Bus driver scheduling enhancement: a derandomizing approach for uncertain bus trip times

The bus driver scheduling problems aim to optimally deploy drivers to fulfil published timetables for bus services subject to drivers' contractual working rules. In this study, we first develop an integer linear programming model for a practical driver scheduling problem. We proceed to formulate another integer linear programming model for the driver scheduling enhancement to incorporate with uncertain bus travel times, which are addressed by an effective derandomizing approach. Moreover, the lower and upper bounds of the developed models are investigated by using the Lagrangian problems with which the solution quality can be evaluated. To assess the efficiency and applicability of the developed models, we conduct a case study based on historical operational data of the bus route #95 in Singapore. Finally, we perform a necessary sensitivity analysis of the bus fleet size and driver workload on the bus driver scheduling problems to identify some valuable managerial insights.