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Optimization of Threshold Control Parameters via Numerical Methods

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Optimal Control and Optimization of Stochastic Supply Chain Systems

Part of the book series: Advances in Industrial Control ((AIC))

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Abstract

This chapter presents numerical methods to optimize the threshold parameters. For the discounted cost, the value iteration algorithm is tailored to evaluate the performance under threshold control policies. Enumerative search method is then used to optimize the threshold parameters by utilizing the structural relationship between the threshold parameters. For the long-run average cost, both the value iteration algorithm and the stationary probability distribution are used to evaluate the performance under given threshold control policies and then further optimize the threshold parameters. The proposed numerical methods are applied to a range of different supply chain systems, and their computational performance is discussed. Finally, we address the robustness of threshold control policies in terms of their sensitivity to the system parameters.

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References

  • Avsar, Z.M., Zijm, W.H., Rodoplu, U.: An approximate model for base-stock-controlled assembly systems. IIE Trans. 41(3), 260–274 (2009)

    Article  Google Scholar 

  • Berg, M., Posner, M.J.M., Zhao, H.: Production-inventory systems with unreliable machines. Oper. Res. 42(1), 111–118 (1994)

    Article  MATH  Google Scholar 

  • Bertsekas, D.P.: Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Cliffs (1987)

    MATH  Google Scholar 

  • Bertsekas, D.P., Tsitsiklis, J.N.: Neuro-Dynamic Programming. Athena Scientific, Belmont (1996)

    MATH  Google Scholar 

  • Das, T.K., Sarkar, S.: Optimal preventive maintenance in a production inventory system. IIE Trans. 31, 537–551 (1999)

    Google Scholar 

  • Haji, R., Haji, A., Saffari, M.: Queueing inventory system in a two-level supply chain with one-for-one ordering policy. J. Ind. Syst. Eng. 5(1), 337–347 (2011)

    Google Scholar 

  • Johansen, S.G.: Base-stock policies for the lost sales inventory system with Poisson demand and Erlangian lead times. Int. J. Prod. Econ. 93–94(8), 429–437 (2005)

    Article  Google Scholar 

  • Liu, B., Cao, J.: Analysis of a production-inventory system with machine breakdowns and shutdowns. Comput. Oper. Res. 26(1), 73–91 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Powell, W.B.: Approximate Dynamic Programming: Solving the Curses of Dimensionality. Wiley, Hoboken (2007)

    Book  MATH  Google Scholar 

  • Powell, W.B., Ruszczynski, A., Topaloglu, H.: Learning algorithms for separable approximations of stochastic optimization problem. Math. Oper. Res. 29(4), 814–836 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York (1994)

    MATH  Google Scholar 

  • Sennott, L.I.: Stochastic Dynamic Programming and the Control of Queueing Systems. Wiley, New York (1999)

    MATH  Google Scholar 

  • Si, J., Barto, A., Powell, W.B., Wunsch, D.: Learning and Approximate Dynamic Programming: Scaling up to the Real World. Wiley, New York (2004)

    Book  Google Scholar 

  • Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. The MIT Press, Cambridge (1998)

    Google Scholar 

  • Topaloglu, H., Powell, W.B.: Dynamic programming approximations for stochastic, time-staged integer multicommodity flow problems. Informs J. Comput. 18(1), 31–42 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Topan, E., Avsar, Z.M.: An approximation for Kanban controlled assembly systems. Ann. Oper. Res. 182(1), 133–162 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Van Houtum, G.J., Zijm, W.H.M.: Computational procedures for stochastic multi-echelon production systems. Int. J. Prod. Econ. 23(1–3), 223–237 (1991)

    Article  Google Scholar 

  • Zhao, N., Lian, Z.T.: A queueing-inventory system with two classes of customers. Int. J. Prod. Econ. 129(1), 225–231 (2011)

    Article  MathSciNet  Google Scholar 

  • Zheng, Y., Zipkin, P.: A queueing model to analyze the value of centralized inventory information. Oper. Res. 38(2), 296–307 (1990)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Management, University of Plymouth, Drake Circus, PL4 8AA, Plymouth, UK

    Dong-Ping Song

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  1. Dong-Ping Song
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Correspondence to Dong-Ping Song .

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Song, DP. (2013). Optimization of Threshold Control Parameters via Numerical Methods. In: Optimal Control and Optimization of Stochastic Supply Chain Systems. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-4724-4_13

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  • DOI: https://doi.org/10.1007/978-1-4471-4724-4_13

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4723-7

  • Online ISBN: 978-1-4471-4724-4

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