Two-machine flow-shop scheduling with rejection

We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejectio...

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Bibliographic Details
Published in:Computers & operations research Vol. 39; no. 5; pp. 1087 - 1096
Main Authors: Shabtay, Dvir, Gasper, Nufar
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2012
Elsevier
Pergamon Press Inc
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Approximation
Approximation algorithm
Bicriteria optimization
Computer science; control theory; systems
Exact sciences and technology
Flow-shop scheduling
formula omitted
FPTAS
Inventory control, production control. Distribution
Job shops
Mathematical analysis
Mathematical models
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Pareto optimum
Production scheduling
Pseudo-polynomial time algorithm
Rejection
Scheduling
Scheduling with rejection
Scheduling, sequencing
Studies
Theoretical computing
NP-hard
Scheduling with rejection
Bicriteria optimization
Pseudo-polynomial time algorithm
Approximation algorithm
FPTAS
Flow-shop scheduling
Costs
Multiple machine
Pareto optimum
Polynomial approximation
Scheduling
Makespan
Optimization
Polynomial time
Rejection
Production management
NP hard problem
Flow shop
Single machine
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Description
Summary:We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1+ɛ)R and a makespan value of at most (1+ɛ)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them. ► We study a two-machine flow-shop scheduling problem with rejection. ► We measure the quality of a schedule by two criteria: the makespan and the total rejection cost. ► We show that the problem of minimizing the sum of the two criteria (problem P1) is ordinary NP-hard. ► We provide an FPTAS and two 2-approximation algorithms for solving the P1 problem. ► The bicriteria problem is shown to be ordinary NP-hard and a two-dimensional FPTAS is provided.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2011.05.023