The prize-collecting single machine scheduling with bounds and penalties
This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of n jobs and a single machine are considered, where each job J j has a processing time p j , a profit π j and a rejection penalty w j . The upper bound on the process...
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| Veröffentlicht in: | Journal of combinatorial optimization 2024-09, Vol.48 (2), Article 12 |
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| container_title | Journal of combinatorial optimization |
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| creator | Hu, Guojun Pan, Pengxiang Liu, Suding Yang, Ping Xie, Runtao |
| description | This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of
n
jobs and a single machine are considered, where each job
J
j
has a processing time
p
j
, a profit
π
j
and a rejection penalty
w
j
. The upper bound on the processing number is
U
. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold
U
while the total profit of the accepted jobs does not fall below a specified profit bound
Π
. We first demonstrate that this problem is
NP
-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms. |
| doi_str_mv | 10.1007/s10878-024-01203-0 |
| format | Article |
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n
jobs and a single machine are considered, where each job
J
j
has a processing time
p
j
, a profit
π
j
and a rejection penalty
w
j
. The upper bound on the processing number is
U
. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold
U
while the total profit of the accepted jobs does not fall below a specified profit bound
Π
. We first demonstrate that this problem is
NP
-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.</description><identifier>ISSN: 1382-6905</identifier><identifier>EISSN: 1573-2886</identifier><identifier>DOI: 10.1007/s10878-024-01203-0</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Combinatorics ; Convex and Discrete Geometry ; Dynamic programming ; Fines & penalties ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Operations Research/Decision Theory ; Optimization ; Polynomials ; Rejection ; Scheduling ; Theory of Computation ; Upper bounds</subject><ispartof>Journal of combinatorial optimization, 2024-09, Vol.48 (2), Article 12</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-8fb7800459c47e647cd3e1f39d0041b185725d29335fa0569bb4e0d8f3402eb03</cites><orcidid>0009-0001-8267-8848</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10878-024-01203-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10878-024-01203-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Hu, Guojun</creatorcontrib><creatorcontrib>Pan, Pengxiang</creatorcontrib><creatorcontrib>Liu, Suding</creatorcontrib><creatorcontrib>Yang, Ping</creatorcontrib><creatorcontrib>Xie, Runtao</creatorcontrib><title>The prize-collecting single machine scheduling with bounds and penalties</title><title>Journal of combinatorial optimization</title><addtitle>J Comb Optim</addtitle><description>This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of
n
jobs and a single machine are considered, where each job
J
j
has a processing time
p
j
, a profit
π
j
and a rejection penalty
w
j
. The upper bound on the processing number is
U
. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold
U
while the total profit of the accepted jobs does not fall below a specified profit bound
Π
. We first demonstrate that this problem is
NP
-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.</description><subject>Algorithms</subject><subject>Combinatorics</subject><subject>Convex and Discrete Geometry</subject><subject>Dynamic programming</subject><subject>Fines & penalties</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Polynomials</subject><subject>Rejection</subject><subject>Scheduling</subject><subject>Theory of Computation</subject><subject>Upper bounds</subject><issn>1382-6905</issn><issn>1573-2886</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LxDAQDaLguvoHPAU8RydfTXqUxS9Y8LKeQ5tMt1267dq0iP56s1bw5mXmMfPeY-YRcs3hlgOYu8jBGstAKAZcgGRwQhZcG8mEtdlpwtIKluWgz8lFjDsASFgtyPOmRnoYmi9kvm9b9GPTbWlMpUW6L3zddEijrzFM7XHz0Yw1LfupC5EWXaAH7Ip2bDBekrOqaCNe_fYleXt82Kye2fr16WV1v2ZeAIzMVqWxAErnXhnMlPFBIq9kHtKQl9xqI3QQuZS6KkBneVkqhGArqUBgCXJJbmbfw9C_TxhHt-unIR0RnYRcWmuAq8QSM8sPfYwDVi79uC-GT8fBHRNzc2IuJeZ-EnNHazmLYiJ3Wxz-rP9RfQOgfW1h</recordid><startdate>20240901</startdate><enddate>20240901</enddate><creator>Hu, Guojun</creator><creator>Pan, Pengxiang</creator><creator>Liu, Suding</creator><creator>Yang, Ping</creator><creator>Xie, Runtao</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0009-0001-8267-8848</orcidid></search><sort><creationdate>20240901</creationdate><title>The prize-collecting single machine scheduling with bounds and penalties</title><author>Hu, Guojun ; Pan, Pengxiang ; Liu, Suding ; Yang, Ping ; Xie, Runtao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-8fb7800459c47e647cd3e1f39d0041b185725d29335fa0569bb4e0d8f3402eb03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Algorithms</topic><topic>Combinatorics</topic><topic>Convex and Discrete Geometry</topic><topic>Dynamic programming</topic><topic>Fines & penalties</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Polynomials</topic><topic>Rejection</topic><topic>Scheduling</topic><topic>Theory of Computation</topic><topic>Upper bounds</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Hu, Guojun</creatorcontrib><creatorcontrib>Pan, Pengxiang</creatorcontrib><creatorcontrib>Liu, Suding</creatorcontrib><creatorcontrib>Yang, Ping</creatorcontrib><creatorcontrib>Xie, Runtao</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of combinatorial optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Hu, Guojun</au><au>Pan, Pengxiang</au><au>Liu, Suding</au><au>Yang, Ping</au><au>Xie, Runtao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The prize-collecting single machine scheduling with bounds and penalties</atitle><jtitle>Journal of combinatorial optimization</jtitle><stitle>J Comb Optim</stitle><date>2024-09-01</date><risdate>2024</risdate><volume>48</volume><issue>2</issue><artnum>12</artnum><issn>1382-6905</issn><eissn>1573-2886</eissn><abstract>This study investigates the prize-collecting single machine scheduling with bounds and penalties (PC-SMS-BP). In this problem, a set of
n
jobs and a single machine are considered, where each job
J
j
has a processing time
p
j
, a profit
π
j
and a rejection penalty
w
j
. The upper bound on the processing number is
U
. The objective of this study is to find a feasible schedule that minimizes the makespan of the accepted jobs and the total rejection penalty of the rejected jobs under the condition that the number of the accepted jobs does not exceed a given threshold
U
while the total profit of the accepted jobs does not fall below a specified profit bound
Π
. We first demonstrate that this problem is
NP
-hard. Then, a pseudo-polynomial time dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS) are proposed. Finally, numerical experiments are conducted to compare the effectiveness of the two proposed algorithms.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10878-024-01203-0</doi><orcidid>https://orcid.org/0009-0001-8267-8848</orcidid></addata></record> |
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| ispartof | Journal of combinatorial optimization, 2024-09, Vol.48 (2), Article 12 |
| issn | 1382-6905 1573-2886 |
| language | eng |
| recordid | cdi_proquest_journals_3093887014 |
| source | SpringerNature Journals |
| subjects | Algorithms Combinatorics Convex and Discrete Geometry Dynamic programming Fines & penalties Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Rejection Scheduling Theory of Computation Upper bounds |
| title | The prize-collecting single machine scheduling with bounds and penalties |
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