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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 are proposed. 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. [ABSTRACT FROM AUTHOR]

The performance measure of total completion time (TCT) plays a key role in manufacturing to improve performance, e.g., reducing inventory levels. Moreover, since uncertainty is an inevitable part of certain manufacturing environments, it is especially important to address cases with uncertain processing times. This paper addresses the four-machine flowshop scheduling problem to minimize TCT with uncertain processing times. Due to the NP-hardness of the problem, different algorithms were presented as solutions in scheduling literature. In this paper, a new substantially improved algorithm is proposed and parameters of the algorithm are fine tuned. The proposed algorithm is compared to the best existing algorithm (RAIRO Operations Research 54, 529-553, 2020) in scheduling literature using extensive computational experiments and statistical analysis. Computational methods using the programming language python, along with statistical inference, is used to confirm the effectiveness of the proposed algorithm over the existing ones. Computational methods reveal that the proposed algorithm is, on average, 86.8% more effective than the best existing one in literature with similar computational times. A test of hypothesis further confirms the effectiveness of the proposed algorithm with a p-value of less than 0.00001, which is practically zero. [ABSTRACT FROM AUTHOR]

We address the four-machine flowshop scheduling problem with the objective of minimizing makespan with uncertain processing times The problem was investigated in the literature (RAIRO Operations Research 54, 529-553) and different algorithms were proposed. In this paper, we propose a new algorithm for the problem. The new proposed algorithm is compared with the best existing algorithm in the literature by using extensive computational experiments. Computational experiments show that the new proposed algorithm performs much better than the best existing algorithm in the literature in terms of error while both have the same computational time. Specifically, the new proposed algorithm reduces the error of the best existing algorithm in the literature about 40%. This result has been confirmed by using hypotheses testing with a significance level of 0.01. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]