Abstract
This paper focuses on a make-to-order production system, where rejection of some orders is inevitable due to limited production capacity. In such a system, accepting all orders may cause overloads, order delays, and customer dissatisfaction. For this reason, firms tend to reject some orders. The order acceptance and scheduling problem is defined as deciding simultaneously which orders to be selected and how to schedule these selected orders. An extension of this problem with sequence-dependent setup times and release dates has been rarely studied, and the existing studies suggest that setup activities wait for the release date to be performed. However, in real production environments this may not be the case. Therefore, this paper examines the relationships between setup times and release dates considering the overall scheduling literature. Previous scheduling studies define two different relationships concerning setup times and release dates. One of them considers setup time is completely dependent on release date, and the other one claims that they are completely independent. In this paper, a new relationship is addressed to propound that setup time may be partially dependent on the release date. The paper also proposes a new mixed integer linear programming formulation with O(n2) binary decision variables and O(n2) constraints. It includes a detailed computational analysis by solving available instances in the literature, which suggests that existing formulation can solve the test problems to optimality with up to 10 orders in a given time limit. Our proposed formulation, however, can solve the test problems to optimality with up to 50 orders within the same time limit. According to the findings, our approach seems to be more suitable for real-life applications, and the proposed formulation is extremely faster than the existing one.
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28 May 2021
A Correction to this paper has been published: https://doi.org/10.1007/s13369-021-05727-z
References
Rom, W.O.; Slotnick, S.A.: Order acceptance using genetic algorithms. Comput. Oper. Res. 36, 1758–1767 (2009)
Slotnick, S.A.: Order acceptance and scheduling: a taxonomy and review. Eur. J. Oper. Res. 212, 1–11 (2011)
Ostwald PF.: Cost estimating. In: Salvendy, G. (ed) Handbook of Industrial Engineering, 2nd edn, pp. 1263–1288 (1992)
Allahverdi, A.; Ng, C.T.; Cheng, T.E.; Kovalyov, M.Y.: A survey of scheduling problems with setup times or costs. Eur. J. Oper. Res. 187(3), 985–1032 (2008)
Allahverdi, A.; Gupta, J.N.; Aldowaisan, T.: A review of scheduling research involving setup considerations. Omega 27, 219–239 (1999)
Allahverdi, A.: The third comprehensive survey on scheduling problems with setup times/costs. Eur. J. Oper. Res. 246, 345–378 (2015)
Schutten, J.M.; Leussink, R.A.M.: Parallel machine scheduling with release dates, due dates and family setup times. Int. J. Prod. Econ. 46, 119–125 (1996)
Thevenin, S.; Zufferey, N.; Widmer, M.: Order acceptance and scheduling with earliness and tardiness penalties. J. Heuristics 22, 849–890 (2016)
Oğuz, C.; Salman, F.S.; Bilgintürk Yalçın, Z.: Order acceptance and scheduling decisions in make-to-order systems. Int. J. Prod. Econ. 125, 200–211 (2010)
Cesaret, B.; Oğuz, C.; Salman, F.S.: A tabu search algorithm for order acceptance and scheduling. Comput. Oper. Res. 39, 1197–1205 (2012)
Chen, C.; Yang, Z.; Tan, Y.; He, R.: Diversity controlling genetic algorithm for order acceptance and scheduling problem. Math. Probl. Eng. 2014, 1–11 (2014)
Lin, S.W.; Ying, K.C.: Increasing the total net revenue for single machine order acceptance and scheduling problems using an artificial bee colony algorithm. J. Oper. Res. Soc. 64, 293–311 (2014)
Nguyen, S.; Zhang, M.; Johnston, M.; Tan, K.C.: Learning reusable initial solutions for multi-objective order acceptance and scheduling problems with genetic programming. In: European Conference on Genetic Programming, pp. 157–168. Springer, Berlin (2014)
Nguyen, S.: A learning and optimizing system for order acceptance and scheduling. Int. J. Adv. Manuf. Technol. 86, 2021–2036 (2016)
Chaurasia, S.N.; Singh, A.: Hybrid evolutionary approaches for the single machine order acceptance and scheduling problem. Appl. Soft Comput. 52, 725–747 (2017)
Silva, Y.L.T.; Subramanian, A.; Pessoa, A.A.: Exact and heuristic algorithms for order acceptance and scheduling with sequence-dependent setup times. Comput. Oper. Res. 90, 142–160 (2018)
Ghosh, J.B.: Job selection in heavily loaded shop. Comput. Oper. Res. 24, 141–145 (1997)
Nogueira, T.H.; Carvalho, C.R.V.D.; Ravetti, M.G.; Souza, M.C.D.: Analysis of mixed integer programming formulations for single machine scheduling problems with sequence dependent setup times and release dates. Pesquisa Operacional 39, 109–154 (2019)
