Multiskilled workforce staffing and scheduling: A logic-based Benders’ decomposition approach

We study the staffing and scheduling problem of a multiskilled workforce with uncertain demand. We formulate the problem as a two-stage stochastic integer program. The first stage considers strategic decisions, including recruiting permanent staff from an available pool and training them with additional skills, and the second stage focuses on operational decisions, involving the allocation of the multiskilled workforce and the hiring of temporary staff to accommodate uncertain demand. To effectively solve problems of practical sizes, we develop a novel solution algorithm based on the logic-based Benders’ decomposition (LBBD) approach, incorporating a customized analytical cut. We validate our approach through a case study using the data from a prefabrication company, demonstrating the significant cost savings achieved through workforce multiskilling. Our experimental results show that the proposed method is substantially more efficient than the latest Gurobi solver, up to 133 times faster and on average 29 times faster than directly solving the monolithic deterministic equivalent problem (MDEP).