Two-machine flow shop scheduling with a common due date to maximize total early work
•Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satis...
Saved in:
| Published in: | European journal of operational research Vol. 300; no. 2; pp. 504 - 511 |
|---|---|
| Main Authors: | , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
16.07.2022
|
| Subjects: | |
| ISSN: | 0377-2217, 1872-6860 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | •Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satisfied.
This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O(n2d2) time (compared with the previous result in O(n2d4) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied. |
|---|---|
| AbstractList | •Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully polynomial time approximation scheme (FPTAS) is developed.•The approximation results work for the weighted model - if a specific constraint is satisfied.
This paper considers scheduling in a two-machine flow shop to maximize the total early work subject to a common due date. The early work of a job is a parameter defined as the total amount of the job that is processed before the specified due date. We mainly focus on the unweighted model in this paper, and propose a dynamic programming approach running in O(n2d2) time (compared with the previous result in O(n2d4) time for the weighted case discussed in the literature). Then we analyse the problem from an approximation point of view, in which we first show that Johnson’s algorithm, one of the most classical ones in flow shop scheduling, can only achieve the worst performance ratio for the considered problem (although it is an optimal one for makespan minimization). With the motivation of proposing better approximation algorithms, we further design a fully polynomial time approximation scheme (FPTAS). Finally, we point out that the approximation results also work for the weighted model - if a specific constraint is satisfied. |
| Author | Chen, Xin Lin, Bertrand M.T. Blazewicz, Jacek Sterna, Malgorzata Miao, Qian |
| Author_xml | – sequence: 1 givenname: Xin surname: Chen fullname: Chen, Xin organization: Liaoning University of Technology, School of Electronics and Information Engineering, Shiying 169, Jinzhou 121001, China – sequence: 2 givenname: Qian surname: Miao fullname: Miao, Qian organization: Dalian University of Technology, School of Software, Tuqiang 321, Dalian 116023, China – sequence: 3 givenname: Bertrand M.T. orcidid: 0000-0003-0456-296X surname: Lin fullname: Lin, Bertrand M.T. email: bmtlin@mail.nctu.edu.tw organization: National Yang Ming Chiao Tung University, Institute of Information Management, Shinchu 300, Taiwan – sequence: 4 givenname: Malgorzata orcidid: 0000-0002-3845-8194 surname: Sterna fullname: Sterna, Malgorzata organization: Poznan University of Technology, Institute of Computing Science, Piotrowo 2, Poznan 60-965, Poland – sequence: 5 givenname: Jacek surname: Blazewicz fullname: Blazewicz, Jacek organization: Poznan University of Technology, Institute of Computing Science, Piotrowo 2, Poznan 60-965, Poland |
| BookMark | eNp90M9LwzAUwPEgE9ym_4Cn_AOtSbomGXiR4S8YeJnnkCWvNrVtRpI5519vyzx52CmPwOfB-87QpPc9IHRLSU4J5XdNDo0POSOM5kTkpCwv0JRKwTIuOZmgKSmEyBij4grNYmwIIbSk5RRtNgefddrUrgdctf6AY-13OJoa7L51_Qc-uFRjjY3vOt9juwdsdQKcPO70t-vczzgn3WLQoT3igw-f1-iy0m2Em793jt6fHjerl2z99vy6elhnpuBlyjRlCwNcm2q7gFJzaQ0vt2RJGcACDJeaySWxRkhZFWT4NIIvBdjKFpoPppgjdtprgo8xQKV2wXU6HBUlauyiGjV2UWMXRYQaugxI_kPGJZ2c71PQrj1P708UhqO-HAQVjYPegHUBTFLWu3P8FyH2gqg |
