Abstract:This paper discusses the flow shop scheduling problem to minimize the makespan with release dates. By resequencing the jobs, a modified heuristic algorithm is obtained for handling large-sized problems. Moreover, based on some properties, a local search scheme is provided to improve the heuristic to gain high-quality solution for moderate-sized problems. A sequence-independent lower bound is presented to evaluate the performance of the algorithms. A series of simulation results demonstrate the effectiveness of… Show more
“…(1) For M 1 : processing time min is (2, 6, 8, 10, 14) (2) For M 2 : processing time max is (2,5,7,8,9) (3) For M 3 : processing time min is (1,3,4,5,6) Here, all the decision parameters are represented by pentagonal fuzzy numbers.…”
Section: Numerical Examplementioning
confidence: 99%
“…Vahedi-Nouri et al [2] presented a more broad version of the FS strategy to minimize the average flow rate. In order to optimize the publication time, Ren et al [3] explored the topic of FS programming. Laribi et al [4] have introduced a mathematical model for two FS-limited machines that address FS time reduction problems where renewables are not constrained.…”
Scheduling involves planning and arranging jobs across a coordinated set of events to satisfy the customer’s demands. In this article, we present a simple approach for the flow-shop (FS) scheduling problem under fuzzy environment in which processing time of jobs are represented by pentagonal fuzzy numbers. This study is intended to reduce the rental cost of the machine in compliance with the rental policy. The fuzzy FS scheduling problem is solved without converting the processing time into its equivalent crisp numbers using a robust ranking technique and a fuzzy arithmetic pentagonal fuzzy numbers. A numerical illustration indicates that the approach is workable, accurate, and relevant.
“…(1) For M 1 : processing time min is (2, 6, 8, 10, 14) (2) For M 2 : processing time max is (2,5,7,8,9) (3) For M 3 : processing time min is (1,3,4,5,6) Here, all the decision parameters are represented by pentagonal fuzzy numbers.…”
Section: Numerical Examplementioning
confidence: 99%
“…Vahedi-Nouri et al [2] presented a more broad version of the FS strategy to minimize the average flow rate. In order to optimize the publication time, Ren et al [3] explored the topic of FS programming. Laribi et al [4] have introduced a mathematical model for two FS-limited machines that address FS time reduction problems where renewables are not constrained.…”
Scheduling involves planning and arranging jobs across a coordinated set of events to satisfy the customer’s demands. In this article, we present a simple approach for the flow-shop (FS) scheduling problem under fuzzy environment in which processing time of jobs are represented by pentagonal fuzzy numbers. This study is intended to reduce the rental cost of the machine in compliance with the rental policy. The fuzzy FS scheduling problem is solved without converting the processing time into its equivalent crisp numbers using a robust ranking technique and a fuzzy arithmetic pentagonal fuzzy numbers. A numerical illustration indicates that the approach is workable, accurate, and relevant.
We consider the problem of minimizing the sum of completion times in a two‐machine permutation flowshop subject to release dates. New procedures are proposed for effectively bounding the completion time of a given job that is processed at a given position. New assignment‐based lower bounds are derived as well as an enhanced mathematical programming formulation. Our computational analysis shows a consistent tightness of the proposed lower bounds and a high outperformance of the enhanced mathematical formulation with respect to the classical one.
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