Coordinated order scheduling and outsourcing on dedicated parallel machines
In this paper we investigate two order scheduling problems with bundled operations on m dedicated parallel machines when outsourcing is allowed. In the first problem, the objective is to minimize the makespan of the accepted jobs (orders) subject to the constraint that the total rejection (outsourci...
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| Vydáno v: | European journal of operational research |
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01.09.2025
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| Abstract | In this paper we investigate two order scheduling problems with bundled operations on m dedicated parallel machines when outsourcing is allowed. In the first problem, the objective is to minimize the makespan of the accepted jobs (orders) subject to the constraint that the total rejection (outsourcing) cost is no more than a budget. In the second problem, the objective is to minimize the makespan of accepted jobs plus the total rejection cost of rejected jobs. We show that the first problem cannot be approximated within a factor less than 2 in polynomial time, unless P = NP. For each of the two problems when m is fixed, we present a quasi-linear-time FPTAS (fully polynomial time approximation scheme). For the second problem when m=2, we develop a faster FPTAS by an interesting problem transformation and advanced rounding method.
•Coordinated order scheduling and outsourcing on dedicated machines in parallel.•No polynomial-time (2-ϵ)-approximation algorithm for the bounded problem.•Quasi-linear-time FPTASes when the number of machines is fixed.•Faster FPTAS for the unbounded problem with two machines.•Interesting problem transformation and advanced rounding method. |
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| AbstractList | In this paper we investigate two order scheduling problems with bundled operations on m dedicated parallel machines when outsourcing is allowed. In the first problem, the objective is to minimize the makespan of the accepted jobs (orders) subject to the constraint that the total rejection (outsourcing) cost is no more than a budget. In the second problem, the objective is to minimize the makespan of accepted jobs plus the total rejection cost of rejected jobs. We show that the first problem cannot be approximated within a factor less than 2 in polynomial time, unless P = NP. For each of the two problems when m is fixed, we present a quasi-linear-time FPTAS (fully polynomial time approximation scheme). For the second problem when m=2, we develop a faster FPTAS by an interesting problem transformation and advanced rounding method.
•Coordinated order scheduling and outsourcing on dedicated machines in parallel.•No polynomial-time (2-ϵ)-approximation algorithm for the bounded problem.•Quasi-linear-time FPTASes when the number of machines is fixed.•Faster FPTAS for the unbounded problem with two machines.•Interesting problem transformation and advanced rounding method. |
| Author | Zhong, Xueling Li, Weidong Ou, Jinwen |
| Author_xml | – sequence: 1 givenname: Jinwen orcidid: 0000-0002-7419-3808 surname: Ou fullname: Ou, Jinwen email: toujinwen@jnu.edu.cn organization: School of Management, Jinan University, Guangzhou, 510632, People’s Republic of China – sequence: 2 givenname: Weidong surname: Li fullname: Li, Weidong email: weidong@ynu.edu.cn organization: School of Mathematics and Statistics, Yunnan University, Kunming 650504, People’s Republic of China – sequence: 3 givenname: Xueling orcidid: 0000-0002-5702-5837 surname: Zhong fullname: Zhong, Xueling email: tzhongxl@gduf.edu.cn organization: School of Computer Science, Guangdong University of Finance, Guangzhou 510521, People’s Republic of China |
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| Cites_doi | 10.1007/s00291-015-0409-8 10.1007/s10878-023-01032-7 10.1016/j.ejor.2025.01.034 10.1137/S0895480196300522 10.1016/0167-6377(93)90041-E 10.1007/s10288-016-0303-5 10.1007/s10288-016-0339-6 10.1016/j.ejor.2021.11.043 10.1007/s10951-020-00657-4 10.1007/s10878-020-00649-2 10.1016/j.ejor.2010.09.042 10.1016/0377-2217(93)90347-P 10.1007/s11590-023-02073-x 10.1145/3618260.3649730 10.1016/j.ejor.2014.09.028 10.1016/S0377-2217(99)00261-1 10.1016/j.ejor.2017.04.036 10.1016/j.tcs.2015.10.007 10.1007/s40305-022-00430-8 10.1007/s10288-017-0356-0 10.1016/j.ejor.2008.10.006 10.1016/j.tcs.2010.02.006 10.1007/s10951-012-0303-z 10.1016/S0377-2217(00)00229-0 10.1287/opre.43.2.346 10.1080/00207160.2019.1711373 10.1016/j.ejor.2018.04.033 10.1145/3577530.3577568 10.1007/s00453-016-0116-0 |
