Abstract
In this paper, we deal with the unrelated parallel machine scheduling problem in which our aim is to minimize the sum of earliness and tardiness penalties with respect to the restrictive common due date. Plateau and Rios-Solis in (Eur J Oper Res 201:729–736, 2009) utilized the power of 0–1 quadratic programming model with linear constraints in order to obtain approximate optimal solutions to this problem and two other parallel machine scheduling problems. We first show that their model suffers from some deficiencies that highly affect the feasibility of the model in real problems. We then modify their model to obviate these deficiencies. To apply our proposed quadratic model to the real problems, we apply the QCR convexification technique that has been used by Plateau and Rios-Solis in wrong way. We finally test our modified quadratic model on the problems of Plateau and Rios-Solis’s paper and some other problems.
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References
Baker K., Scudder G.: Sequencing with earliness and tardiness penalties: a review. Oper. Res. 38(1), 1–25 (2002)
Billionnt A., Elloumi S., Plateau M.-C.: Improving the performance of standard solvers for quadratic 0-1 programs by a tight convex reformulation: The QCR method. Discrete Appl. Math. 157(6), 1185–1197 (2009)
Biskup D., Feldmann M.: Benchmarks for scheduling on a single machine against restrictive and unrestrictive common due date. Comput. Oper. Res. 28(8), 787–801 (2001)
Feldmann M., Biskup D.: Single-machine scheduling for minimizing earliness–tardiness penalties by meta-heuristic approach. Comput. Ind. Eng. 44(2), 307–323 (2003)
Gordon V., Porth J., Chu A.: A survey of the state-of-the-art of common due date assignment and scheduling research. Eur. J. Oper. Res. 38(1), 1–25 (2002)
Pardalos P.M.: Continuous approaches to discrete optimization problems. In: Di Pillo, G., Giannessi, F. (eds) Nonlinear Optimization and Applications, pp. 313–328. Plenum Publishing, New Jersey (1996)
Pleateau M.-C., Rios-Solis Y.A.: Optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations. Eur. J. Oper. Res. 201, 729–736 (2010)
Ravetti M., Pardalos P.M., Robson Mateus G., Leite Rocha P.: Solving parallel machines scheduling problems with sequence-dependent setup times using variable neighborhood search. IMA J. Manag. Math. 18(2), 101–115 (2007)
Rocha P.L., Ravetti M., Robson Mateus G., Pardalos P.M.: Exact algorithms for a scheduling problem with unrelated parallel machines and sequence and machine-dependent setup times. Comput. Oper. Res. 35(4), 1250–1264 (2008)
Sourd F.: A reinforced Lagrangean relaxation for non-preemptive single machine problem. In: Tenth International Workshop on Project Management and Scheduling, pp. 330–334 (2006)
van den Akker M., Hoogeveen J., van den Veld S.: Combining column generation and Lagrangian relaxation to solve a single-machine common due date problem. INFORMS J. Comput. 14(1), 37–51 (2002)
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Beyranvand, M.S., Peyghami, M.R. & Ghatee, M. On the quadratic model for unrelated parallel machine scheduling problem with restrictive common due date. Optim Lett 6, 1897–1911 (2012). https://doi.org/10.1007/s11590-011-0385-0
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DOI: https://doi.org/10.1007/s11590-011-0385-0