (or slack time) depends on bus drivers’ schedule recovery behavior and on decision makers’ scheduling philosophies.