Two-machine no-wait flowshop scheduling problem with uncertain setup times to minimize maximum lateness

Abstract

We consider the two-machine no-wait flowshop scheduling problem to minimize maximum lateness, where setup times are considered separate from processing times. Moreover, setup times are uncertain (within some intervals), where only lower and upper bounds are known. The objective is to obtain a set of dominating schedules, which contain the optimal solution. The size of dominating set can be reduced by the development of dominance relations. In this paper, we establish local and global dominance relations. Furthermore, we provide examples to illustrate how the developed dominance relations either help in finding the optimal schedule or in reducing the size of dominating set. Moreover, we establish an algorithm to find the number of developed dominance relations for given input parameters. Computational experiments indicate that the established dominance relations are helpful in reducing the size of dominating schedules.