Skip to main content

Multi-machine earliness and tardiness scheduling problem: an interconnected neural network approach

Abstract

This paper addresses the problem of scheduling a set of independent jobs with sequence-dependent setups and distinct due dates on non-uniform multi-machines to minimize the total weighted earliness and tardiness, and explores the use of artificial neural networks as a valid alternative to the traditional scheduling approaches. The objective is to propose a dynamical gradient neural network, which employs a penalty function approach with time varying coefficients for the solution of the problem which is known to be NP-hard. After the appropriate energy function was constructed, the dynamics are defined by steepest gradient descent on the energy function. The proposed neural network system is composed of two maximum neural networks, three piecewise linear and one log-sigmoid network all of which interact with each other. The motivation for using maximum networks is to reduce the network complexity and to obtain a simplified energy function. To overcome the tradeoff problem encountered in using the penalty function approach, a time varying penalty coefficient methodology is proposed to be used during simulation experiments. Simulation results of the proposed approach on a scheduling problem indicate that the proposed coupled network yields an optimal solution which makes it attractive for applications of larger sized problems.

This is a preview of subscription content, access via your institution.

References

  1. Kanet JJ (1981) Minimizing the average deviation of job completion times about a common due date. Nav Res Logist Q 28:643–651

    MATH  Article  Google Scholar 

  2. Sundararaghavan P, Ahmed MU (1984) Minimizing the sum of absolute lateness in single-machine and multimachine scheduling. Nav Res Logist Q 31:25–33

    Article  Google Scholar 

  3. Hall NG (1986) Single and multiple-processor models for minimizing completion time variance. Nav Res Logist Q 33:49–54

    MATH  Article  Google Scholar 

  4. Bagchi U, Sullivan RS, Chang YL (1986) Minimizing mean absolute deviation of completion times about a common due date. Nav Res Logist Q 33:227–240

    MATH  Article  MathSciNet  Google Scholar 

  5. Abdul-Razaq T, Potts C (1988) Dynamic programming state-space relaxation for single-machine scheduling. J Oper Res Soc 39:141–152

    MATH  Article  Google Scholar 

  6. Ow PS, Morton TE (1988) Filtered beam search in scheduling. Int J Prod Res 26:35–62

    Article  Google Scholar 

  7. Ow PS, Morton TE (1989) The single machine early/tardy problem. Manage Sci 35:177–191

    MATH  MathSciNet  Google Scholar 

  8. Sidney JB (1977) Optimal single machine scheduling with earliness and tardiness penalties. Oper Res 25(1):62–69

    MATH  MathSciNet  Google Scholar 

  9. Rachavachari M (1988) Scheduling problems with non-regular penalty functions-a review. Opsearch 25:144–164

    MathSciNet  Google Scholar 

  10. Baker KR, Scudder GD (1990) Sequencing with earliness and tardiness penalties: a review. Oper Res 38:22–36

    MATH  MathSciNet  Google Scholar 

  11. Arkin E, Roundy RO (1991) Weighted-tardiness scheduling on parallel machines with proportional weights. Oper Res 39:64–81

    MATH  MathSciNet  Google Scholar 

  12. De P, Ghosh JB, Wells CE (1994) Due dates and early/tardy scheduling on identical parallel machines. Nav Res Logist 41:17–32

    MATH  Article  MathSciNet  Google Scholar 

  13. Heady R, Zhu Z (1998) Minimizing the sum of job earliness and tardiness in a multimachine system. Int J Prod Res 36:1619–1632

    MATH  Article  Google Scholar 

  14. Sivrikaya-Serifoglu F, Ulusoy G (1999) Parallel machine scheduling with earliness and tardiness penalties. Comput Oper Res 26:773–787

    MATH  Article  MathSciNet  Google Scholar 

  15. Balakrishan N, Kanet JJ, Sridharan S’V (1999) Early/tardy scheduling with sequence dependent setups on uniform parallel machines. Comput Oper Res 26:127–141

    Article  MathSciNet  Google Scholar 

  16. Radhakrishnan S, Ventura JA (2000) Simulated annealing for parallel machine scheduling with earliness-tardiness penalties and sequence dependent setup times. Int J Oper Res 8:2233–2252

    Google Scholar 

  17. Sun H, Wang G (2003) Parallel machine earliness and tardiness scheduling with proportional weights. Comput Oper Res 30:801–808

    MATH  Article  Google Scholar 

  18. Garey MR, Tarjan RE, Wilfong GT (1988) One-processor scheduling with symmetric earliness and tardiness penalties. Math Oper Res 13:330–348

    MATH  MathSciNet  Google Scholar 

  19. Hopfield J, Tank TW (1985) Neural computation of decisions in optimization problems. Biol Cybern 52:141–152

    MATH  MathSciNet  Google Scholar 

  20. Zhou DN, Cherkassy V, Baldwin TR, Olson DE (1991) A neural network approach to job-shop scheduling. IEEE Trans Neural Netw 2:175–179

    Article  Google Scholar 

  21. Vaithyanathan S, Ignizio JP (1992) A stochastic neural network for resource constrained scheduling. Comput Oper Res 19:241–254

    Article  MATH  Google Scholar 

  22. Lo ZP, Bavarian B (1993) Multiple job scheduling with artificial neural Networks. Comput Electr Eng 19:87–101

    Article  Google Scholar 

  23. Satake T, Morikawa K, Nakamura N (1994) Neural network approach for minimizing the makespan of the general job-shop. Int J Prod Econ 33:67–74

    Article  Google Scholar 

  24. Foo SY, Takefuji YH, Szu H (1995) Scaling properties of neural networks for job-shop scheduling. Neurocomputing 8:79–91

