Improved Algorithms for Single-Machine Serial-Batch Scheduling With Rejection to Minimize Total Completion Time and Total Rejection Cost
Recently, Shabtay considered a scheduling problem on a single serial-batching machine with rejection to minimize the dual criteria of total completion time and total rejection cost, where the number of jobs to be included in each batch is not restricted. He studied four variants of the problem: the...
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| Vydané v: | IEEE transactions on systems, man, and cybernetics. Systems Ročník 46; číslo 11; s. 1578 - 1588 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York
IEEE
01.11.2016
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 2168-2216, 2168-2232 |
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| Abstract | Recently, Shabtay considered a scheduling problem on a single serial-batching machine with rejection to minimize the dual criteria of total completion time and total rejection cost, where the number of jobs to be included in each batch is not restricted. He studied four variants of the problem: the first is to minimize the sum of the two criteria; the second and third are to minimize one criterion, subject to the other criterion not exceeding a given value; and the last is to find the Pareto-optimal solutions for the bicriterion problem. Shabtay provided an O(n 5 ) algorithm for the first variant and an O(n 6 /ε 2 ) fully polynomialtime approximation scheme (FPTAS) for the fourth variant. In this paper, we provide an alternative O(n 4 ) algorithm to solve the first variant and an O(n 5 /ε) FPTAS for the fourth variant, which are more efficient than those developed by Shabtay from a theoretical perspective. However, when the size of each batch is bounded by a given number b > 1, the corresponding time complexities of our algorithms for the first and fourth variants reduce to O(bn 3 ) and O(bn 4 /ε), respectively. |
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| AbstractList | Recently, Shabtay considered a scheduling problem on a single serial-batching machine with rejection to minimize the dual criteria of total completion time and total rejection cost, where the number of jobs to be included in each batch is not restricted. He studied four variants of the problem: the first is to minimize the sum of the two criteria; the second and third are to minimize one criterion, subject to the other criterion not exceeding a given value; and the last is to find the Pareto-optimal solutions for the bicriterion problem. Shabtay provided an [Formula Omitted]([Formula Omitted]) algorithm for the first variant and an [Formula Omitted]([Formula Omitted]) fully polynomial-time approximation scheme (FPTAS) for the fourth variant. In this paper, we provide an alternative [Formula Omitted]([Formula Omitted]) algorithm to solve the first variant and an [Formula Omitted]([Formula Omitted]) FPTAS for the fourth variant, which are more efficient than those developed by Shabtay from a theoretical perspective. However, when the size of each batch is bounded by a given number [Formula Omitted], the corresponding time complexities of our algorithms for the first and fourth variants reduce to [Formula Omitted]( bn [Formula Omitted]) and [Formula Omitted]( bn [Formula Omitted]), respectively. Recently, Shabtay considered a scheduling problem on a single serial-batching machine with rejection to minimize the dual criteria of total completion time and total rejection cost, where the number of jobs to be included in each batch is not restricted. He studied four variants of the problem: the first is to minimize the sum of the two criteria; the second and third are to minimize one criterion, subject to the other criterion not exceeding a given value; and the last is to find the Pareto-optimal solutions for the bicriterion problem. Shabtay provided an O(n 5 ) algorithm for the first variant and an O(n 6 /ε 2 ) fully polynomialtime approximation scheme (FPTAS) for the fourth variant. In this paper, we provide an alternative O(n 4 ) algorithm to solve the first variant and an O(n 5 /ε) FPTAS for the fourth variant, which are more efficient than those developed by Shabtay from a theoretical perspective. However, when the size of each batch is bounded by a given number b > 1, the corresponding time complexities of our algorithms for the first and fourth variants reduce to O(bn 3 ) and O(bn 4 /ε), respectively. |
| Author | Cheng, Tai Chiu Edwin Yunqiang Yin Chin-Chia Wu Dujuan Wang |
| Author_xml | – sequence: 1 surname: Yunqiang Yin fullname: Yunqiang Yin email: yinyunqiang@126.com organization: Fac. of Sci., Kunming Univ. of Sci. & Technol., Kunming, China – sequence: 2 givenname: Tai Chiu Edwin surname: Cheng fullname: Cheng, Tai Chiu Edwin email: edwin.cheng@polyu.edu.hk organization: Dept. of Logistics & Maritime Studies, Hong Kong Polytech. Univ., Hong Kong, China – sequence: 3 surname: Dujuan Wang fullname: Dujuan Wang email: wangdujuan@dlut.edu.cn organization: Sch. of Manage. Sci. & Eng., Dalian Univ. of Technol., Dalian, China – sequence: 4 surname: Chin-Chia Wu fullname: Chin-Chia Wu email: cchwu@fcu.edu.tw organization: Dept. of Stat., Feng Chia Univ., Taichung, Taiwan |
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| SubjectTerms | Approximation algorithms Approximation methods Batch processing Batch scheduling bicriterion scheduling dynamic programming Dynamic scheduling Heuristic algorithms Job shop scheduling Production scheduling rejection Single machine scheduling total completion time |
| Title | Improved Algorithms for Single-Machine Serial-Batch Scheduling With Rejection to Minimize Total Completion Time and Total Rejection Cost |
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