Exact and matheuristic algorithms for robust lot-sizing and scheduling problems with uncertain capacity

Uncertain capacity, resulting from unforeseen events such as machinery breakdowns and operator errors, etc., poses significant risks to the production stability and efficiency. In this paper, we consider capacity uncertainty and develop production plans with robust capabilities to withstand risks. Specifically, this study extends the traditional lot-sizing and scheduling problem (LSP) to the robust LSP (R-LSP) by addressing a multi-period LSP in a flexible flow shop with uncertain machine capacity, which means that the available working time for each machine is uncertain and fluctuates within a certain range during each period. This paper develops a two-stage robust optimization model, where the first stage focuses on the scheduling problem determining the configuration of each flexible machine during each period, while the second stage addresses the lot-sizing problem determining the lot sizes of each operation for each product. Furthermore, a tailored column-and-constraint generation algorithm and a genetic algorithm-based matheuristic are proposed. Extensive numerical experiments demonstrate that the tailored column-and-constraint generation algorithm effectively solves the proposed two-stage robust optimization model, resulting in optimal production plans with high resilience to capacity uncertainty. Moreover, the genetic algorithm-based matheuristic offers satisfactory solutions for large-scale complex problems. Sensitivity analysis of the robust parameters and performance evaluations verify the effectiveness and efficiency of the proposed robust model and algorithms.