Incorporating equity into the school bus scheduling problem

We consider the school bus scheduling problem (SBSP) which simultaneously determines school bell times and route schedules. Often, the goal of the SBSP is to minimize the number of buses required by a school district. We extend a time-indexed integer programming model to incorporate additional considerations related to equity and efficiency. We seek to equitably reduce the disutilities associated with changing school start times via a minimax model, then propose a lexicographic minimax approach to improve minimax solutions. We apply our models to randomized instances based on a moderately-sized public school district to show the impact of incorporating equity.