Modelling and robust scheduling of two-stage assembly flow shop under uncertainty in assembling times

This paper focuses on robust scheduling for an assembly flow shop where assembling times are uncertain. The considered manufacturing environment is a two-stage production system that consists of a processing stage followed by an assembly stage. There are two parallel machines in the first stage to process the components followed by an assembly stage wherein, the components are assembled to products. The majority of scheduling research considers a deterministic environment with pre-known and fixed data. However, in real-world condition, several kinds of uncertainties should be considered. In this article, the scheduling problem is tackle under uncertainty and the assembling time of each product at the second stage is the source of uncertainty. The problem is described and formulated as a mixed-integer linear programming model under deterministic condition. After that, the uncertainty issue is discussed and the robust scheduling procedure is introduced to minimize the maximum completion time of all products based on the min-max regret approach. To solve the robust scheduling an exact method is proposed to solve the problem on the small scales. Moreover, two approximate methods are modified and used to solve this NP-hard problem on the small and practical scales. The performances of the proposed methods are evaluated by several numerical examples taken from valid references. Computational results indicate that the proposed robust scheduling methods provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance.