Flow shop scheduling algorithms for minimizing the completion time variance and the sum of squares of completion time deviations from a common due date
TL;DR: A branch and bound algorithm based on breadth-first search procedure for scheduling n jobs on m -machines with the objective of minimizing completion time variance (CTV) is developed to obtain the best permutation sequence.
About: This article is published in European Journal of Operational Research.The article was published on 2001-08-01. It has received 50 citations till now. The article focuses on the topics: Flow shop scheduling & Explained sum of squares.
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TL;DR: This paper surveys some results on multimachine scheduling problems with a given common due date, where the focus is on possible approaches for shop scheduling problems.
126 citations
Cites background from "Flow shop scheduling algorithms for..."
...In this sense, the problem considered in [25] is a simplification of the (two-machine) problem considered in [20, 21, 22]....
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...• Concerning the development of algorithms for the problems without considering storage costs and a larger number of machines than two, there do not exist algorithms up to now (except the algorithm given in [25] which, however, considers only schedules starting at time zero)....
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...[25] consider the problem of minimizing the sum of squares of the deviations of the completion times from a given common due date (and the related problem of minimizing the variance of the completion times of jobs - CTV problem) in the case of a flow shop problem with an arbitrary number of machines (i....
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...In the branch and bound algorithm given in [25], the authors restrict to permutation schedules....
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TL;DR: In this article, a new ant-colony algorithm (NACO) has been developed in order to solve the flow shop scheduling problem, where the objective is to minimize the completion-time variance of jobs.
91 citations
TL;DR: Three heuristic algorithms namely HAMC1, HAMC2 and HAMC3 have been proposed and two new hybrid algorithms are developed by taking the seed sequences yielded by a method proposed by Rajendran in his work to minimize flow time and improving it using search algorithm.
Abstract: This paper deals with the multicriterion approach to flow shop scheduling [FSS] problems by considering makespan time and total flow time. The primary concern of flow shop scheduling is to obtain the best sequence, which minimizes the makespan, flow time, idle time, tardiness, etc. In this work, makespan and total flow time of the jobs are considered for minimization. Three heuristic algorithms namely HAMC1, HAMC2 and HAMC3 have been proposed in this paper. The effectiveness of the heuristics has been analyzed using the problems generated by Taillard [16]. The results of the problems are compared with the solution procedures proposed by Rajendran [15]. The new hybrid algorithms are developed by taking the seed sequences yielded by a method proposed by Rajendran [14] in his work to minimize flow time and improving it using search algorithm. The hybrid algorithm gives better results.
65 citations
Journal Article•
23 Jul 2007-World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
TL;DR: In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed and a mathematical model and its main representation schemes are presented.
Abstract: In this paper, mathematical models for permutation flow shop scheduling and job shop scheduling problems are proposed. The first problem is based on a mixed integer programming model. As the problem is NP-complete, this model can only be used for smaller instances where an optimal solution can be computed. For large instances, another model is proposed which is suitable for solving the problem by stochastic heuristic methods. For the job shop scheduling problem, a mathematical model and its main representation schemes are presented. Keywords—Flow shop, job shop, mixed integer model, representation scheme.
50 citations
TL;DR: In this paper, the authors considered the permutation flow shop scheduling problem with earliness and tardiness penalties (E/T) and common due date for jobs, and proposed a heuristic based approach for solving the problem over the entire range of due dates.
Abstract: We consider the permutation flow shop scheduling problem with earliness and tardiness penalties (E/T) and common due date for jobs. We show that the problem can be sub-divided into three cases: (i) the due date is such that all jobs are necessarily tardy; (ii) the due date is unrestricted; and (iii) the due date is between the two. Based on analytical results we provide partial characterisation of the optimal solution and develop a comprehensive approach for solving the problem over the entire range of due dates. Our approach, which draws upon the existing literature and results for the single machine problem, successfully exploits the properties of the optimal solution. Limited computational results indicate that the performance of the heuristic is reasonable and has the potential to significantly improve performance. This approach has been incorporated as part of the scheduling module of the production planning and scheduling system we developed for a medium-sized bulk drug manufacturer.
48 citations
References
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TL;DR: A simple algorithm is presented in this paper, which produces very good sequences in comparison with existing heuristics, and performs especially well on large flow-shop problems in both the static and dynamic sequencing environments.
Abstract: In a general flow-shop situation, where all the jobs must pass through all the machines in the same order, certain heuristic algorithms propose that the jobs with higher total process time should be given higher priority than the jobs with less total process time. Based on this premise, a simple algorithm is presented in this paper, which produces very good sequences in comparison with existing heuristics. The results of the proposed algorithm have been compared with the results from 15 other algorithms in an independent study by Park [13], who shows that the proposed algorithm performs especially well on large flow-shop problems in both the static and dynamic sequencing environments.
2,255 citations
TL;DR: A simple algorithm for the solution of very large sequence problems without the use of a computer that produces approximate solutions to the n job, m machine sequencing problem where no passing is considered and the criterion is minimum total elapsed time.
Abstract: This paper describes a simple algorithm for the solution of very large sequence problems without the use of a computer. It produces approximate solutions to the n job, m machine sequencing problem where no passing is considered and the criterion is minimum total elapsed time. Up to m-1 sequences may be found.
921 citations
TL;DR: In this paper, the branch-and-bound technique was applied to two flow-shop scheduling problems, i.e., 2-machine and 3-machine, with the objective of minimizing the makespan.
Abstract: The branch-and-bound technique of Little, et al. and Land and Doig is presented and then applied to two flow-shop scheduling problems. Computational results for up to 9 jobs are given for the 2-machine problem when the objective is minimizing the mean completion time. This problem was previously untreated. Results for up to 10 jobs, including comparisons with other techniques, are given for the 3-machine problem when the objective is minimizing the makespan.
575 citations
TL;DR: By combining Roy's graph-theoretical interpretation of the problem of job scheduling on machines and some general results of his theory with the “branch-and-bound” method recently applied by Little et al. to the travelling salesman problem an algorithm has been obtained for the exact solution of the scheduling problem in the case of three machines.
Abstract: By combining Roy's graph-theoretical interpretation of the problem of job scheduling on machines and some general results of his theory with the “branch-and-bound” method recently applied by Little et al. to the travelling salesman problem an algorithm has been obtained for the exact solution of the scheduling problem in the case of three machines. The working of the algorithm has been illustrated by numerical examples and possibilities of further investigations have been indicated.
250 citations
TL;DR: This paper addresses the problem of n jobs to be scheduled on a single machine in such a way that flow time variation is minimized and a heuristic method for scheduling is proposed.
Abstract: This paper addresses the problem of n jobs to be scheduled on a single machine in such a way that flow time variation is minimized. When the measure of variation is total absolute difference of completion times TADC the problem is shown to be quite simple. Sufficient conditions are shown for minimal TADC and a simple method for generating an optimal solution is provided.
When the measure of variation is variance of flow time the problem is much more difficult. For this case a heuristic method for scheduling is proposed. The heuristic is simple and provides solutions which compare favorably with others found in the literature.
199 citations