Modern manufacturing faces growing challenges from market volatility, resource uncertainty, and the need for quick adaptation. Reconfigurable Manufacturing Systems (RMSs) offer a flexible adaptable solution; however, scheduling becomes more complex when worker availability is uncertain. Workers in RMSs represent limited and mobile resources, whose uncertain availability can severely disrupt production efficiency. This paper investigates the non-identical parallel machine scheduling problem in an RMS under stochastic worker availability. To tackle this complex optimisation problem, a two-stage stochastic programming model is developed. In the first stage, job-to-machine assignments are determined as here-and-now decisions. The second stage involves optimising job sequencing, machine configurations, and worker assignments after the worker availability scenarios are revealed. To solve this problem, a Mixed-Integer Linear Programming (MILP) model and an L-shaped Decomposition (LD) method are developed to minimise the expected makespan. To enhance solution efficiency, a novel CP-LD is proposed, where the master problem uses MILP while subproblems employ Constraint Programming (CP). Computational results show that the proposed CP-LD method outperforms the MILP and LD methods in terms of solution quality and computational efficiency. The sensitivity analysis provides insights into the impact of various system parameters on the expected makespan performance, highlighting the critical importance of workforce management.
Bakhshi-Khaniki et al. (Sun,) studied this question.