| CitedBy_id | crossref_primary_10_1287_ijoc_2023_0038 crossref_primary_10_1016_j_jmsy_2023_12_006 crossref_primary_10_1016_j_asoc_2024_111842 crossref_primary_10_1002_nav_22076 crossref_primary_10_46399_muhendismakina_1504239 crossref_primary_10_1080_0305215X_2024_2372633 crossref_primary_10_3390_math11194060 crossref_primary_10_1016_j_cie_2024_109915 |
| Cites_doi | 10.1016/j.omega.2010.06.006 10.1007/s10951-015-0464-7 10.1016/j.dam.2020.05.023 10.1080/00207543.2018.1456693 10.1080/0305215X.2018.1519073 10.1016/j.cie.2009.05.011 10.1016/j.cie.2005.09.001 10.1080/03052150500420439 10.1002/nav.21813 10.1016/j.cie.2020.106449 10.1016/S0166-218X(03)00339-1 10.1080/0305215X.2018.1554066 10.1007/s11590-011-0334-y 10.1007/978-3-540-30176-9_9 10.1016/S0167-5060(08)70356-X 10.1016/j.ejor.2020.03.032 10.1016/j.ejor.2019.12.003 10.1016/0167-6377(92)90001-J 10.1287/opre.40.3.586 10.1002/nav.21863 10.1002/nav.3800010110 10.1007/s10951-012-0303-z 10.1016/j.cor.2006.03.021 10.1016/j.omega.2021.102453 10.1016/j.ejor.2004.04.011 10.1002/nav.21936 10.1287/moor.19.1.86 10.1007/s10957-017-1147-7 10.1016/j.cie.2017.07.016 10.1002/nav.21684 |
| ContentType | Journal Article |
| Copyright | 2021 Elsevier B.V. |
| Copyright_xml | – notice: 2021 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.ejor.2021.07.055 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Computer Science Business |
| EISSN | 1872-6860 |
| EndPage | 511 |
| ExternalDocumentID | 10_1016_j_ejor_2021_07_055 S0377221721006652 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6OB 7-5 71M 8P~ 9JN 9JO AAAKF AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AARIN AAXUO AAYFN ABAOU ABBOA ABFNM ABFRF ABJNI ABMAC ABUCO ABYKQ ACAZW ACDAQ ACGFO ACGFS ACIWK ACNCT ACRLP ACZNC ADBBV ADEZE ADGUI AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIGVJ AIKHN AITUG AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR AXJTR BKOJK BKOMP BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HAMUX IHE J1W KOM LY1 M41 MHUIS MO0 MS~ N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. PQQKQ Q38 ROL RPZ RXW SCC SDF SDG SDP SDS SES SPC SPCBC SSB SSD SSV SSW SSZ T5K TAE TN5 U5U XPP ZMT ~02 ~G- 1OL 29G 41~ 9DU AAAKG AAQXK AATTM AAXKI AAYWO AAYXX ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADIYS ADJOM ADMUD ADNMO ADXHL AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AI. AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS EJD FEDTE FGOYB HVGLF HZ~ R2- SEW VH1 WUQ ~HD |
| ID | FETCH-LOGICAL-c365t-a124ce6acfb4e5a68dc65b0912ee4ec68a2890dc788f302eec7697edfd3a6fb43 |
| ISICitedReferencesCount | 10 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000819872700009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-2217 |
| IngestDate | Tue Nov 18 20:47:29 EST 2025 Sat Nov 29 07:20:29 EST 2025 Fri Feb 23 02:41:10 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Early and late work Dynamic programming Combinatorial optimization FPTAS Flow shop scheduling |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c365t-a124ce6acfb4e5a68dc65b0912ee4ec68a2890dc788f302eec7697edfd3a6fb43 |
| ORCID | 0000-0003-0456-296X 0000-0002-3845-8194 |
| PageCount | 8 |
| ParticipantIDs | crossref_primary_10_1016_j_ejor_2021_07_055 crossref_citationtrail_10_1016_j_ejor_2021_07_055 elsevier_sciencedirect_doi_10_1016_j_ejor_2021_07_055 |
| PublicationCentury | 2000 |
| PublicationDate | 2022-07-16 |
| PublicationDateYYYYMMDD | 2022-07-16 |
| PublicationDate_xml | – month: 07 year: 2022 text: 2022-07-16 day: 16 |
| PublicationDecade | 2020 |
| PublicationTitle | European journal of operational research |