    MATH  Article  Google Scholar 

  25. Willems TM, Brandts EMW (1995) Implementing heuristics as an optimization criterion in neural networks for job-shop scheduling. J Intell Manuf 6:377–387

    Article  Google Scholar 

  26. Chen M, Dong Y (1999) Applications of neural networks to solving SMT scheduling problems-a case study. Int J Prod Res 37:4007–4020

    MATH  Article  Google Scholar 

  27. Liansheng G, Gang S, Shuchun W (2000) Intelligent scheduling model and algorithm for manufacturing. Prod Plan Control 11:234–243

    Article  Google Scholar 

  28. Takefuji Y, Lee K-C, Aiso H (1992) An artificial maximum neural network: a winner-take-all neuron model forcing the state of the system in a solution domain. Biol Cybern 67(3):243–251

    MATH  Article  Google Scholar 

  29. Lee KC, Funabiki N, Takefuji Y (1992) A parallel improvement algorithm for the bipartite subgraph problem. IEEE Trans Neural Netw 3:139–145

    Article  Google Scholar 

  30. Lee KC, Takefuji Y (1992) A generalized maximum neural network for the module orientation problem. Int J Electron 72(3):331–355

    Article  Google Scholar 

  31. Takefuji Y (1992) Neural network parallel computing. Kluwer, Boston, MA

    MATH  Google Scholar 

  32. Funabiki N, Takenaka Y, Nishikawa S (1997) A maximum neural network approach for N-queens problem. Biol Cybern 76:251–255

    MATH  Article  Google Scholar 

  33. Chung PC, Tsai CT, Chen EL, Sun YN (1994) Polygonal approximation using a competitive Hopfield neural network. Pattern Recogn 27(11):1505–1512

    Article  Google Scholar 

  34. Galan-Marin G, Munoz-Perez J (2001) Design and analysis of maximum Hopfield networks. IEEE Trans Neural Netw 12(2):329–339

    Article  Google Scholar 

  35. Galan-Marin G, Merida-Casermeiro E, Munoz-Perez J (2003) Modelling competitive Hopfield networks for the maximum clique problem. Comput Oper Res 30:603–624

    MATH  Article  MathSciNet  Google Scholar 

  36. Fang L, Li T (1990) Design of competition based neural networks for combinatorial optimization. Int J Neural Syst 1(3):221–235

    Article  MathSciNet  Google Scholar 

  37. Sabuncuoglu I, Gurgun B (1996) A neural network model for scheduling problems. Eur J Oper Res 93:288–299

    MATH  Article  Google Scholar 

  38. Chen RM, Huang YM (2001) Competitive neural network to solve scheduling problems. Neurocomputing 37:177–196

    MATH  Article  Google Scholar 

  39. Min HS, Yih Y (2003) Selection of dispatching rules on multiple dispatching decision points in real-time scheduling of a semiconductor wafer fabrication system. Int J Prod Res 41(16):3921–3941

    MATH  Article  Google Scholar 

  40. Zhu Z, Heady RB (2000) Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach. Comput Ind Eng 38:297–305

    Article  Google Scholar 

  41. Hopfield J (1984) Neurons with graded response have collective computational properties like of two-state neurons. In: Proceedings of the National Academy of Sciences of the USA 81:3088–3092

  42. Sengor NS, Cakir Y, Guzelis C, Pekergin F, Morgul O (1999) An analysis of maximum clique formulations and saturated linear dynamical network. ARI 51:268–276

    Article  Google Scholar 

  43. Watta PB, Hassoun MH (1996) A coupled gradient network approach for static and temporal mixed-integer optimization. IEEE Trans Neural Netw 7:578–593

    Article  Google Scholar 

  44. Smith K (1999) Neural networks for combinatorial optimization: a review of more than a decade of research. INFORMS J Comput 11:15–34

    MATH  MathSciNet  Article  Google Scholar 

  45. Aiyer SVB, Niranjan M, Fallside F (1990) A theoretical investigation into the performance of the Hopfield model. IEEE Trans Neural Netw 1:204–215

    Article  Google Scholar 

  46. Brandt RD, Wang Y, Laub AJ, Mitra SK (1988) Alternative networks for solving the travelling salesman problem and the list-matching problem. In: Proceedings of the International Conference on Neural Networks 2:333–340

  47. Van Den Bout DE, Miller TK (1988) A traveling salesman objective function that works. In: Proceedings of IEEE International Conference on Neural Networks 2:299–303

  48. Hedge S, Sweet J, Levy W (1988) Determination of parameters in a Hopfield/Tank computational network. In: Proceedings IEEE International Conference on Neural Networks 2:291–298

  49. Kamgar-Parsi B, Kamgar-Parsi B (1992) Dynamical stability and parameter selection in neural optimization. In: Proceedings of International Joint Conference on Neural Networks 4:566–571

  50. Lai WK, Coghill GG (1992) Genetic breeding of control parameters for the Hopfield/Tank neural net. In: Proceedings of the International Joint Conference on Neural Networks 4:618–623

  51. Wang J (1991) A time-varying recurrent neural system for convex programming. In: Proceedings of IJCNN-91-Seattle International Joint Conference on Neural Networks, 147–152

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Derya Eren Akyol.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Akyol, D.E., Bayhan, G.M. Multi-machine earliness and tardiness scheduling problem: an interconnected neural network approach. Int J Adv Manuf Technol 37, 576–588 (2008). https://doi.org/10.1007/s00170-007-0993-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-007-0993-0

Keywords

  • Scheduling
  • Sequence-dependent setups
  • Earliness and tardiness
  • Neural networks