A Bounded Formulation for The School Bus Scheduling Problem

This paper proposes a new formulation for the school bus scheduling problem (SBSP) which optimizes starting times for schools and associated bus routes to minimize transportation cost. Specifically, the problem determines the minimum number of buses required to complete all bus routes under the constraint that routes for the same school must arrive within a set time window before that school starts. We present a new integer linear programming (ILP) formulation for this problem which is based on a time-indexed formulation. We develop a randomized rounding algorithm based on the linear relaxation of the ILP that yields near-optimal solutions for large-scale problem instances.