| PublicationYear | 2022 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Wang, Yu, Qiu, Yin, Cheng (bib0032) 2020; 67 Błażewicz (bib0001) 1984; 3 Chen, Chau, Xie, Sterna, Błażewicz (bib0011) 2017; 111 Chen, Sterna, Han, Błażewicz (bib0015) 2016; 19 Kovalyov, Potts, Van Wassenhove (bib0022) 1994; 19 Yin, Yang, Wang, Cheng, Wu (bib0036) 2018; 65 Györgyi, Kis (bib0020) 2020; 286 Sterna, M. (2021). Late and early work scheduling: A survey. Omega, 104, 102453. Sterna, Czerniachowska (bib0031) 2017; 174 Chen, Kovalev, Liu, Sterna, Chalamon, Błażewicz (bib0012) 2021; 290 Lin, Lin, Lee (bib0024) 2006; 38 Błażewicz, Pesch, Sterna, Werner (bib0006) 2004; 134 Błażewicz, Pesch, Sterna, Werner (bib0008) 2005; 3698 Potts, Van Wassenhove (bib0026) 1992; 11 Potts, Van Wassenhove (bib0027) 1992; 40 Błażewicz, Ecker, Pesch, Sterna, Schmidt, Weglarz (bib0003) 2019 Wang, Ji, Cheng, Wang (bib0033) 2012; 6 Shabtay, Gaspar, Kaspi (bib0028) 2013; 16 Chen, Wang, Pesch, Sterna, Błażewicz (bib0017) 2019; 51 Chen, Kovalev, Sterna, Błażewicz (bib0013) 2020 Chen, Wang, Xie, Zhang, Sterna, Błażewicz (bib0016) 2020; 144 Błażewicz, Pesch, Sterna, Werner (bib0007) 2005; 49 Błażewicz, Chen, Lee, Lin, Lin, Pesch (bib0002) 2019; 51 Yin, Xu, Cheng, Wu, Wang (bib0035) 2016; 63 Johnson (bib0021) 1954; 1 Pesch, Sterna (bib0025) 2009; 57 Gerstl, Mor, Mosheiov (bib0018) 2019; 57 Chen, Liang, Sterna, Wang, Błażewicz (bib0014) 2020; 284 Leung (bib0023) 2004 Błażewicz, Pesch, Sterna, Werner (bib0005) 2004; 3285 Błażewicz, Pesch, Sterna, Werner (bib0004) 2000 Błażewicz, Pesch, Sterna, Werner (bib0010) 2008; 35 Sterna (bib0029) 2011; 39 Graham, Lawler, Lenstra, Kan (bib0019) 1979; 5 Xiong, Zhou, Yin, Cheng, Li (bib0034) 2019; 66 Błażewicz, Pesch, Sterna, Werner (bib0009) 2005; 165 Błażewicz (10.1016/j.ejor.2021.07.055_bib0004) 2000 10.1016/j.ejor.2021.07.055_bib0030 Pesch (10.1016/j.ejor.2021.07.055_bib0025) 2009; 57 Błażewicz (10.1016/j.ejor.2021.07.055_bib0002) 2019; 51 Kovalyov (10.1016/j.ejor.2021.07.055_bib0022) 1994; 19 Yin (10.1016/j.ejor.2021.07.055_bib0036) 2018; 65 Yin (10.1016/j.ejor.2021.07.055_bib0035) 2016; 63 Chen (10.1016/j.ejor.2021.07.055_bib0012) 2021; 290 Chen (10.1016/j.ejor.2021.07.055_bib0011) 2017; 111 Błażewicz (10.1016/j.ejor.2021.07.055_bib0007) 2005; 49 Chen (10.1016/j.ejor.2021.07.055_bib0017) 2019; 51 Leung (10.1016/j.ejor.2021.07.055_bib0023) 2004 Sterna (10.1016/j.ejor.2021.07.055_bib0031) 2017; 174 Chen (10.1016/j.ejor.2021.07.055_bib0016) 2020; 144 Wang (10.1016/j.ejor.2021.07.055_bib0033) 2012; 6 Sterna (10.1016/j.ejor.2021.07.055_bib0029) 2011; 39 Błażewicz (10.1016/j.ejor.2021.07.055_bib0001) 1984; 3 Györgyi (10.1016/j.ejor.2021.07.055_bib0020) 2020; 286 Lin (10.1016/j.ejor.2021.07.055_bib0024) 2006; 38 Błażewicz (10.1016/j.ejor.2021.07.055_bib0006) 2004; 134 Błażewicz (10.1016/j.ejor.2021.07.055_bib0008) 2005; 3698 Graham (10.1016/j.ejor.2021.07.055_bib0019) 1979; 5 Błażewicz (10.1016/j.ejor.2021.07.055_bib0005) 2004; 3285 Xiong (10.1016/j.ejor.2021.07.055_bib0034) 2019; 66 Wang (10.1016/j.ejor.2021.07.055_bib0032) 2020; 67 Błażewicz (10.1016/j.ejor.2021.07.055_bib0009) 2005; 165 Potts (10.1016/j.ejor.2021.07.055_bib0026) 1992; 11 Potts (10.1016/j.ejor.2021.07.055_bib0027) 1992; 40 Błażewicz (10.1016/j.ejor.2021.07.055_bib0003) 2019 Gerstl (10.1016/j.ejor.2021.07.055_bib0018) 2019; 57 Chen (10.1016/j.ejor.2021.07.055_bib0015) 2016; 19 Johnson (10.1016/j.ejor.2021.07.055_bib0021) 1954; 1 Shabtay (10.1016/j.ejor.2021.07.055_bib0028) 2013; 16 Chen (10.1016/j.ejor.2021.07.055_bib0013) 2020 Chen (10.1016/j.ejor.2021.07.055_bib0014) 2020; 284 Błażewicz (10.1016/j.ejor.2021.07.055_bib0010) 2008; 35 |
