An efficient methodology for solving multi-period shift scheduling problems with shift transition preference optimization

This study proposes a novel mathematical program that relates the schedules of consecutive periods to ensure consistency over a multiperiod scheduling horizon and optimizes shift transition preferences. The initial quadratic program is represented as a linear-integer model by applying the appropriate transformations in the quadratic objective function. In addition to the proposed formulation, we further develop a simulated annealing-based metaheuristic and a hybrid approach to address larger instances within reasonable computational times. We also test the approaches on a real-life problem as well as on experimental scenarios reflecting different ergonomic conditions. The results indicate that the metaheuristic and the hybrid approaches are particularly more effective for large-scale problems, whereas the mathematical program remains well-suited for smaller instances. It is noted, for very large cases, that the simulated annealing-based approach delivers high-quality solutions quickly. The results also imply the potential of the proposed framework for use in real-life shift scheduling problems.