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| Keywords | Bundled operation Dedicated machines Approximation algorithm FPTAS Order scheduling |
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| References | Kellerer, Pferschy, Pisinger (b15) 2004 Megiddo, Tamir (b19) 1993; 13 (pp. 283–294). Ou (b20) 2020; 23 Caprara, Kellerer, Pferschy, Pisinger (b6) 2000; 123 Chen, L., Lian, J. Y., Mao, Y. C., & Zhang, G. C. (2024). A nearly quadratic-time FPTAS for knapsack. In Zhang, Lu, Yuan (b30) 2016; 38 Agnetis, Billaut, Pinedo, Shabtay (b1) 2025; 327 Dai, Li (b9) 2020; 97 Bansal, Oosterwijk, Vredeveld, Zwaan (b2) 2016; 76 Zhang, Lu, Yuan (b28) 2009; 198 Li, Cui (b16) 2018; 16 Garey, Johnson (b12) 1979 Wagneur, Sriskandarajah (b27) 1993; 71 Shabtay, Gaspar, Kaspi (b24) 2013; 16 Framinan, Perez-Gonzalez, Fernandez-Viagas (b10) 2019; 273 He, Leung, Lee, Pinedo (b13) 2016; 14 Hou, Zheng, Liu, Du, Gao (b14) 2024; 18 Ou, Zhong (b21) 2015; 241 Frederix (b11) 2001; 129 Sun, R. Q., & Deng, B. (2022). W-prize-collecting scheduling problem on a single machine. In (pp. 237–242). Chen, Li (b7) 2020; 40 Li, Li, Zhang, Chen (b17) 2015; 607 Boysen, Schulze, Scholl (b4) 2022; 301 Zheng, Gao, Liu, Hou (b31) 2024; 12 Slotnick (b25) 2011; 212 Potts, Sevastjanov, Strusevich, Van Wassenhove, Zwaneveld (b23) 1995; 43 Ou, Zhong (b22) 2017; 262 Bartal, Leonardi, Marchetti-Spaccamela, Sgall, Stougie (b3) 2000; 13 Zhong, Ou (b32) 2017; 15 Liu, Xiao, Li, Zhu, Ma (b18) 2023; 45 Zhang, Lu, Yuan (b29) 2010; 411 Cacchiani, Iori, Locatelli, Martello (b5) 2022; 143 Cacchiani (10.1016/j.ejor.2025.08.035_b5) 2022; 143 Kellerer (10.1016/j.ejor.2025.08.035_b15) 2004 He (10.1016/j.ejor.2025.08.035_b13) 2016; 14 Garey (10.1016/j.ejor.2025.08.035_b12) 1979 Liu (10.1016/j.ejor.2025.08.035_b18) 2023; 45 10.1016/j.ejor.2025.08.035_b26 Zhang (10.1016/j.ejor.2025.08.035_b30) 2016; 38 Ou (10.1016/j.ejor.2025.08.035_b20) 2020; 23 Li (10.1016/j.ejor.2025.08.035_b17) 2015; 607 Ou (10.1016/j.ejor.2025.08.035_b21) 2015; 241 Slotnick (10.1016/j.ejor.2025.08.035_b25) 2011; 212 Zhang (10.1016/j.ejor.2025.08.035_b29) 2010; 411 10.1016/j.ejor.2025.08.035_b8 Megiddo (10.1016/j.ejor.2025.08.035_b19) 1993; 13 Ou (10.1016/j.ejor.2025.08.035_b22) 2017; 262 Zhong (10.1016/j.ejor.2025.08.035_b32) 2017; 15 Bansal (10.1016/j.ejor.2025.08.035_b2) 2016; 76 Chen (10.1016/j.ejor.2025.08.035_b7) 2020; 40 Zhang (10.1016/j.ejor.2025.08.035_b28) 2009; 198 Agnetis (10.1016/j.ejor.2025.08.035_b1) 2025; 327 Boysen (10.1016/j.ejor.2025.08.035_b4) 2022; 301 Framinan (10.1016/j.ejor.2025.08.035_b10) 2019; 273 Zheng (10.1016/j.ejor.2025.08.035_b31) 2024; 12 Frederix (10.1016/j.ejor.2025.08.035_b11) 2001; 129 Bartal (10.1016/j.ejor.2025.08.035_b3) 2000; 13 Dai (10.1016/j.ejor.2025.08.035_b9) 2020; 97 Li (10.1016/j.ejor.2025.08.035_b16) 2018; 16 Shabtay (10.1016/j.ejor.2025.08.035_b24) 2013; 16 Caprara (10.1016/j.ejor.2025.08.035_b6) 2000; 123 Potts (10.1016/j.ejor.2025.08.035_b23) 1995; 43 Wagneur (10.1016/j.ejor.2025.08.035_b27) 1993; 71 Hou (10.1016/j.ejor.2025.08.035_b14) 2024; 18 |
| References_xml | – volume: 15 start-page: 387 year: 2017 end-page: 406 ident: b32 article-title: Improved approximation algorithms for parallel machine scheduling with release dates and rejection publication-title: 4OR. A Quarterly Journal of Operations Research – volume: 76 start-page: 1077 year: 2016 end-page: 1096 ident: b2 article-title: Approximating vector scheduling: Almost matching upper and lower bounds publication-title: Algorithmica – reference: Chen, L., Lian, J. Y., Mao, Y. C., & Zhang, G. C. (2024). A nearly quadratic-time FPTAS for knapsack. In – volume: 97 start-page: 2507 year: 2020 end-page: 2515 ident: b9 article-title: Vector scheduling with rejection on two machines publication-title: International Journal of Computer Mathematics – volume: 607 start-page: 181 year: 2015 end-page: 192 ident: b17 article-title: Penalty