A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system
We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize...
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| Vydáno v: | International journal of production economics Ročník 136; číslo 1; s. 67 - 74 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
01.03.2012
Elsevier Sequoia S.A |
| Témata: | |
| ISSN: | 0925-5273, 1873-7579 |
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| Abstract | We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be
NP
-
hard
even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution. |
|---|---|
| AbstractList | We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be NP - hard even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution. We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be NP-hard even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution. [PUBLICATION ABSTRACT] We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be NP - hard even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution. |
| Author | Bensoussan, Yaron Shabtay, Dvir Kaspi, Moshe |
| Author_xml | – sequence: 1 givenname: Dvir surname: Shabtay fullname: Shabtay, Dvir email: dvirs@bgu.ac.il – sequence: 2 givenname: Yaron surname: Bensoussan fullname: Bensoussan, Yaron email: bensousy@bgu.ac.il – sequence: 3 givenname: Moshe surname: Kaspi fullname: Kaspi, Moshe email: moshe@bgu.ac.il |
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| Keywords | Just-in-time scheduling Flow shop FPTAS Controllable processing times Resource allocation Pseudo-polynomial time algorithm |
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| SubjectTerms | Algorithms Allocations Approximation Controllable processing times Cost engineering Criteria Flow shop FPTAS Job shops Just in time Just-in-time scheduling Mathematical analysis Operations research Pareto optimum Production scheduling Pseudo-polynomial time algorithm Resource allocation Resource scheduling Scheduling Studies |
| Title | A bicriteria approach to maximize the weighted number of just-in-time jobs and to minimize the total resource consumption cost in a two-machine flow-shop scheduling system |
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