Data mining-driven shift enumeration for accelerating the solution of large-scale personnel scheduling problems

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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 to 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. Consequently, we propose to use a data mining technique, namely, the \(k\)-nearest neighbors algorithm, to expedite the solution process while upholding solution quality. In particular, we suggest using schedules of past solutions to reduce the problem size. Specifically, 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 effectively address the problem using a commercial solver within a reasonable timeframe while preserving solution quality. Significantly, our methodology offers decision-makers the flexibility to determine the extent to which they wish to scale down the problem. Our experiments, conducted on a total of 80 instances with up to 12 jobs and 190 employees, yield an average removal of 85.5% of decision variables. This resulted in a noteworthy average speedup factor of 15.5, with a marginal average cost increase of 1.2%.

, 19 pages

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