Abstract
In the past decade, multi-agent scheduling studies have become more widespread. However, the evaluation of these issues in the flow shop scheduling environment has received almost no attention. In this article, we investigate two problems. One problem is a common due date problem of constrained two-agent scheduling of jobs in a two-machine flow shop environment to minimize the weighted sum of maximum earliness and maximum tardiness of first-agent jobs and restrictions of non-eligibility on the tardiness of second-agent jobs. Another problem is a single-agent form of the two-agent problem when the number of second-agent jobs is zero. So, an optimal algorithm with polynomial time complexity is presented for the single-agent problem. For the two-agent problem, after it was shown to have minimum complexity of ordinary NP-hardness, a branch and bound algorithm, based on efficient lower and upper bounds and dominance rules, was developed. The computational results show that the algorithm can solve the large-size instances optimally.
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References
Agnetis A, Mirchandani PB, Pacciarelli D, Pacifici A (2004) Scheduling problems with two competing agents. Oper Res 52:229–242. https://doi.org/10.1287/opre.1030.0092
Agnetis A, Billaut J-C, Gawiejnowicz S, Pacciarelli D, Soukhal A (2014) Multiagent scheduling: models and algorithms. Springer, Berlin
Ahmadi-Darani MH, Moslehi G, Reisi-Nafchi M (2018) A two-agent scheduling problem in a two-machine flowshop. Int J Ind Eng Comput 9:289–306. https://doi.org/10.5267/j.ijiec.2017.8.005
Amin-Nayeri MR, Moslehi G (2000) Optimal algorithm for single machine sequencing to minimize early/tardy cost. Esteghlal J Eng 19:35–48 (In Persian)
Armentano VA, Ronconi R (1999) Tabu search for total tardiness minimization in flowshop scheduling problems. Comput Oper Res 26:219–235. https://doi.org/10.1016/S0305-0548(98)00060-4
Baker KR, Cole Smith J (2003) A multiple-criterion model for machine scheduling. J Sched 6:7–16. https://doi.org/10.1023/a:1022231419049
Benmansour R, Allaoui H, Artiba A, Hanafi S (2014) Minimizing the weighted sum of maximum earliness and maximum tardiness costs on a single machine with periodic preventive maintenance. Comput Oper Res 47:106–113. https://doi.org/10.1016/j.cor.2014.02.004
Chen R-X, Li S-S, Li W-J (2018) Multi-agent scheduling in a no-wait flow shop system to maximize the weighted number of just-in-time jobs. Eng Optim. https://doi.org/10.1080/0305215x.2018.1458844
Emmons H, Vairaktarakis G (2013) The two-machine flow shop. In: Flow shop scheduling: theoretical results, algorithms, and applications. Springer: New York
Fan BQ, Cheng TCE (2016) Two-agent scheduling in a flowshop. Eur J Oper Res 252:376–384. https://doi.org/10.1016/j.ejor.2016.01.009
Gelders LF, Sambandam N (1978) Four simple heuristics for scheduling a flow-shop. Int J Prod Res 16:221–231. https://doi.org/10.1080/00207547808930015
Graham RL, Lawler EL, Lenstra JK, Kan AHGR (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. In: Hammer PL, Korte BH (eds) Annals of discrete mathematics, vol 5. Elsevier, London, pp 287–326. https://doi.org/10.1016/S0167-5060(08)70356-X
Hamdi I, Loukil T (2015) Minimizing total tardiness in the permutation flowshop scheduling problem with minimal and maximal time lags. Oper Res Int Journal 15:95–114. https://doi.org/10.1007/s12351-014-0166-5
Hasija S, Rajendran C (2004) Scheduling in flowshops to minimize total tardiness of jobs. Int J Prod Res 42:2289–2301. https://doi.org/10.1080/00207540310001657595
Jeong B, Kim YD, Shim SO (2018) Algorithms for a two-machine flowshop problem with jobs of two classes. Int Trans Oper Res. https://doi.org/10.1111/itor.12530