cost constrained identical parallel machine scheduling problem publication-title: Theoretical Computer Science – reference: Sun, R. Q., & Deng, B. (2022). W-prize-collecting scheduling problem on a single machine. In – volume: 273 start-page: 401 year: 2019 end-page: 417 ident: b10 article-title: Deterministic assembly scheduling problems: A review and classification of concurrent-type scheduling models and solution procedures publication-title: European Journal of Operational Research – volume: 241 start-page: 653 year: 2015 end-page: 661 ident: b21 article-title: An improved heuristic for parallel machine scheduling with rejection publication-title: European Journal of Operational Research – reference: (pp. 283–294). – volume: 212 start-page: 1 year: 2011 end-page: 11 ident: b25 article-title: Order acceptance and scheduling: A taxonomy and review publication-title: European Journal of Operational Research – volume: 43 start-page: 346 year: 1995 end-page: 355 ident: b23 article-title: The two-stage assembly scheduling problem: Complexity and approximation publication-title: Operations Research – volume: 123 start-page: 333 year: 2000 end-page: 345 ident: b6 article-title: Approximation algorithms for knapsack problems with cardinality constraints publication-title: European Journal of Operational Research – volume: 71 start-page: 366 year: 1993 end-page: 378 ident: b27 article-title: Openshops with jobs overlap publication-title: European Journal of Operational Research – volume: 12 start-page: 495 year: 2024 end-page: 504 ident: b31 article-title: An approximation algorithm for the parallel-machine customer order scheduling with delivery time and submodular rejection penalties publication-title: Journal of the Operations Research Society of China – volume: 262 start-page: 904 year: 2017 end-page: 907 ident: b22 article-title: Bicriteria order acceptance and scheduling with consideration of fill rate publication-title: European Journal of Operational Research – reference: (pp. 237–242). – volume: 411 start-page: 1877 year: 2010 end-page: 1882 ident: b29 article-title: Single-machine scheduling under the job rejection constraint publication-title: Theoretical Computer Science – volume: 13 start-page: 203 year: 1993 end-page: 211 ident: b19 article-title: Linear time algorithms for some separable quadratic programming problems publication-title: Operations Research Letters – volume: 198 start-page: 975 year: 2009 end-page: 978 ident: b28 article-title: Single machine scheduling with release dates and rejection publication-title: European Journal of Operational Research – volume: 301 start-page: 797 year: 2022 end-page: 814 ident: b4 article-title: Assembly line balancing: What happened in the last fifteen years? publication-title: European Journal of Operational Research – volume: 38 start-page: 519 year: 2016 end-page: 529 ident: b30 article-title: Two-machine open-shop scheduling with rejection to minimize the makespan publication-title: OR Spectrum – volume: 16 start-page: 95 year: 2018 end-page: 104 ident: b16 article-title: Vector scheduling with rejection on a single machine publication-title: 4OR. A Quarterly Journal of Operations Research – volume: 23 start-page: 525 year: 2020 end-page: 538 ident: b20 article-title: Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection publication-title: Journal of Scheduling – volume: 14 start-page: 41 year: 2016 end-page: 55 ident: b13 article-title: Improved algorithms for single machine scheduling with release dates and rejections publication-title: 4OR. A Quarterly Journal of Operations Research – volume: 13 start-page: 64 year: 2000 end-page: 78 ident: b3 article-title: Multi-processor scheduling with rejection publication-title: SIAM Journal on Discrete Mathematics – volume: 45 year: 2023 ident: b18 article-title: Algorithms for single machine scheduling problem with release dates and submodular penalties publication-title: Journal of Combinatorial Optimization – volume: 16 start-page: 3 year: 2013 end-page: 28 ident: b24 article-title: A survey on offline scheduling with rejection publication-title: Journal of Scheduling – volume: 143 year: 2022 ident: b5 article-title: Knapsack problems – An overview of recent advances. Part II: Multiple, multidimensional, and