| References_xml | – volume: 57 start-page: 531 year: 2019 end-page: 543 ident: bib0018 article-title: Scheduling on a proportionate flowshop to minimise total late work publication-title: International Journal of Production Research – volume: 57 start-page: 1202 year: 2009 end-page: 1209 ident: bib0025 article-title: Late work minimization in flow shops by a genetic algorithm publication-title: Computers & Industrial Engineering – volume: 3 start-page: 415 year: 1984 end-page: 420 ident: bib0001 article-title: Scheduling preemptible tasks on parallel processors with information loss publication-title: Technique et Science Informatiques – volume: 39 start-page: 120 year: 2011 end-page: 129 ident: bib0029 article-title: A survey of scheduling problems with late work criteria publication-title: Omega – volume: 5 start-page: 287 year: 1979 end-page: 326 ident: bib0019 article-title: Optimization and approximation in deterministic sequencing and scheduling: A survey publication-title: Annals of Discrete Mathematics – volume: 19 start-page: 729 year: 2016 end-page: 736 ident: bib0015 article-title: Scheduling on parallel identical machines with late work criterion: Offline and online cases publication-title: Journal of Scheduling – volume: 174 start-page: 927 year: 2017 end-page: 944 ident: bib0031 article-title: Polynomial time approximation scheme for two parallel machines scheduling with a common due date to maximize early work publication-title: Journal of Optimization Theory and Applications – year: 2019 ident: bib0003 article-title: Handbook on scheduling. From theory to practice – volume: 63 start-page: 172 year: 2016 end-page: 183 ident: bib0035 article-title: Approximation schemes for single-machine scheduling with a fixed maintenance activity to minimize the total amount of late work publication-title: Naval Research Logistics – volume: 111 start-page: 176 year: 2017 end-page: 182 ident: bib0011 article-title: Complexity of late work minimization in flow shop systems and a particle swarm optimization algorithm for learning effect publication-title: Computers & Industrial Engineering – volume: 3698 start-page: 222 year: 2005 end-page: 234 ident: bib0008 article-title: Metaheuristics for late work minimization in two-machine flow shop with common due date publication-title: Lecture Notes in Artificial Intelligence – start-page: 354 year: 2000 end-page: 359 ident: bib0004 article-title: Total late work criteria for shop scheduling problems publication-title: Operations research proceedings – volume: 49 start-page: 611 year: 2005 end-page: 624 ident: bib0007 article-title: A comparison of solution procedures for two-machine flow shop scheduling with late work criterion publication-title: Computers & Industrial Engineering – volume: 144 start-page: 106449 year: 2020 ident: bib0016 article-title: Exact and heuristic algorithms for scheduling on two identical machines with early work maximization publication-title: Computers & Industrial Engineering – year: 2020 ident: bib0013 article-title: Mirror scheduling problems with early work and late work criteria publication-title: Journal of Scheduling – volume: 290 start-page: 71 year: 2021 end-page: 78 ident: bib0012 article-title: Semi-online scheduling on two identical machines with a common due date to maximize total early work publication-title: Discrete Applied Mathematics – volume: 165 start-page: 408 year: 2005 end-page: 415 ident: bib0009 article-title: The two-machine flow-shop problem with weighted late work criterion and common due date publication-title: European Journal of Operational Research – volume: 51 start-page: 1279 year: 2019 end-page: 1280 ident: bib0002 article-title: Clarification of lower bounds of two-machine flow-shop scheduling to minimize total late work publication-title: Engineering Optimization – volume: 66 start-page: 502 year: 2019 end-page: 516 ident: bib0034 article-title: An exact branch-and-price algorithm