Grammar-Based Integer Programming Models for Multiactivity Shift Scheduling

Authors:
Marie-Claude Côté;Bernard Gendron;Louis-Martin Rousseau
Affiliations:
CIRRELT and Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Montréal, Québec H3C 3A7, Canada;CIRRELT and Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Montréal, Québec H3C 3J7, Canada;CIRRELT and Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, Montréal, Québec H3C 3A7, Canada
Venue:
Management Science
Year:
2011

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Abstract

This paper presents a new implicit formulation for shift scheduling problems, using context-free grammars to model the rules for the composition of shifts. From the grammar, we generate an integer programming (IP) model having a linear programming relaxation equivalent to that of the classical set covering model. When solved by a state-of-the-art IP solver on problem instances with a small number of shifts, our model, the set covering formulation, and a typical implicit model from the literature yield comparable solution times. On instances with a large number of shifts, our formulation shows superior performance and can model a wider variety of constraints. In particular, multiactivity cases, which cannot be modeled by existing implicit formulations, can easily be handled with grammars. We present comparative experimental results on a large set of instances involving one work activity, as well as on problems dealing with up to 10 work activities. This paper was accepted by Dimitris Bertsimas, optimization.