Abstract
In this study we address several two-agent problems in which the measure criterion is to minimize the maximum cost or total weighted completion of all the jobs, while subject to an upper bound on the maximum cost of agent A. In term of minimizing the maximum cost of all the jobs subject to an upper bound on the maximum cost of agent A, we discuss some optimal properties and propose polynomial time solution algorithm to solve it. In term of minimizing the total weighted completion of all the jobs subject to an upper bound on the maximum cost of agent A, we analyze the complexity, show that this problem is NP-hard, and discuss it under special cases. In addition, for minimizing the total weighted completion of all the jobs subject to an upper bound on the makespan of agent A, we derive some dominance rules to be used in a branch-and-bound method and propose a heuristic for finding the optimal and near-optimal solution, respectively. A computational simulation is also provided to determine the performance of the proposed algorithms.
Similar content being viewed by others
References
Agnetis A, Mirchandani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242
Agnetis A, Pacciarelli D, Pacifici A (2007) Multi-agent single machine scheduling. Ann Oper Res 150:3–15
Agnetis A, Pascale G, Pacciarelli D (2009) A Lagrangian approach to single-machine scheduling problems with two competing agents. J Sched 12:401–415
Agnetis A, Billaut J-C, Gawiejnovicz S, Pacciarelli D, Soukhal A (2014) Multiagent scheduling. Models and algorithms. Springer, Berlin
Baker KR, Smith JC (2003) A multiple criterion model for machine scheduling. J Sched 6:7–16
Cheng SR (2014) Some new problems on two-agent scheduling to minimize the earliness costs. Int J Prod Econ 156:24–30
Cheng TCE, Ng CT, Yuan JJ (2006) Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theor Comput Sci 362:273–281
Cheng TCE, Ng CT, Yuan JJ (2008) Multi-agent scheduling on a single machine with max-form criteria. Eur J Oper Res 188:603–609
Cheng TCE, Cheng SR, Wu WH, Hsu PH, Wu CC (2011) A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations. Comput Ind Eng 60:534–541
Dao SD, Abhary K, Marian R (2016) An innovative model for resource scheduling in VCIM systems. Int J Oper Res. doi:10.1007/s12351-016-0252-y
Fan BQ, Cheng TCE (2016) Two-agent scheduling in a flowshop. Eur J Oper Res 252(2):376–384
Ng CT, Cheng CTE, Yuan JJ (2006) A note on the complexity of the two-agent scheduling on a single machine. J Comb Optim 12:387–394
Lei D (2015) Two-phase neighborhood search algorithm for two-agent hybrid flow shop scheduling problem. Appl Soft Comput 34:721–727
Luo W, Chen L, Zhang G (2012) Approximation schemes for two-machine flow shop scheduling with two agents. J Comb Optim 24(3):229–239
Lun YHV, Lai KH, Ng CT, Wong CWY, Cheng TCE (2011) Research in shipping and transport logistics. Int J Shipp Transp Logist 3:1–5
Li D-C, Hsu P-H (2012) Solving a two-agent single-machine scheduling problem considering learning effect. Comput Oper Res 39(7):1644–1651
Lee K, Choi BC, Leung JYT, Pinedo ML (2009) Approximation algorithms for multi-agent scheduling to minimize total weighted completion time. Inf Process Lett 109:913–917
Lee IS (2013) Minimizing total tardiness for the order scheduling problem. Int J Prod Econ 144:128–134
Leung JYT, Li H, Pinedo M (2006) Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel. Nav Res Logist 53:243–260
Mor B, Mosheiov G (2010) Scheduling problems with two competing agents to minimize minmax and minsum earliness measures. Eur J Oper Res 206:540–546
Pinedo M (2011) Scheduling: theory, algorithms and systems, 4th edn. Prentice-Hall, Englewood Cliffs
Riahi V, Kazemi M (2016) A new hybrid ant colony algorithm for scheduling of no-wait flowshop. Int J Oper Res. doi:10.1007/s12351-016-0253-x
Wan G, Vakati RS, Leung JYT, Pinedo M (2010) Scheduling two agents with controllable processing times. Eur J Oper Res 205:528–539
Wan L, Yuan J, Wei L (2016) Pareto optimization scheduling with two competing agents to minimize the number of tardy jobs and the maximum cost. Appl Math Comput 273:912–923
Wu WH, Cheng SR, Wu CC, Yin Y (2012) Ant colony algorithms for two-agent scheduling with sum-of-processing-times-based learning and deteriorating considerations. J Intell Manuf 23:1985–1993
Xu J, Wu C-C, Yin Y, Zhao CL, Chiou Y-T, Lin WC (2016) An order scheduling problem with position-based learning effect. Comput Oper Res 74:175–186
Yin Y, Wu W-H, Cheng S-R, Wu C-C (2012) An investigation on a two-agent single-machine scheduling problem with unequal release dates. Comput Oper Res 39(12):3062–3073
Yin Y, Cheng S-R, Cheng TCE, Wu W-H, Wu C-C (2013a) Two-agent single-machine scheduling with release times and deadlines. Int J Shipp Transp Logist 5(1):75–94
Yin Y, Wu C-C, Wu W-H, Hsu C-J, Wu W-H (2013b) A branch-and- bound procedure for a single-machine earliness scheduling problem with two agents. Appl Soft Comput 13(2):1042–1054
Yin Y, Cheng SR, Cheng TCE, Wang D-J, Wu C-C (2016a) Just-in-time scheduling with two competing agents on unrelated parallel machines. Omega 63:41–47
Yin Y, Wang Y, Cheng TCE, Wang D-J, Wu C-C (2016b) Two-agent single-machine scheduling to minimize the batch delivery cost. Comput Ind Eng 92:16–30
Yin Y, Cheng TCE, Wang D-J, Wu C-C (2015) Improved algorithms for single-machine serial-batch scheduling with rejection to minimize total completion time and total rejection cost. IEEE Trans Syst Man Cybern. doi:10.1109/TSMC.2015.2505644
Yin Y, Xu J, Cheng TCE, Wu C-C, Wang D-J (2016c) Approximation schemes for single-machine scheduling with a fixed maintenance activity to minimize the total amount of late work. Nav Res Logist 63:172–183
Yu X, Zhang Y, Xu D, Yin Y (2013) Single machine scheduling problem with two synergetic agents and piece-rate maintenance. Appl Math Model 37(1):1390–1399
Zhang F, Ng CT, Tang G, Cheng TCE, Lun YHV (2011) Inverse scheduling: applications in shipping. Int J Shipp Transp Logist 3:312–322
Zhang X, Wang Y (2016) Two-agent scheduling problems on a single-machine to minimize the total weighted late work. J Comb Optim. doi:10.1007/s10878-016-0017-9
Acknowledgments
We thank the Editor, an Associate Editor, and anonymous referees for their helpful comments on earlier versions of our paper. This paper was supported in part by the Ministry of Science Technology (MOST) of Taiwan under grant numbers MOST 105-2221-E-035-053-MY3 and MOST 103-2410-H-035-022-MY2.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cao, X., Wu, WH., Wu, WH. et al. Some two-agent single-machine scheduling problems to minimize minmax and minsum of completion times. Oper Res Int J 18, 293–314 (2018). https://doi.org/10.1007/s12351-016-0265-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12351-016-0265-6