Common due window assignment scheduling with job rejection in the proportionate flowshop setting

This paper considers a proportionate flowshop scheduling problem with a common due window (CONW) and position-dependent weights. The objective is to determine the set of jobs to be processed, their processing sequence, and the rejected jobs so as to minimize a composite cost function, which consists of scheduling costs (earliness, tardiness, and due window costs) and rejection costs. We establish an equivalence between the proportionate flowshop model and a corresponding single machine model under the CONW setting, and exploit structural properties of the single machine problem to solve the proportionate flowshop problem with job rejection. For this setting, we develop a dynamic programming algorithm with a time complexity of $O({n^3})$.