for multitasking scheduling on unrelated parallel machines publication-title: Naval Research Logistics – volume: 286 start-page: 129 year: 2020 end-page: 137 ident: bib0020 article-title: A common approximation framework for early work, late work, and resource leveling problems publication-title: European Journal of Operational Research – volume: 67 start-page: 573 year: 2020 end-page: 591 ident: bib0032 article-title: Two-agent scheduling with linear resource-dependent processing times publication-title: Naval Research Logistics – volume: 3285 start-page: 68 year: 2004 end-page: 75 ident: bib0005 article-title: Flow shop scheduling with late work criterion choosing the best solution strategy publication-title: Lecture Notes in Computer Science – volume: 51 start-page: 1268 year: 2019 end-page: 1278 ident: bib0017 article-title: Two-machine flow-shop scheduling to minimize total late work: Revisited publication-title: Engineering Optimization – reference: Sterna, M. (2021). Late and early work scheduling: A survey. Omega, 104, 102453. – volume: 65 start-page: 393 year: 2018 end-page: 409 ident: bib0036 article-title: Integrated production, inventory, and batch delivery scheduling with due date assignment and two competing agents publication-title: Naval Research Logistics – year: 2004 ident: bib0023 article-title: Minimizing total weighted error for imprecise computation tasks and related problems publication-title: Handbook of scheduling: Algorithms, models, and performance analysis – volume: 40 start-page: 586 year: 1992 end-page: 595 ident: bib0027 article-title: Single machine scheduling to minimize total late work publication-title: Operations Research – volume: 284 start-page: 67 year: 2020 end-page: 74 ident: bib0014 article-title: Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date publication-title: European Journal of Operational Research – volume: 19 start-page: 86 year: 1994 end-page: 93 ident: bib0022 article-title: A fully polynomial approximation scheme for scheduling a single machine to minimize total weighted late work publication-title: Mathematics of Operations Research – volume: 11 start-page: 261 year: 1992 end-page: 266 ident: bib0026 article-title: Approximation algorithms for scheduling a single machine to minimize total late work publication-title: Operations Research Letters – volume: 6 start-page: 1393 year: 2012 end-page: 1409 ident: bib0033 article-title: Minimizing makespan in a two-machine flow shop with effects of deterioration and learning publication-title: Optimization Letters – volume: 35 start-page: 574 year: 2008 end-page: 599 ident: bib0010 article-title: Metaheuristic approaches for the two-machine flow-shop problem with weighted late work criterion and common due date publication-title: Computers & Operations Research – volume: 38 start-page: 501 year: 2006 end-page: 509 ident: bib0024 article-title: Two-machine flow-shop scheduling to minimize total late work publication-title: Engineering Optimization – volume: 16 start-page: 3 year: 2013 end-page: 28 ident: bib0028 article-title: A survey on offline scheduling with rejection publication-title: Journal of Scheduling – volume: 134 start-page: 1 year: 2004 end-page: 24 ident: bib0006 article-title: Open shop scheduling problems with late work criteria publication-title: Discrete Applied Mathematics – volume: 1 start-page: 61 year: 1954 end-page: 68 ident: bib0021 article-title: Optimal two and three stage production schedules with setup times included publication-title: Naval Research Logistics Quarterly – start-page: 354 year: 2000 ident: 10.1016/j.ejor.2021.07.055_bib0004 article-title: Total late work criteria for shop