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We address a two-machine no-wait flowshop scheduling problem with respect to the performance measure of total completion time. Minimizing total completion time is important when inventory cost is of concern. Setup times are treated separately from processing times. Furthermore, setup times are uncertain with unknown distributions and are within some lower and upper bounds. We develop a dominance relation and propose eight algorithms to solve the problem. The proposed algorithms, which assign different weights to the processing and setup times on both machines, convert the two-machine problem into a single-machine one for which an optimal solution is known. We conduct computational experiments to evaluate the proposed algorithms.Computational experiments reveal that one of the proposed algorithms, which assigns the same weight to setup and processing times, is superior to the rest of the algorithms. The results are statistically verified by constructing confidence intervals and test of hypothesis.

We consider the four-machine flowshop scheduling problem to minimize makespan where processing times are uncertain. The processing times are within some intervals, where the only available information is the lower and upper bounds of job processing times. Some dominance relations are developed, and twelve algorithms are proposed. The proposed algorithms first convert the four-machine problem into two stages, then, use the well-known Johnson’s algorithm, known to yield the optimal solution for the two-stage problem. The algorithms also use the developed dominance relations. The proposed algorithms are extensively evaluated through randomly generated data for different numbers of jobs and different gaps between the lower and upper bounds of processing times. Computational experiments indicate that the proposed algorithms perform well. Moreover, the computational experiments reveal that one of the proposed algorithms, Algorithm A7, performs significantly better than the other eleven algorithms for all possible combinations of the number of jobs and the gaps between the lower and upper bounds. More specifically, error percentages of the other eleven algorithms range from 2.3 to 27.7 times that of Algorithm A7. The results have been confirmed by constructing 99% confidence intervals and tests of hypotheses using a significance level of 0.01.

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.

We address a manufacturing environment with the no-wait constraint which is common in industries such as metal, plastic, and semiconductor. Setup times are modelled as uncertain with the objective of minimizing maximum lateness which is an important performance measure for customer satisfaction. This problem has been addressed in scheduling literature for the two-machine no-wait flowshop where dominance relations were presented. Recently, another dominance relation was presented and shown to be about 90% more efficient than the earlier ones. In the current paper, we propose two new dominance relations, which are less restrictive than the earlier ones in the literature. The new dominance relations are shown to be 140% more efficient than the most recent one in the literature. As the level of uncertainty increases, the newly proposed dominance relation performs better, which is another strength of the newly proposed dominance relation. Moreover, we also propose constructive heuristics and show that the best of the newly proposed heuristics is 95% more efficient than the existing one in the literature under the same CPU time.