CREW-OPT: Subproblem Modeling in a Column Generation Approach to Urban Crew Scheduling

Abstract

CREW-OPT is a new software module in the HASTUS family of scheduling software. CREW-OPT produces optimal or near-optimal crew schedules for small problems (usually a single bus line or a small transit operation.) It is based on the resolution of a set covering formulation of the crew scheduling problem. Each row of the set covering problem corresponds to a task to perform and each column to a feasible workday. The objective is to construct a minimum cost set of workdays which covers all of the tasks. As the number of columns in this formulation is very large, we use a column generation approach to solve it. As is generally the case with column generation, the cornerstone of the approach is the design of an appropriate subproblem to generate proposed columns for the master problem. In this paper, we discuss the art of modeling such subproblems using a model of the constrained shortest path type.