A Heuristic Algorithm for the n Job, m Machine Sequencing Problem
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.
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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
01 Jan 1989
TL;DR: This survey focuses on the area of deterministic machine scheduling, and reviews complexity results and optimization and approximation algorithms for problems involving a single machine, parallel machines, open shops, flow shops and job shops.
1,401 citations
TL;DR: This work presents a new iterated greedy algorithm that applies two phases iteratively, named destruction, were some jobs are eliminated from the incumbent solution, and construction, where the eliminated jobs are reinserted into the sequence using the well known NEH construction heuristic.
923 citations
Cites methods from "A Heuristic Algorithm for the n Job..."
...Subsequent work includes the one on the CDS heuristic by Campbell et al. (1970) and constructive and improvement heuristics by Dannenbring (1977)....
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TL;DR: The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling.
Abstract: Production scheduling can be defined as the allocation of available production resources over time to best satisfy some set of criteria. Typically, the scheduling problem involves a set of tasks to be performed, and the criteria may involve both tradeoffs between early and late completion of a task, and between holding inventory for the task and frequent production changeovers. The intent of this paper is to present a broad classification for various scheduling problems, to review important theoretical developments for these problem classes, and to contrast the currently available theory with the practice of production scheduling. This paper will highlight problem areas for which there is both a significant discrepancy between practice and theory, and for which the practice corresponds closely to the theory.
767 citations
TL;DR: In this article, simulated annealing is proposed as a heuristic to obtain approximate solutions to the problem of scheduling jobs in a flow shop, where job processing order must be the same on each machine and the objective is to minimize the maximum completion time.
Abstract: The problem of scheduling jobs in a flow-shop is considered. The job processing order must be the same on each machine and the objective is to minimize the maximum completion time. Simulated annealing is proposed as a heuristic to obtain approximate solutions. Extensive computational tests with problems having up to 20 machines and 100 jobs show simulated annealing to compare favourably with known constructive heuristics and with descent methods.
589 citations
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TL;DR: A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum.
Abstract: Each of a collection of items are to be produced on two machines (or stages). Each machine can handle only one item at a time and each item must be processed through machine one and then through machine two. The setup time plus work time for each item for each machine is known. A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum. A three-machine problem is also discussed and solved for a restricted case.
3,082 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: It is suggested that the optimum (minimum total time) scheduling may be approximated by giving priority to items according to the extent to which process time increases with process number in order.
Abstract: In the situation where a number of items must pass through a number of processes in the same order, it is suggested that the optimum (minimum total time) scheduling may be approximated by giving priority to items according to the extent to which process time increases with process number in order; this criterion is put in arithmetical form. This is confirmed by (a) a simple geometrical argument; (b) comparison with the known optimum schedules of a number of published three-process cases; (c) experiments on larger cases; it is not practical here to find the exact optimum.
568 citations
"A Heuristic Algorithm for the n Job..." refers methods in this paper
...The jmsrang c& jobs is not oonada^d by the algorithm; however a paasing ptY}cedure Eqpedfied by Palniar [8] may be employed to fur&er r^ne the sequence generated by this algoritiun....
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...The Palmer [8] algorithm based upon a ranking of dope indices of jobs has several amilarities witJi t ^ algorithm presented here....
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340 citations
TL;DR: This paper describes an algorithm that will yield an optimum sequence for n jobs requiring processing through M machines when no passing is allowed and an example problem.
Abstract: This paper describes an algorithm that will yield an optimum sequence for n jobs requiring processing through M machines when no passing is allowed. Theoretical development utilizing combinatorial analysis precedes the algorithm and an example problem.
85 citations