Data Mining-Driven Shift Enumeration for Accelerating the Solution of Large-Scale Personnel Scheduling Problems

This study addresses large-scale personnel scheduling problems in the service industry by combining mathematical programming with data mining techniques to enhance efficiency. The studied problem aims at efficiently scheduling skilled employees over a one-week planning horizon, minimizing costs while meeting diverse job demands. In service industries, shift planning is intricately tied to customer presence, leading to a multitude of potential shifts and a difficult optimization problem that cannot be easily solved using a commercial mixed-integer programming solver. Nevertheless, these problems are categorized as recurrent problems, where distinct instances share common characteristics and solution structures that differ only in a few parameters over time. We propose to use a data mining technique, namely, the \(k\) -nearest neighbors algorithm, to expedite the solution process while upholding solution quality. We suggest using schedules of past solutions to reduce the problem size. Thus, for an upcoming instance, we identify similar historical instances and streamline the enumeration of shifts to align with the comparable historical instances’ schedules. This approach allows us to solve the problem using a commercial solver within a reasonable timeframe while preserving solution quality. Moreover, our methodology offers decision-makers the flexibility to determine the extent to which they wish to scale down the problem. Our experiments conducted on instances generated from real historical data with up to 12 jobs and 252 employees, yield an average removal of up to 85.5% of decision variables. This resulted in an average speedup factor of up to 15.5, with a marginal average cost increase of approximately 1.2%.