scheduling problems – volume: 39 start-page: 120 issue: 2 year: 2011 ident: 10.1016/j.ejor.2021.07.055_bib0029 article-title: A survey of scheduling problems with late work criteria publication-title: Omega doi: 10.1016/j.omega.2010.06.006 – volume: 19 start-page: 729 issue: 6 year: 2016 ident: 10.1016/j.ejor.2021.07.055_bib0015 article-title: Scheduling on parallel identical machines with late work criterion: Offline and online cases publication-title: Journal of Scheduling doi: 10.1007/s10951-015-0464-7 – volume: 290 start-page: 71 year: 2021 ident: 10.1016/j.ejor.2021.07.055_bib0012 article-title: Semi-online scheduling on two identical machines with a common due date to maximize total early work publication-title: Discrete Applied Mathematics doi: 10.1016/j.dam.2020.05.023 – volume: 57 start-page: 531 issue: 2 year: 2019 ident: 10.1016/j.ejor.2021.07.055_bib0018 article-title: Scheduling on a proportionate flowshop to minimise total late work publication-title: International Journal of Production Research doi: 10.1080/00207543.2018.1456693 – volume: 3 start-page: 415 issue: 6 year: 1984 ident: 10.1016/j.ejor.2021.07.055_bib0001 article-title: Scheduling preemptible tasks on parallel processors with information loss publication-title: Technique et Science Informatiques – volume: 51 start-page: 1268 issue: 7 year: 2019 ident: 10.1016/j.ejor.2021.07.055_bib0017 article-title: Two-machine flow-shop scheduling to minimize total late work: Revisited publication-title: Engineering Optimization doi: 10.1080/0305215X.2018.1519073 – volume: 57 start-page: 1202 issue: 4 year: 2009 ident: 10.1016/j.ejor.2021.07.055_bib0025 article-title: Late work minimization in flow shops by a genetic algorithm publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2009.05.011 – volume: 49 start-page: 611 issue: 4 year: 2005 ident: 10.1016/j.ejor.2021.07.055_bib0007 article-title: A comparison of solution procedures for two-machine flow shop scheduling with late work criterion publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2005.09.001 – volume: 38 start-page: 501 issue: 04 year: 2006 ident: 10.1016/j.ejor.2021.07.055_bib0024 article-title: Two-machine flow-shop scheduling to minimize total late work publication-title: Engineering Optimization doi: 10.1080/03052150500420439 – volume: 65 start-page: 393 year: 2018 ident: 10.1016/j.ejor.2021.07.055_bib0036 article-title: Integrated production, inventory, and batch delivery scheduling with due date assignment and two competing agents publication-title: Naval Research Logistics doi: 10.1002/nav.21813 – volume: 144 start-page: 106449 year: 2020 ident: 10.1016/j.ejor.2021.07.055_bib0016 article-title: Exact and heuristic algorithms for scheduling on two identical machines with early work maximization publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2020.106449 – volume: 134 start-page: 1 issue: 1 year: 2004 ident: 10.1016/j.ejor.2021.07.055_bib0006 article-title: Open shop scheduling problems with late work criteria publication-title: Discrete Applied Mathematics doi: 10.1016/S0166-218X(03)00339-1 – volume: 51 start-page: 1279 issue: 7 year: 2019 ident: 10.1016/j.ejor.2021.07.055_bib0002 article-title: Clarification of lower bounds of two-machine flow-shop scheduling to minimize total late work publication-title: Engineering Optimization doi: 10.1080/0305215X.2018.1554066 – year: 2019 ident: 10.1016/j.ejor.2021.07.055_bib0003 – volume: 6 start-page: 1393 issue: 7 year: 2012 ident: 10.1016/j.ejor.2021.07.055_bib0033 article-title: Minimizing makespan in a two-machine flow shop with effects of deterioration and learning publication-title: Optimization Letters doi: 10.1007/s11590-011-0334-y – volume: 3285 start-page: 68 year: 2004 ident: 10.1016/j.ejor.2021.07.055_bib0005 article-title: Flow shop scheduling with late work criterion choosing the best solution strategy publication-title: Lecture Notes in Computer Science doi: 10.1007/978-3-540-30176-9_9 – year: 2020 ident: 10.1016/j.ejor.2021.07.055_bib0013 article-title: Mirror scheduling problems with early work and late work criteria publication-title: Journal of Scheduling – volume: 5 start-page: 287 year: 1979 ident: 10.1016/j.ejor.2021.07.055_bib0019 article-title: Optimization and approximation in deterministic sequencing and scheduling: A survey publication-title: Annals of Discrete Mathematics doi: 10.1016/S0167-5060(08)70356-X – volume: 286 start-page: 129 issue: 1 year: 2020 ident: 10.1016/j.ejor.2021.07.055_bib0020 article-title: A common approximation framework for early work, late work, and resource leveling problems publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2020.03.032 – volume: 284 start-page: 67 issue: 1 year: 2020 ident: 10.1016/j.ejor.2021.07.055_bib0014 article-title: Fully polynomial time approximation scheme to maximize early work on parallel machines with common due date publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2019.12.003 – volume: 11 start-page: 261 issue: 5 year: 1992 ident: 10.1016/j.ejor.2021.07.055_bib0026 article-title: Approximation algorithms for scheduling a single machine to minimize total late work publication-title: Operations Research Letters doi: 10.1016/0167-6377(92)90001-J – volume: 40 start-page: 586 issue: 3 year: 1992 ident: 10.1016/j.ejor.2021.07.055_bib0027 article-title: Single machine scheduling to minimize total late work publication-title: Operations Research doi: 10.1287/opre.40.3.586 – volume: 66 start-page: 502 year: 2019 ident: 10.1016/j.ejor.2021.07.055_bib0034 article-title: An exact branch-and-price algorithm for multitasking scheduling on unrelated parallel machines publication-title: Naval Research Logistics doi: 10.1002/nav.21863 – volume: 1 start-page: 61 issue: 1 year: 1954 ident: 10.1016/j.ejor.2021.07.055_bib0021 article-title: Optimal two and three stage production schedules with setup times included publication-title: Naval Research Logistics Quarterly doi: 10.1002/nav.3800010110 – volume: 16 start-page: 3 issue: 1 year: 2013 ident: 10.1016/j.ejor.2021.07.055_bib0028 article-title: A survey on offline scheduling with rejection publication-title: Journal of Scheduling doi: 10.1007/s10951-012-0303-z – volume: 35 start-page: 574 issue: 2 year: 2008 ident: 10.1016/j.ejor.2021.07.055_bib0010 article-title: Metaheuristic approaches for the two-machine flow-shop problem with weighted late work criterion and common due date publication-title: Computers & Operations Research doi: 10.1016/j.cor.2006.03.021 – ident: 10.1016/j.ejor.2021.07.055_bib0030 doi: 10.1016/j.omega.2021.102453 – volume: 165 start-page: 408 issue: 2 year: 2005 ident: 10.1016/j.ejor.2021.07.055_bib0009 article-title: The two-machine flow-shop problem with weighted late work criterion and common due date publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2004.04.011 – year: 2004 ident: 10.1016/j.ejor.2021.07.055_bib0023 article-title: Minimizing total weighted error for imprecise computation tasks and related problems – volume: 67 start-page: 573 year: 2020 ident: 10.1016/j.ejor.2021.07.055_bib0032 article-title: Two-agent scheduling with linear resource-dependent processing times publication-title: Naval Research Logistics doi: 10.1002/nav.21936 – volume: 3698 start-page: 222 year: 2005 ident: 10.1016/j.ejor.2021.07.055_bib0008 article-title: Metaheuristics for late work minimization in two-machine