Multi-activity shift scheduling under uncertainty: The value of shift flexibility

In this paper, we consider a multi-activity shift scheduling problem under demand uncertainty, exploring various levels of flexibility in adapting aspects of the shift schedule (e.g., activity assignment, break assignment, selection of shift type and shift end time) to late-arriving demand information. To address the resulting complex two-stage stochastic combinatorial optimisation problems, we propose a novel two-stage stochastic mixed-integer programming formulation leveraging state-expanded networks and a clustering-based sequential sampling approach for efficiently solving large-scale problem instances. In computational experiments on stochastic problems derived from well-known multi-activity shift scheduling instances, we show that this method effectively solves instances with up to 10 activities and 100 demand scenarios, approaching near-optimality within an average time of less than one hour. From a managerial standpoint, our study provides insights into the structure of good first-stage scheduling decisions as well as into the impact of different flexibility levels on expected costs of the solutions, thereby offering valuable support for decisions such as adjusting employees’ salaries in exchange for increased shift flexibility.