A Bounded Formulation for The School Bus Scheduling Problem

TL;DR

This paper introduces a new time-indexed ILP formulation for the school bus scheduling problem, optimizing start times and bus usage to reduce costs, and provides a randomized rounding algorithm for large instances.

Contribution

It presents a novel ILP formulation and a dependent randomized rounding algorithm for efficient, near-optimal school bus scheduling, including a robust problem extension.

Findings

The new ILP formulation improves solution quality.

The randomized rounding algorithm scales to large problem instances.

The methodology effectively handles robust scheduling scenarios.

Abstract

This paper proposes a new formulation for the school bus scheduling problem (SBSP) which optimizes school start times and bus operation times to minimize transportation cost. Our goal is to minimize the number of buses to serve all bus routes such that each route arrives in a time window before school starts. We present a new time-indexed integer linear programming (ILP) formulation for this problem. Based on a strengthened version of the linear relaxation of the ILP, we develop a dependent randomized rounding algorithm that yields near-optimal solutions for large-scale problem instances. We also generalize our methodologies to solve a robust version of the SBSP.