Scheduling Batches with Sequential Job Processing for Two-Machine Flow and Open Shops

In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only...

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Vydáno v:INFORMS journal on computing Ročník 13; číslo 2; s. 120 - 137
Hlavní autoři: Glass, C.A, Potts, C.N, Strusevich, V.A
Médium: Journal Article
Jazyk:angličtina
Vydáno: Linthicum INFORMS 22.03.2001
Institute for Operations Research and the Management Sciences
Témata:
Algorithms
Analysis of Algorithms: Computational Complexity
Batch processing
Flow-Shop
Heuristic
Job shops
Open-Shop
Production-Scheduling
Scheduling
Studies
Suboptimal Algorithms
ISSN:1091-9856, 1526-5528, 1091-9856
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Shrnutí:In this paper, we study a problem of scheduling and batching on two machines in a flow-shop and open-shop environment. Each machine processes operations in batches, and the processing time of a batch is the sum of the processing times of the operations in that batch. A setup time, which depends only on the machine, is required before a batch is processed on a machine, and all jobs in a batch remain at the machine until the entire batch is processed. The aim is to make batching and sequencing decisions, which specify a partition of the jobs into batches on each machine, and a processing order of the batches on each machine, respectively, so that the makespan is minimized. The flow-shop problem is shown to be strongly NP-hard. We demonstrate that there is an optimal solution with the same batches on the two machines; we refer to these as consistent batches . A heuristic is developed that selects the best schedule among several with one, two, or three consistent batches, and is shown to have a worst-case performance ratio of 4/3. For the open-shop, we show that the problem is NP-hard in the ordinary sense. By proving the existence of an optimal solution with one, two or three consistent batches, a close relationship is established with the problem of scheduling two or three identical parallel machines to minimize the makespan. This allows a pseudo-polynomial algorithm to be derived, and various heuristic methods to be suggested.
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ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.13.2.120.10521