Bianco, L.; Dell’Olmo, P.; Giordani, S.: Flow shop no-wait scheduling with sequence dependent setup times and release dates. INFOR 37, 3–19 (1999)
Liu, Z.; Cheng, T.C.E.: Minimizing total completion time subject to job release dates and preemption penalties. J. Sched. 7, 313–327 (2004)
Nogueira, T.H.; Ramalhinho, H.L.; de Carvalho, C.R.; Ravetti, M.G.: A hybrid VNS-Lagrangean heuristic framework applied on single machine scheduling problem with sequence-dependent setup times, release dates and due dates. Optim. Lett. (2020). https://doi.org/10.1007/s11590-019-01525-7
Qamhan, M.A.; Qamhan, A.A.; Al-Harkan, I.M.; Alotaibi, Y.A.: Mathematical modeling and discrete firefly algorithm to optimize scheduling problem with release date, sequence-dependent setup time, and periodic maintenance. Math. Probl. Eng. 1–16 (2019)
Velez-Gallego, M.C.; Maya, J.; Montoya-Torres, J.R.: A beam search heuristic for scheduling a single machine with release dates and sequence dependent setup times to minimize the makespan. Comput. Oper. Res. 73, 132–140 (2016)
Balakrishnan, N.; Kanet, J.J.; Sridharan, S.V.: Early/tardy scheduling with sequence dependent setups on uniform parallel machines. Comput. Oper. Res. 26, 127–141 (1999)
Gharehgozli, A.H.; Tvakkoli-Moghaddam, R.; Zaerpour, N.: A fuzzy-mixed-integer goal programming model for a parallel-machine scheduling problem with sequence-dependent setup times and release dates. Robot. Comput. Integr. Manuf. 25, 853–859 (2009)
Lopes, M.J.P.; Carvalho, J.M.V.: A branch-and-price algorithm for scheduling parallel machines with sequence dependent setup times. Eur. J. Oper. Res. 176, 1508–1527 (2007)
Manne, A.S.: On the job-shop scheduling problem. INFORMS 8, 219–223 (1959)
Nessah, R.; Chu, C.; Yalaoui, F.: An exact method for Pm/sds, ri/∑ i = 1nCi problem. Comput. Oper. Res. 34, 2840–2848 (2007)
Allahverdi, A.; Soroush, H.M.: The significance of reducing setup times/setup costs. Eur. J. Oper. Res. 187, 978–984 (2008)
Stern, H.I.; Avivi, Z.: The selection and scheduling of textile orders. Eur. J. Oper. Res. 44, 11–16 (1990)
Slotnick, S.A.; Morton, T.E.: Order acceptance with weighted tardiness. Comput. Oper. Res. 34, 3029–3042 (2007)
Keskinocak, P.; Ravi, R.; Tayur, S.: Algorithms for reliable lead time quotation. GSIA Working Paper. Carnegie Mellon University, Pittsburgh, PA (1997)
Keskinocak, P.; Ravi, R.; Tayur, S.: Scheduling and reliable lead-time quotation for orders with availability intervals and lead-time sensitive revenues. Manag. Sci. 47, 264–279 (2001)
Lewis, H.F.; Slotnick, S.A.: Multi-period job selection: planning work loads to maximize profit. Comput. Oper. Res. 29, 1081–1098 (2002)
Charnsirisakskul, K.; Griffin, P.M.; Keskinocak, P.: Order selection and scheduling with leadtime flexibility. IIE Trans. 36, 697–707 (2004)
Charnsirisakskul, K.; Griffin, P.M.; Keskinocak, P.: Pricing and scheduling decisions with leadtime flexibility. Eur. J. Oper. Res. 171, 153–169 (2006)
Slotnick, S.A.; Morton, T.E.: Selecting jobs for a heavily loaded shop with lateness penalties. Comput. Oper. Res. 23, 131–140 (1996)
Yang, B.; Geunes, J.: A single resource scheduling problem with job-selection flexibility, tardiness costs and controllable processing times. Comput. Ind. Eng. 53, 420–432 (2007)
Nobibon, F.T.; Leus, R.: Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment. Comput. Oper. Res. 38, 367–378 (2011)
Reisi-Nafchi, M.; Moslehi, G.: A hybrid genetic and linear programming algorithm for two-agent order acceptance and scheduling problem. Appl. Soft Comput. 33, 37–47 (2015)
Wang, X.; Zhu, Q.; Cheng, T.C.E.: Subcontracting price schemes for order acceptance and scheduling. Omega 54, 1–10 (2015)
Hosteins, P.; Cordone, R.; Righini, G.: The prize-collecting scheduling problem with deadlines. Electron. Not. Discrete Math. 55, 57–60 (2016)
Garcia, C.: Resource-constrained scheduling with hard due windows and rejection penalties. Eng. Optim. 48, 1515–1528 (2016)
Trigos, F.; López, E.M.: Maximising profit for multiple-product, single-period, single-machine manufacturing under sequential set-up constraints that depend on lot size. Int. J. Prod. Res. 54, 1134–1151 (2016)
Xie, X.; Wang, X.: An enhanced ABC algorithm for single machine order acceptance and scheduling with class setups. Appl. Soft Comput. 44, 255–266 (2016)
Zandieh, M.; Roumani, M.: A biogeography-based optimization algorithm for order acceptance and scheduling. J. Ind. Prod. Eng. 34, 312–321 (2017)
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Bıçakcı, P.S., Kara, İ. & Sağır, M. Single-Machine Order Acceptance and Scheduling Problem Considering Setup Time and Release Date Relations. Arab J Sci Eng 46, 1549–1559 (2021). https://doi.org/10.1007/s13369-020-04759-1
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DOI: https://doi.org/10.1007/s13369-020-04759-1