Johnson SM (1954) Optimal two-and three-stage production schedules with setup times included. Naval Res Log Quart 1:61–68
Kim B-G, Choi B-C, Park M-J (2017) Two-machine and two-agent flow shop with special processing times structures. Asia-Pac J Oper Res 34:1750017
Lee WC, Chen SK, Wu CC (2010) Branch-and-bound and simulated annealing algorithms for a two-agent scheduling problem. Expert Syst Appl 37:6594–6601
Lee W-C, Chen S-K, Chen C-W, Wu C-C (2011) A two-machine flowshop problem with two agents. Comput Oper Res 38:98–104. https://doi.org/10.1016/j.cor.2010.04.002
Li Z, Zhong RY, Barenji AV, Liu JJ, Yu CX, Huang GQ (2019) Bi-objective hybrid flow shop scheduling with common due date. Oper Res Int J. https://doi.org/10.1007/s12351-019-00470-8
Luo W, Chen L, Zhang G (2012) Approximation schemes for two-machine flow shop scheduling with two agents. J Comb Optim 24:229–239. https://doi.org/10.1007/s10878-011-9378-2
Mahnam M, Moslehi G (2009) A branch-and-bound algorithm for minimizing the sum of maximum earliness and tardiness with unequal release times. Eng Optim 41:521–536. https://doi.org/10.1080/03052150802657290
Moslehi G, Mirzaee M, Vasei M, Modarres M, Azaron A (2009) Two-machine flow shop scheduling to minimize the sum of maximum earliness and tardiness. Int J Prod Econ 122:763–773. https://doi.org/10.1016/j.ijpe.2009.07.003
Moslehi G, Mahnam M, Amin-Nayeri M, Azaron A (2010) A branch-and-bound algorithm to minimise the sum of maximum earliness and tardiness in the single machine. Int J Oper Res 8:458–482
Perez-Gonzalez P, Framinan JM (2010) Setting a common due date in a constrained flowshop: a variable neighbourhood search approach. Comput Oper Res 37:1740–1748. https://doi.org/10.1016/j.cor.2010.01.002
Perez-Gonzalez P, Framinan JM (2014) A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems. Eur J Oper Res 235:1–16. https://doi.org/10.1016/j.ejor.2013.09.017
Rakrouki MA, Kooli A, Chalghoumi S, Ladhari T (2020) A branch-and-bound algorithm for the two-machine total completion time flowshop problem subject to release dates. Oper Res Int Journal 20:21–35. https://doi.org/10.1007/s12351-017-0308-7
Shiau Y-R, Tsai M-S, Lee W-C, Cheng TCE (2015) Two-agent two-machine flowshop scheduling with learning effects to minimize the total completion time. Comput Ind Eng 87:580–589. https://doi.org/10.1016/j.cie.2015.05.032
Tavakkoli-Moghaddam R, Moslehi G, Vasei M, Azaron A (2005) Optimal scheduling for a single machine to minimize the sum of maximum earliness and tardiness considering idle insert. Appl Math Comput 167:1430–1450. https://doi.org/10.1016/j.amc.2004.08.022
Yazdani M, Aleti A, Khalili SM, Jolai F (2017) Optimizing the sum of maximum earliness and tardiness of the job shop scheduling problem. Comput Ind Eng 107:12–24. https://doi.org/10.1016/j.cie.2017.02.019
Yin Y, Cheng TCE, Wang DJ, Wu CC (2017) Two-agent flowshop scheduling to maximize the weighted number of just-in-time jobs. J Sched 20:313–335. https://doi.org/10.1007/s10951-017-0511-7
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We would like to thank the anonymous referees; whose comments undoubtedly improved the manuscript.
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Nasrollahi, V., Moslehi, G. & Reisi-Nafchi, M. Minimizing the weighted sum of maximum earliness and maximum tardiness in a single-agent and two-agent form of a two-machine flow shop scheduling problem. Oper Res Int J 22, 1403–1442 (2022). https://doi.org/10.1007/s12351-020-00577-3
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DOI: https://doi.org/10.1007/s12351-020-00577-3