Abstract
We study the order acceptance and scheduling problem on two identical parallel machines. At the beginning of the planning horizon, a firm receives a set of customer orders, each of which has a revenue value, processing time, due date, and tardiness weight. The firm needs to select orders to accept and schedule the accepted orders on two identical parallel machines so as to maximize the total profit. The problem is intractable, so we develop two heuristics and an exact algorithm based on some optimal properties and the Lagrangian relaxation technique. We evaluate the performance of the proposed solution methods via computational experiments. The computational results show that the heuristics are efficient and effective in approximately solving large-sized instances of the problem, while the exact algorithm can only solve small-sized instances.
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References
Cesaret B, Oğuz C and Salman FS (2012). A tabu search algorithm for order acceptance and scheduling. Computers and Operations Research 39 (6): 1197–1205.
Emmons H (1969). One machine sequencing to minimize certain functions of job tardiness. Operations Research 17 (4): 701–715.
Fisher ML (1976). A dual algorithm for the one-machine scheduling problem. Mathematical Programming 11 (1): 229–231.
Gharbi A, Ladhari T, Msakni MK and Serairi M (2013). The two-machine flowshop scheduling problem with sequence-independent setup times: New lower bounding strategies. European Journal of Operational Research 231 (1): 69–78.
Ghosh JB (1997). Job selection in a heavily loaded shop. Computers and Operations Research 24 (2): 141–145.
Graham RL, Lawler EL, Lenstra JK and Rinnooy Kan AHG (1979). Optimization and approximation in deterministic sequencing and scheduling: A survey. Annals of Discrete Mathematics 5: 287–326.
Keskinocak P and Tayur S (2004). Due date management policies. In: Simchi-Levi D, Wu SD and Shen ZJ (eds). Handbook of Quantitative Supply Chain Analysis: Modeling in the E-business Era. Kluwer: Boston, MA, pp 485–547.
Lenstra JK, Rinnooy Kan AHG and Brucker P (1977). Complexity of machine scheduling problems. Annals of Discrete Mathematics 1: 343–362.
Lin S-W and Ying K-C (2013). Increasing the total net revenue for single machine order acceptance and scheduling problems using an artificial bee colony algorithm. Journal of the Operational Research Society 64 (2): 293–311.
Mao K, Pan Q-K, Pang XF and Chai T-Y (2014). A novel Lagrangian relaxation approach for a hybrid flowshop scheduling problem in the steelmaking-continuous casting process. European Journal of Operational Research 236 (1): 51–60.
Oğuz C, Salman FS and Yalcin ZB (2010). Order acceptance and scheduling decisions in make-to-order systems. International Journal of Production Economics 125 (1): 200–211.
Potts CN and van Wassenhove LN (1985). A branch and bound algorithm for the total weighted tardiness problem. Operations Research 33 (2): 363–377.
Rom WO and Slotnick SA (2009). Order acceptance using genetic algorithms. Computers and Operations Research 36 (6): 1758–1767.
Slotnick SA (2011). Order acceptance and scheduling: A taxonomy and review. European Journal of Operational Research 212 (1): 1–11.
Slotnick SA and Morton TE (1996). Selecting jobs for a heavily loaded shop with lateness penalties. Computers and Operations Research 23 (2): 131–140.
Slotnick SA and Morton TE (2007). Order acceptance with weighted tardiness. Computers and Operations Research 34 (10): 3029–3042.
Talla Nobibon F and Leus R (2011). Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment. Computers and Operations Research 38 (1): 367–378.
Tanaka S and Araki M (2008). A branch and bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines. International Journal of Production Economics 113 (1): 446–458.
Wang X-L, Xie X-Z and Cheng TCE (2013a). Order acceptance and scheduling in a two-machine flowshop. International Journal of Production Economics 141 (1): 366–376.
Wang X-L, Xie X-Z and Cheng TCE (2013b). A modified artificial bee colony algorithm for order acceptance in two-machine flow shops. International Journal of Production Economics 141 (1): 14–23.
Wang X-L, Zhu Q-Q and Cheng TCE (2015). Subcontracting price schemes for order acceptance and scheduling, Omega, The International Journal of Management Science. http://dx.doi.org/10.1016/j.omega.2015.01.005.
Acknowledgements
We thank the Editor, an Associate Editor, and five anonymous referees for their helpful comments on an earlier version of our paper. Wang was supported in part by the National Natural Science Foundation of China under grant number 71171114. Cheng was supported in part by the National Natural Science Foundation of China under grant number 71390334.
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Wang, X., Huang, G., Hu, X. et al. Order acceptance and scheduling on two identical parallel machines. J Oper Res Soc 66, 1755–1767 (2015). https://doi.org/10.1057/jors.2015.3
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DOI: https://doi.org/10.1057/jors.2015.3