Grammar-Based Integer Programing Models for Multi-Activity Shift Scheduling

Authors Marie-Claude Cote, Bernard Gendron, Louis-Martin Rousseau

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Marie-Claude Cote
Bernard Gendron
Louis-Martin Rousseau

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Marie-Claude Cote, Bernard Gendron, and Louis-Martin Rousseau. Grammar-Based Integer Programing Models for Multi-Activity Shift Scheduling. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


We present a new implicit formulation for shift scheduling problems, using context-free grammars to model regulation in the composition of shifts. From the grammar, we generate an integer programming (IP) model allowing the same set of shifts as Dantzig’s set covering model. When solved by a state-of-the- art IP solver on problems allowing a small number of shifts, our model, the set covering formulation and a typical implicit model from the literature yield comparable solving times. Moreover, on instances where many shifts are allowed, our model is superior and can encode a wider variety of constraints. Among others, multi-activity cases, which cannot be modeled by existing implicit formulations, can easily be captured with grammars.
  • Shift Scheduling
  • Implicit models
  • Integer Programming
  • Context-free grammars


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