Motivated by a real-world application, we model and solve a complex staff scheduling problem. Tasks are to be assigned to workers for supervision. Multiple tasks can be covered in parallel by a single worker, with worker shifts being flexible within availabilities. Each worker has a different skill set, enabling them to cover different tasks. Tasks require assignment according to priority and skill requirements. The objective is to maximize the number of assigned tasks weighted by their priorities, while minimizing assignment penalties. We develop an adaptive large neighborhood search (ALNS) algorithm, relying on tailored destroy and repair operators. It is tested on benchmark instances derived from real-world data and compared to optimal results obtained by means of a commercial MIP-solver. Furthermore, we analyze the impact of considering three additional alternative objective functions. When applied to large-scale company data, the developed ALNS outperforms the previously applied solution approach.

翻译：受实际应用场景启发，本文对一类复杂的人员调度问题进行了建模与求解。任务需分配给工人进行监督，单个工人可并行处理多项任务，且工人的班次可依据可用时间灵活调整。每位工人拥有不同的技能组合，能够覆盖不同类型的任务。任务需根据优先级和技能要求进行分配。目标是在最大化按优先级加权的已分配任务数量的同时，最小化分配惩罚。我们开发了一种自适应大邻域搜索算法，该算法依赖于定制化的破坏与修复算子。算法基于实际数据生成的基准实例进行测试，并与通过商业整数线性规划求解器获得的最优结果进行对比。此外，我们分析了采用三种其他替代目标函数时的影响。将所提出的自适应大邻域搜索算法应用于大规模企业数据时，其性能优于此前采用的求解方案。