quadratic knapsack problems publication-title: Computers & Operations Research – volume: 40 start-page: 1044 year: 2020 end-page: 1064 ident: b7 article-title: Minimizing maximum delivery completion time for order scheduling with rejection publication-title: Journal of Combinatorial Optimization – volume: 129 start-page: 317 year: 2001 end-page: 325 ident: b11 article-title: An extended enterprise planning methodology for the discrete manufacturing industry publication-title: European Journal of Operational Research – year: 2004 ident: b15 article-title: Knapsack problems – volume: 18 start-page: 1747 year: 2024 end-page: 1754 ident: b14 article-title: Improved approximation algorithm for the parallel machine customer order scheduling with delivery time and submodular rejection penalties publication-title: Optimization Letters – volume: 327 start-page: 367 year: 2025 end-page: 393 ident: b1 article-title: Fifty years of research in scheduling – Theory and applications publication-title: European Journal of Operational Research – year: 1979 ident: b12 article-title: Computers and intractability: a guide to the theory of NP-completeness – volume: 38 start-page: 519 year: 2016 ident: 10.1016/j.ejor.2025.08.035_b30 article-title: Two-machine open-shop scheduling with rejection to minimize the makespan publication-title: OR Spectrum doi: 10.1007/s00291-015-0409-8 – volume: 143 year: 2022 ident: 10.1016/j.ejor.2025.08.035_b5 article-title: Knapsack problems – An overview of recent advances. Part II: Multiple, multidimensional, and quadratic knapsack problems publication-title: Computers & Operations Research – volume: 45 year: 2023 ident: 10.1016/j.ejor.2025.08.035_b18 article-title: Algorithms for single machine scheduling problem with release dates and submodular penalties publication-title: Journal of Combinatorial Optimization doi: 10.1007/s10878-023-01032-7 – year: 2004 ident: 10.1016/j.ejor.2025.08.035_b15 – volume: 327 start-page: 367 issue: 2 year: 2025 ident: 10.1016/j.ejor.2025.08.035_b1 article-title: Fifty years of research in scheduling – Theory and applications publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2025.01.034 – volume: 13 start-page: 64 issue: 1 year: 2000 ident: 10.1016/j.ejor.2025.08.035_b3 article-title: Multi-processor scheduling with rejection publication-title: SIAM Journal on Discrete Mathematics doi: 10.1137/S0895480196300522 – volume: 13 start-page: 203 issue: 4 year: 1993 ident: 10.1016/j.ejor.2025.08.035_b19 article-title: Linear time algorithms for some separable quadratic programming problems publication-title: Operations Research Letters doi: 10.1016/0167-6377(93)90041-E – volume: 14 start-page: 41 year: 2016 ident: 10.1016/j.ejor.2025.08.035_b13 article-title: Improved algorithms for single machine scheduling with release dates and rejections publication-title: 4OR. A Quarterly Journal of Operations Research doi: 10.1007/s10288-016-0303-5 – volume: 15 start-page: 387 year: 2017 ident: 10.1016/j.ejor.2025.08.035_b32 article-title: Improved approximation algorithms for parallel machine scheduling with release dates and rejection publication-title: 4OR. A Quarterly Journal of Operations Research doi: 10.1007/s10288-016-0339-6 – volume: 301 start-page: 797 issue: 3 year: 2022 ident: 10.1016/j.ejor.2025.08.035_b4 article-title: Assembly line balancing: What happened in the last fifteen years? publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2021.11.043 – volume: 23 start-page: 525 issue: 6 year: 2020 ident: 10.1016/j.ejor.2025.08.035_b20 article-title: Near-linear-time approximation algorithms for scheduling a batch-processing machine with setups and job rejection publication-title: Journal of Scheduling doi: 10.1007/s10951-020-00657-4 – volume: 40 start-page: 1044 year: 2020 ident: 10.1016/j.ejor.2025.08.035_b7 article-title: Minimizing maximum delivery completion time for order scheduling with rejection publication-title: Journal of Combinatorial Optimization doi: 10.1007/s10878-020-00649-2 – volume: 212 start-page: 1 issue: 1 year: 2011 ident: 10.1016/j.ejor.2025.08.035_b25 article-title: Order acceptance and scheduling: A taxonomy and review publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2010.09.042 – volume: 71 start-page: 366 