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

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 having a linear programming (LP) relaxation equivalent to that of Dantzig 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, multi-activity cases, which cannot be modeled by existing implicit formulations, can easily be handled with grammars.