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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Elsevier B.V
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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