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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Veröffentlicht in:	Computers & operations research Jg. 39; H. 5; S. 1087 - 1096
Hauptverfasser:	Shabtay, Dvir, Gasper, Nufar
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Kidlington Elsevier Ltd 01.05.2012 Elsevier Pergamon Press Inc
Schlagworte:	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
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Abstract	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.
AbstractList	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 [inline image] 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 [inline image] due to the [inline image] 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+[var epsilon])R and a makespan value of at most (1+[var epsilon])K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them. 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. 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+ε)R and a makespan value of at most (1+ε)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them. [PUBLICATION ABSTRACT]
Author	Gasper, Nufar Shabtay, Dvir
Author_xml	– sequence: 1 givenname: Dvir surname: Shabtay fullname: Shabtay, Dvir email: dvirs@bgu.ac.il – sequence: 2 givenname: Nufar surname: Gasper fullname: Gasper, Nufar email: nufarg@bgu.ac.il
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Keywords	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
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Snippet	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:...
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SubjectTerms	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
Title	Two-machine flow-shop scheduling with rejection
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