issue: 3 year: 1993 ident: 10.1016/j.ejor.2025.08.035_b27 article-title: Openshops with jobs overlap publication-title: European Journal of Operational Research doi: 10.1016/0377-2217(93)90347-P – year: 1979 ident: 10.1016/j.ejor.2025.08.035_b12 – volume: 18 start-page: 1747 year: 2024 ident: 10.1016/j.ejor.2025.08.035_b14 article-title: Improved approximation algorithm for the parallel machine customer order scheduling with delivery time and submodular rejection penalties publication-title: Optimization Letters doi: 10.1007/s11590-023-02073-x – ident: 10.1016/j.ejor.2025.08.035_b8 doi: 10.1145/3618260.3649730 – volume: 241 start-page: 653 year: 2015 ident: 10.1016/j.ejor.2025.08.035_b21 article-title: An improved heuristic for parallel machine scheduling with rejection publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2014.09.028 – volume: 123 start-page: 333 issue: 2 year: 2000 ident: 10.1016/j.ejor.2025.08.035_b6 article-title: Approximation algorithms for knapsack problems with cardinality constraints publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(99)00261-1 – volume: 262 start-page: 904 year: 2017 ident: 10.1016/j.ejor.2025.08.035_b22 article-title: Bicriteria order acceptance and scheduling with consideration of fill rate publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2017.04.036 – volume: 607 start-page: 181 issue: 2 year: 2015 ident: 10.1016/j.ejor.2025.08.035_b17 article-title: Penalty cost constrained identical parallel machine scheduling problem publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2015.10.007 – volume: 12 start-page: 495 year: 2024 ident: 10.1016/j.ejor.2025.08.035_b31 article-title: An approximation algorithm for the parallel-machine customer order scheduling with delivery time and submodular rejection penalties publication-title: Journal of the Operations Research Society of China doi: 10.1007/s40305-022-00430-8 – volume: 16 start-page: 95 year: 2018 ident: 10.1016/j.ejor.2025.08.035_b16 article-title: Vector scheduling with rejection on a single machine publication-title: 4OR. A Quarterly Journal of Operations Research doi: 10.1007/s10288-017-0356-0 – volume: 198 start-page: 975 year: 2009 ident: 10.1016/j.ejor.2025.08.035_b28 article-title: Single machine scheduling with release dates and rejection publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2008.10.006 – volume: 411 start-page: 1877 year: 2010 ident: 10.1016/j.ejor.2025.08.035_b29 article-title: Single-machine scheduling under the job rejection constraint publication-title: Theoretical Computer Science doi: 10.1016/j.tcs.2010.02.006 – volume: 16 start-page: 3 issue: 1 year: 2013 ident: 10.1016/j.ejor.2025.08.035_b24 article-title: A survey on offline scheduling with rejection publication-title: Journal of Scheduling doi: 10.1007/s10951-012-0303-z – volume: 129 start-page: 317 issue: 2 year: 2001 ident: 10.1016/j.ejor.2025.08.035_b11 article-title: An extended enterprise planning methodology for the discrete manufacturing industry publication-title: European Journal of Operational Research doi: 10.1016/S0377-2217(00)00229-0 – volume: 43 start-page: 346 issue: 2 year: 1995 ident: 10.1016/j.ejor.2025.08.035_b23 article-title: The two-stage assembly scheduling problem: Complexity and approximation publication-title: Operations Research doi: 10.1287/opre.43.2.346 – volume: 97 start-page: 2507 issue: 12 year: 2020 ident: 10.1016/j.ejor.2025.08.035_b9 article-title: Vector scheduling with rejection on two machines publication-title: International Journal of Computer Mathematics doi: 10.1080/00207160.2019.1711373 – volume: 273 start-page: 401 issue: 2 year: 2019 ident: 10.1016/j.ejor.2025.08.035_b10 article-title: Deterministic assembly scheduling problems: A review and classification of concurrent-type scheduling models and solution procedures publication-title: European Journal of Operational Research doi: 10.1016/j.ejor.2018.04.033 – ident: 10.1016/j.ejor.2025.08.035_b26 doi: 10.1145/3577530.3577568 – volume: 76 start-page: 1077 issue: 4 year: 2016 ident: 10.1016/j.ejor.2025.08.035_b2 article-title: Approximating vector scheduling: Almost matching upper and lower bounds publication-title: Algorithmica doi: 10.1007/s00453-016-0116-0 |
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