A decomposition-based heuristic for large employee scheduling problems with inter-department transfers

We consider a personalized employee scheduling problem with characteristics present in retail stores consisting of multiple departments. In the setting under study, each department generally covers its demand in employees over the planning horizon of a week by assigning shifts to its own staff. However, the employees can also be transferred to other departments under certain conditions for executing entire shifts or parts of shifts there. The transfer feature enables to improve the overall schedule quality considerably when compared to the nontransfer case. Given the complexity of the problem, we propose a three-phase decomposition-based heuristic. In the first phase, we consider each department separately and solve a simplified version of the mono-department scheduling problems. From the obtained solutions, we deduce inter-department shifts that could potentially reduce the overall cost. This is examined in the second phase by resolving the scheduling problem of the first phase where the deduced inter-department shifts are included. In this phase, however, we decompose the scheduling problem by time, looking at each day separately. From the obtained schedules, we then devise inter-department demand curves, which specify the number of transfers between departments over time. In the third phase, we decompose the initial scheduling problem into mono-department problems using these inter-department demand curves. Consequently, our approach makes it possible to solve mono-department optimization problems to get an overall schedule while still benefiting from the employee transfer feature. In all three phases, the scheduling problems are formulated as mixed-integer linear programs. We show through extensive computational experiments on instances with up to 25 departments and 1000 employees that the method provides high-quality solutions within reasonable computation times.