Significantly improved dominance relation for no-wait flowshop scheduling problems with uncertain setup times

The problem of minimizing total completion time (TCT) in an uncertain environment is a crucial problem in production engineering. Minimizing the TCT of a two-machine no-wait scheduling problem with uncertain and bounded setup times is known to be very difficult, and is very likely to have no optimal solution. Such problems are known as Non-deterministic Polynomial-time hard. Scheduling literature provides a mathematical dominance relation for the problem. In this article, a substantially more effective mathematical dominance relation is established. In fact, computational methods reveal that the average percentage improvement comparing the established one in this article to the one in the literature is 1407.80%. Furthermore, statistical hypothesis testing is conducted to compare the means of the established dominance relation to that given in the literature, with p-values of (almost) 0 for every case, meaning that the mean of the established dominance relation is substantially larger than the one given in the literature. Additionally, confidence intervals are constructed for each mean of the randomly generated cases for the proposed dominance relation to confirm the accuracy of the means.