Two-stage assembly scheduling problem for minimizing total tardiness with setup times

Abstract

The two-stage assembly flowshop scheduling problem has received much attention from researchers because it is applicable to many real-life environments. The objective of minimizing total tardiness is important because the fulfillment of due dates for customers must be considered when making scheduling decisions. However, the setup times were assumed to be zero in previous studies, which may not be realistic or appropriate for some scheduling environments because treating the setup times separately from the processing times increases the level of machine utilization and reduces total tardiness. In this study, we investigate the two-stage assembly flowshop scheduling problem with separate setup times to minimize the total tardiness. We propose two new algorithms and adapt four existing algorithms, which are different versions of simulated annealing, genetic, and insertion algorithms. Moreover, we formulate the problem mathematically, where we develop a dominance relation and we utilize the dominance relation in our proposed algorithms. Extensive computational experiments indicated that one of the proposed algorithms performed much better than the others on average, i.e., the error using the best algorithm was 54% to 98% less than that with the other algorithms. Computational experiments were also conducted with zero setup times in order to compare the performance of our proposed algorithms with that of the best known previously reported algorithm in the zero setup time case. When the setup times were zero, the best proposed algorithm reduced the error of the best previously reported algorithm by 48% when both algorithms were run for the same computational time. Therefore, our best proposed algorithm can be used for both zero and non-zero setup times. Hence, for the first time, the present study considers the problem with separate setup times as well as proposing much better algorithms for the zero setup time case.