The just-in-time scheduling problem in a flow-shop scheduling system

► We study several variants of the problem of maximizing the weighted number of JIT jobs in a flow-shop scheduling system. ► We show that the unweighted version of the problem on two machines is solvable in O( n 3) time. ► We show that the problem is ordinary NP-hard even if the processing times are...

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Vydané v:European journal of operational research Ročník 216; číslo 3; s. 521 - 532
Hlavný autor: Shabtay, Dvir
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.02.2012
Elsevier
Elsevier Sequoia S.A
Predmet:
Algorithms
Applied sciences
Approximation
Complexity
Customers
Exact sciences and technology
Flow-shop
Gain
Inventory control, production control. Distribution
Job shops
Just in time
Just-in-time scheduling
Mathematical analysis
Mathematical programming
No-wait restriction
Operational research
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Production scheduling
Pseudo-polynomial time algorithm
Scheduling
Scheduling, sequencing
Studies
Just-in-time scheduling
No-wait restriction
Flow-shop
Pseudo-polynomial time algorithm
Complexity
Script
Multiple machine
Polynomial approximation
Job shop
Processing time
Scheduling
Polynomial method
Approximation algorithm
Real time
Polynomial time
Just in time
NP hard problem
Flow shop
Time complexity
Execution time
ISSN:0377-2217, 1872-6860
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Shrnutí:► We study several variants of the problem of maximizing the weighted number of JIT jobs in a flow-shop scheduling system. ► We show that the unweighted version of the problem on two machines is solvable in O( n 3) time. ► We show that the problem is ordinary NP-hard even if the processing times are machine-independent. ► We show that the case of job-independent processing times is solvable in polynomial time. ► A polynomial time solution is provided for the problem under a no-wait restriction. We study the problem of maximizing the weighted number of just-in-time ( JIT) jobs in a flow-shop scheduling system under four different scenarios. The first scenario is where the flow-shop includes only two machines and all the jobs have the same gain for being completed JIT. For this scenario, we provide an O( n 3) time optimization algorithm which is faster than the best known algorithm in the literature. The second scenario is where the job processing times are machine-independent. For this scenario, the scheduling system is commonly referred to as a proportionate flow-shop. We show that in this case, the problem of maximizing the weighted number of JIT jobs is NP -hard in the ordinary sense for any arbitrary number of machines. Moreover, we provide a fully polynomial time approximation scheme (FPTAS) for its solution and a polynomial time algorithm to solve the special case for which all the jobs have the same gain for being completed JIT. The third scenario is where a set of identical jobs is to be produced for different customers. For this scenario, we provide an O( n 3) time optimization algorithm which is independent of the number of machines. We also show that the time complexity can be reduced to O( n log n) if all the jobs have the same gain for being completed JIT. In the last scenario, we study the JIT scheduling problem on m machines with a no-wait restriction and provide an O( mn 2) time optimization algorithm.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2011.07.053