flow shop with common due date publication-title: Lecture Notes in Artificial Intelligence – volume: 19 start-page: 86 issue: 1 year: 1994 ident: 10.1016/j.ejor.2021.07.055_bib0022 article-title: A fully polynomial approximation scheme for scheduling a single machine to minimize total weighted late work publication-title: Mathematics of Operations Research doi: 10.1287/moor.19.1.86 – volume: 174 start-page: 927 issue: 3 year: 2017 ident: 10.1016/j.ejor.2021.07.055_bib0031 article-title: Polynomial time approximation scheme for two parallel machines scheduling with a common due date to maximize early work publication-title: Journal of Optimization Theory and Applications doi: 10.1007/s10957-017-1147-7 – volume: 111 start-page: 176 year: 2017 ident: 10.1016/j.ejor.2021.07.055_bib0011 article-title: Complexity of late work minimization in flow shop systems and a particle swarm optimization algorithm for learning effect publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2017.07.016 – volume: 63 start-page: 172 issue: 2 year: 2016 ident: 10.1016/j.ejor.2021.07.055_bib0035 article-title: Approximation schemes for single-machine scheduling with a fixed maintenance activity to minimize the total amount of late work publication-title: Naval Research Logistics doi: 10.1002/nav.21684 |
| SSID | ssj0001515 |
| Score | 2.447923 |
| Snippet | •Two-machine ow shop scheduling to maximize total early work is considered.•A dynamic programming approach running in O(n2d2) time is proposed.•A fully... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 504 |
| SubjectTerms | Combinatorial optimization Dynamic programming Early and late work Flow shop scheduling FPTAS |
| Title | Two-machine flow shop scheduling with a common due date to maximize total early work |
| URI | https://dx.doi.org/10.1016/j.ejor.2021.07.055 |
| Volume | 300 |
| WOSCitedRecordID | wos000819872700009&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: ScienceDirect Freedom Collection - Elsevier customDbUrl: eissn: 1872-6860 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001515 issn: 0377-2217 databaseCode: AIEXJ dateStart: 19950105 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3db9MwELfKhhA88FFAjC_5gbcoVePEcfw4TUOAYAKpSH2LHMeBVGlSZdlW7U_hr-Uc22k02MQeeIkiq3aT3q935_P97hB6x1hOCBfcV6D5_IgWmS-oCPyikAVheUKCOOubTbCTk2S55F8nk1-OC3NesbpOtlu--a-ihjEQtqbO3kLcw6IwAPcgdLiC2OH6b4K_aPx1nyKpvKJqLrzTn83Gg00sGJVqCL0KnUwOz-TlZ8rTu37thK7FtlyXl_pecyRVX_xYZ25dG7-3viwMtC6qaMsHDWHmI8v_WJYDDr-Uoo_Qfhth87NtHK_aru2TP2aL2RD-6aOWhlpU_WjaS0OoG8IVpE9tNWxKR9NizCfEEDadCg7n8xHWyEihUtOc2NpmahTzH2rfRCBWM7VqdI1XEpiCrHRn5NzB_hXbN2QkumS3VarXSPUa6ZylsMYdtE8Y5aAx9w8_Hi8_DXZeu4L9GZV9IUvJMtmDV5_k727PyJVZPEYP7R4EHxrsPEETVU_RPUeBmKJHrtUHtpp_ih6M6lY-RYsRxrDGGNYYwzuMYY0xLLDBGAaMYS0q3DXYYQz3GMM9xrDG2DP0_f3x4uiDb9tz-DKMaecLcA2lioUsskhRESe5jGkG_idRKlIyToQ-xM4lS5IinMOgZDFnKi_yUMQwJ3yO9uqmVi8QhulBmMRcRkJEUR7xDBRLxBSPFeciIwcocL9eKm3tet1CpUqvl9sB8oY5G1O55cZPUyeU1PqexqdMAWM3zHt5q295he7v_hOv0V7Xnqk36K4878rT9q0F2G9h7KjO |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Two-machine+flow+shop+scheduling+with+a+common+due+date+to+maximize+total+early+work&rft.jtitle=European+journal+of+operational+research&rft.au=Chen%2C+Xin&rft.au=Miao%2C+Qian&rft.au=Lin%2C+Bertrand+M.T.&rft.au=Sterna%2C+Malgorzata&rft.date=2022-07-16&rft.issn=0377-2217&rft.volume=300&rft.issue=2&rft.spage=504&rft.epage=511&rft_id=info:doi/10.1016%2Fj.ejor.2021.07.055&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_ejor_2021_07_055 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-2217&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-2217&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-2217&client=summon |