Minimizing total completion time for flowshop scheduling problem with uncertain processing times

Abstract

The four-machine flowshop scheduling problem is investigated with the objective of minimizing total completion time. Job processing times are uncertain where only the lower and upper bounds are known. This problem is common in some manufacturing environments. Some mathematical (dominance) relations are established, and an algorithm (with ten scenarios) is proposed. The proposed algorithm converts the four-machine problem to a single machine problem for which an optimal solution is known for the deterministic problem. The difference among the scenarios is related to the weights assigned to the lower and upper bounds of processing times on the machines. The proposed algorithm is further improved by the established mathematical relations and are evaluated based on extensive computational experiments. The computational results indicate that three scenarios of the proposed algorithm perform much better than the others, and the errors of these three scenarios get better as the size of the problem increases. The results are statistically verified by constructing the confidence intervals.