Minimizing total tardiness in a two-machine flowshop with uncertain and bounded processing times

Abstract

The two-machine flowshop scheduling problem with the performance measure of total tardiness is addressed. This performance measure is essential since meeting deadlines is a crucial part of scheduling and a major concern for some manufacturing systems. The processing times on both machines are uncertain variables and within some lower and upper bounds. This is due to uncertainty being an integral part of some manufacturing settings, making it impossible to predict processing times in advance. To the best of the author’s knowledge, this problem is addressed for the first time in this paper. A dominance relation is established and nineteen algorithms, which incorporate the established dominance relation, are presented. These algorithms are extensively evaluated through randomly generated data for different numbers of jobs and four different distributions, representing both symmetric and non-symmetric distributions. Computational experiments show that the presented algorithms perform extremely well when compared with a random solution. In particular, the best of the considered 19 algorithms reduces the error of the random solution by 99.99% and the error of the worst algorithm (among the 19 algorithms) by 99.96%. The results are confirmed by a test of hypothesis and this algorithm is recommended.