Staff scheduling is a well-known problem in operations research and finds its application at hospitals, airports, supermarkets, and many others. Its goal is to assign shifts to staff members such that a certain objective function, e.g. revenue, is maximized. Meanwhile, various constraints of the staff members and the organization need to be satisfied. Typically in staff scheduling problems, there are hard constraints on the minimum number of employees that should be available at specific points of time. Often multiple hard constraints guaranteeing the availability of specific number of employees with different roles need to be considered. Staff scheduling for demand-responsive services, such as, e.g., ride-pooling and ride-hailing services, differs in a key way from this: There are often no hard constraints on the minimum number of employees needed at fixed points in time. Rather, the number of employees working at different points in time should vary according to the demand at those points in time. Having too few employees at a point in time results in lost revenue, while having too many employees at a point in time results in not having enough employees at other points in time, since the total personnel-hours are limited. The objective is to maximize the total reward generated over a planning horizon, given a monotonic relationship between the number of shifts active at a point in time and the instantaneous reward generated at that point in time. This key difference makes it difficult to use existing staff scheduling algorithms for planning shifts in demand-responsive services. In this article, we present a novel approach for modelling and solving staff scheduling problems for demand-responsive services that optimizes for the relevant reward function.

翻译：员工排班是运筹学领域的经典问题，广泛应用于医院、机场、超市等场景。其目标是为员工分配班次，使得特定目标函数（如收益）最大化，同时需满足员工与组织的各类约束条件。在传统员工排班问题中，通常存在硬性约束，要求特定时间点必须保持最低员工数量，且常需同时满足不同角色员工数量的多重硬性约束。然而，按需服务（如拼车、网约车服务）的员工排班具有本质差异：此类场景通常不存在固定时间点最低员工数量的硬性约束，而需要根据各时间点的实际需求动态调整员工数量。若某时间点员工过少将导致收益损失，员工过多则会因总工时有限而影响其他时段的人员配置。其目标是在规划期内最大化总收益，前提是某时刻活跃班次数量与该时刻即时收益之间存在单调关联。这一关键差异使得传统排班算法难以直接应用于按需服务的班次规划。本文提出一种新型建模与求解方法，专门针对按需服务的员工排班问题，以优化相关收益函数。