Complexity of Cyclic Job Shop Scheduling Problems for Identical Jobs with No-Wait Constraints

We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a few machines. A job is processed by performing a given set of operations in a predetermined sequence. Each operation can be performed on exac...

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Vydáno v:Journal of applied and industrial mathematics Ročník 13; číslo 4; s. 706 - 716
Hlavní autoři: Romanova, A. A., Servakh, V. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Moscow Pleiades Publishing 01.10.2019
Springer Nature B.V
Témata:
Algorithms
Complexity
Cycle time
Downtime
Job shop scheduling
Job shops
Mathematics
Mathematics and Statistics
Polynomials
Production scheduling
pseudopolynomial algorithm
cyclic job shop
computational complexity theory
scheduling theory
polynomial algorithm
identical jobs
ISSN:1990-4789, 1990-4797
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Abstract We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a few machines. A job is processed by performing a given set of operations in a predetermined sequence. Each operation can be performed on exactly one machine. We consider the problem of minimization the cycle time with no-wait constraints between some pairs of sequential operations and investigate the complexity of the problem and some of its subproblems. In general, the problem is proved to be strongly NP-hard. In the case when the job is processed without downtime between operations, polynomial solvability is proved and the two algorithms are proposed. Also we develop an algorithm for the general case which is pseudopolynomial if the number of admissible downtime is fixed. The case of a single no-wait constraint is polynomially solvable. The problem with two no-wait constraints becomes NP-hard. We found effectively solvable cases and propose the corresponding algorithms.
AbstractList We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a few machines. A job is processed by performing a given set of operations in a predetermined sequence. Each operation can be performed on exactly one machine. We consider the problem of minimization the cycle time with no-wait constraints between some pairs of sequential operations and investigate the complexity of the problem and some of its subproblems. In general, the problem is proved to be strongly NP-hard. In the case when the job is processed without downtime between operations, polynomial solvability is proved and the two algorithms are proposed. Also we develop an algorithm for the general case which is pseudopolynomial if the number of admissible downtime is fixed. The case of a single no-wait constraint is polynomially solvable. The problem with two no-wait constraints becomes NP-hard. We found effectively solvable cases and propose the corresponding algorithms.
Author Romanova, A. A.
Servakh, V. V.
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10.1016/0377-2217(94)90332-8
10.1287/moor.17.4.842
10.1002/jos.92
10.1002/jos.100
10.1007/s10951-005-1639-4
10.1080/00207540110047711
10.1002/jos.72
10.1016/0895-7177(94)90210-0
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Issue 4
Keywords pseudopolynomial algorithm
cyclic job shop
computational complexity theory
scheduling theory
polynomial algorithm
identical jobs
Language English
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Snippet We consider the cyclic job shop problem with no-wait constraints which consists in minimizing the cycle time. We assume that a single product is produced on a...
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SubjectTerms Algorithms
Complexity
Cycle time
Downtime
Job shop scheduling
Job shops
Mathematics
Mathematics and Statistics
Polynomials
Production scheduling
Title Complexity of Cyclic Job Shop Scheduling Problems for Identical Jobs with No-Wait Constraints
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