Asiye Aydilek

Single machine scheduling problem with interval processing times to minimize mean weighted completion time

The single resource scheduling problem is commonly applicable in practice not only when there is a single resource but also in some multiple-resource production systems where only one of the resources is bottle neck. Thus, the single resource (machine) scheduling problem has been widely addressed in the scheduling literature. In this paper, the single machine scheduling problem with uncertain and interval processing times is addressed. The objective is to minimize mean weighted completion time. The problem has been addressed in the literature and efficient heuristics have been presented. In this paper, some new polynomial time heuristics, utilizing the bounds of processing times, are proposed. The proposed and existing heuristics are compared by extensive computational experiments. The conducted experiments include a generalized simulation environment and several additional representative distributions in addition to the restricted experiments used in the literature. The results indicate that the proposed heuristics perform significantly better than the existing heuristics. Specifically, the best performing proposed heuristic reduces the error of the best existing heuristic in the literature by more than 75% while the computational time of the best performing proposed heuristic is less than that of the best existing heuristic. Moreover, the absolute error of the best performing heuristic is only about 1% of the optimal solution. Having a very small absolute error along with a negligible computational time indicates the superiority of the proposed heuristics.

Increasing the profitability and competitiveness in a production environment with random and bounded setup times

The link between makespan and the profitability and competitiveness of a firm is addressed first. We then study the problem of minimising makespan in a two-machine flowshop with setup times. Jobs have random setup times that are bounded within certain intervals. The distributions of job setup times are not known. We propose a polynomial time algorithm that generalises Yoshida and Hitomis algorithm. The algorithm uses a weighted average of lower and upper bounds for setup times. Different combinations of weights result in nine different versions of the algorithm. The computational results indicate that one of the versions, with equal weights given to the lower and upper bounds of setup times, performs much better than the others. Next, the performance of this best version is compared with that of the optimal solution, which is obtained by Yoshida and Hitomis algorithm applied to the problem after setup times have been realised. Computational analysis shows that the overall average absolute error of the best algorithm is 0.03%, and this decreases in size as the number of jobs increases. The analysis also shows that the proposed best version yields robust results regardless of setup-time distributions and the range of setup times.

Production in a two-machine flowshop scheduling environment with uncertain processing and setup times to minimize makespan

A wide range of uncertainties exists in some real-world production environments which result in uncertain setup and/or processing times. Factors such as crew skills, shortages in equipment and resource breakdowns can be the sources of these uncertainties. This study considers a two-machine production flowshop scheduling problem where both setup and processing times are treated as uncertain variables. The objective is to minimise makespan which is an effective way of resource utilisation. There exists a dominance relation in the literature for the two-machine flowshop scheduling problem with uncertain setup and processing times. However, the dominance relation has not been evaluated. In this study, we evaluate the existing dominance relation. Moreover, a new dominance relation is established and shown to be more effective than the existing one. Furthermore, twenty-five implementations of a polynomial time algorithm are developed. Extensive computational experiments are conducted to evaluate the performance of the implementations of the algorithm. The computational experiments indicate that the overall gap (error) of the best implementation of the algorithm is less than 0.3% when compared to the optimal solution. Moreover, the performance of this implementation of the algorithm is the best one when compared to the remaining implementations for all the considered experimental environments. Additionally, the performance of this implementation of the algorithm is shown to be insensitive to the uncertainty in setup times.

Minimizing the number of tardy jobs on a two-stage assembly flowshop

The objective of minimizing the number of tardy jobs is important as it is directly related to the percentage of on-time shipments, which is often used to rate managers’ performance in many manufacturing environments. To the best of our knowledge, the assembly flowshop scheduling problem with this objective has not been addressed so far, and thus is addressed in this paper. Given that the problem is NP-hard, different heuristics are proposed for the problem in this paper. The proposed heuristics are genetic algorithm (GA), improved genetic algorithm (IGA), simulated annealing algorithm with three different neighborhood structures (SA-1, SA-2, SA-3), Dhouib et al.’s simulated annealing algorithm (DSA), and an improved cloud theory-based simulated annealing algorithm (CSA). The heuristics are evaluated based on extensive computational experiments and all the heuristics were run for the same computational time for a fair comparison. The experiments reveal that the overall average errors of DSA, GA, IGA, CSA, SA-1, SA-2, SA-3 were 20.53, 13.49, 11.64, 3.27, 2.81, 1.92, and 0.56, respectively. Therefore, the proposed heuristic of SA-3 reduces the error of DSA, GA, IGA, CSA, SA-1, SA-2 by about 97, 96, 95, 83, 80, and 71%, respectively. All the results are statistically confirmed.

Minimising maximum tardiness in assembly flowshops with setup times

This paper addresses a two-stage assembly flowshop scheduling problem with the objective of minimising maximum tardiness where set-up times are considered as separate from processing times. The performance measure of maximum tardiness is important for some scheduling environments, and hence, it should be taken into account while making scheduling decisions for such environments. Given that the problem is strongly NP-hard, different algorithms have been proposed in the literature. The algorithm of Self-Adaptive Differential Evolution (SDE) performs as the best for the problem in the literature. We propose a new hybrid simulated annealing and insertion algorithm (SMI). The insertion step, in the SMI algorithm, strengthens the exploration step of the simulated annealing algorithm at the beginning and reinforces the exploitation step of the simulated annealing algorithm towards the end. Furthermore, we develop several dominance relations for the problem which are incorporated in the proposed SMI algorithm. We compare the performance of the proposed SMI algorithm with that of the best existing algorithm, SDE. The computational experiments indicate that the proposed SMI algorithm performs significantly better than the existing SDE algorithm. More specifically, under the same CPU time, the proposed SMI algorithm, on average, reduces the error of the best existing SDE algorithm over 90%, which indicates the superiority of the proposed SMI algorithm.

No-wait flowshop scheduling problem with two criteria; total tardiness and makespan

We consider the m-machine no-wait flowshop scheduling problem with respect to two performance measures; total tardiness and makespan. Our objective is to minimize total tardiness subject to the constraint that the makespan is not larger than a given value. We develop dominance relations and propose an algorithm, called Algorithm AA, which is a combination of simulated annealing and insertion algorithm. Moreover, we adapt five existing algorithms, including three well performing algorithms known to minimize total tardiness, to our problem. We conduct extensive computational experiments to compare the performance of the proposed Algorithm AA with the existing algorithms under the same CPU times. We also evaluate the effect of the dominance relations. The computational analysis indicates that the proposed Algorithm AA performs significantly better than the existing algorithms. Specifically, the relative error of the Algorithm AA is about 60% less than that of the best algorithm among the five existing algorithms considered. All the results are statistically verified. Hence, the proposed Algorithm AA is recommended for the considered problem.