This paper addresses a real-life personnel scheduling problem in the context of Covid-19 pandemic, arising in a large Italian pharmaceutical distribution warehouse. In this case study, the challenge is to determine a schedule that attempts to meet the contractual working time of the employees, considering the fact that they must be divided into mutually exclusive groups to reduce the risk of contagion. To solve the problem, we propose a mixed integer linear programming formulation (MILP). The solution obtained indicates that optimal schedule attained by our model is better than the one generated by the company. In addition, we performed tests on random instances of larger size to evaluate the scalability of the formulation. In most cases, the results found using an open-source MILP solver suggest that high quality solutions can be achieved within an acceptable CPU time. We also project that our findings can be of general interest for other personnel scheduling problems, especially during emergency scenarios such as those related to Covid-19 pandemic.

本文解决了在 Covid-19 大流行背景下的现实人员调度问题，该问题出现在意大利一家大型药品配送仓库。在这个案例研究中，挑战是确定一个试图满足员工合同工作时间的时间表，考虑到必须将他们分成相互排斥的组以降低传染风险的事实。为了解决这个问题，我们提出了一种混合整数线性规划公式（MILP）。获得的解决方案表明，我们的模型获得的最优进度比公司生成的要好。此外，我们对较大规模的随机实例进行了测试，以评估公式的可扩展性。在大多数情况下，使用开源 MILP 求解器发现的结果表明，可以在可接受的 CPU 时间内实现高质量的解决方案。我们还预计，我们的发现可能对其他人员调度问题具有普遍意义，尤其是在与 Covid-19 大流行相关的紧急情况下。