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Sensitivity analysis in inventory models by means of ergodicity coefficients

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  • Rabta, Boualem

Abstract

We investigate the sensitivity of a class of (s,S) inventory models with respect to the perturbation of the demand distribution in terms of ergodicity coefficients. Ergodicity coefficients can be regarded as matrix norms that are useful to study qualitative as well as quantitative properties of some classes of stochastic systems. We obtain estimations of the absolute deviation of the stationary vector of the underlying Markov chain subject to perturbations. The particular structure of the transition matrix of this class of models allows us to derive simple closed form formulae for the computation of the ergodicity coefficients as well as the perturbation bounds. The perturbation bounds obtained can help us to decide whether or not the model remains an acceptable representation of the real system and thus decide whether or not it can be trusted for real life applications. Under perturbation, e.g. estimation errors or approximations, an optimal solution for the mathematical model may not be optimal for the real system and if implemented, the real performance measures may deteriorate considerably and deviate from the targeted values. Numerical examples are given to illustrate how the perturbation of the demand distribution may have a considerable impact on the optimal inventory policy and the performance measures in some cases. In a practical setting, the understanding of the sensitivity results for inventory models can help us to identify the parameters that have to be estimated with most attention and how to build models that are robust and as close as possible to the real systems they represent.

Suggested Citation

  • Rabta, Boualem, 2017. "Sensitivity analysis in inventory models by means of ergodicity coefficients," International Journal of Production Economics, Elsevier, vol. 188(C), pages 63-71.
    • Handle: RePEc:eee:proeco:v:188:y:2017:i:c:p:63-71
    DOI: 10.1016/j.ijpe.2017.03.014
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    References listed on IDEAS

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    1. Ray, J. & Chaudhuri, K. S., 1997. "An EOQ model with stock-dependent demand, shortage, inflation and time discounting," International Journal of Production Economics, Elsevier, vol. 53(2), pages 171-180, November.
    2. Bogataj, L. & Cibej, J. A., 1994. "Perturbations in living stock and similar biological inventory systems," International Journal of Production Economics, Elsevier, vol. 35(1-3), pages 233-239, June.
    3. Bogataj, Marija & Bogataj, Ludvik, 2004. "On the compact presentation of the lead times perturbations in distribution networks," International Journal of Production Economics, Elsevier, vol. 88(2), pages 145-155, March.
    4. Yang, Gino K., 2007. "Note on sensitivity analysis of inventory model with partial backorders," European Journal of Operational Research, Elsevier, vol. 177(2), pages 865-871, March.
    5. Khanra, Avijit & Soman, Chetan & Bandyopadhyay, Tathagata, 2014. "Sensitivity analysis of the newsvendor model," European Journal of Operational Research, Elsevier, vol. 239(2), pages 403-412.
    6. Rabta, Boualem & AIssani, Djamil, 2005. "Strong stability in an (R,s,S) inventory model," International Journal of Production Economics, Elsevier, vol. 97(2), pages 159-171, August.
    7. Gregory Dobson, 1988. "Sensitivity of the EOQ Model to Parameter Estimates," Operations Research, INFORMS, vol. 36(4), pages 570-574, August.
    8. Ray, Pradip K. & Sahu, S., 1992. "Productivity measurement in multi-product manufacturing firms: Evaluation and control through sensitivity analysis," International Journal of Production Economics, Elsevier, vol. 28(1), pages 71-84, November.
    9. Matheus, Peter & Gelders, Ludo, 2000. "The (R, Q) inventory policy subject to a compound Poisson demand pattern," International Journal of Production Economics, Elsevier, vol. 68(3), pages 307-317, December.
    10. Chu, Peter & Chung, Kun-Jen, 2004. "The sensitivity of the inventory model with partial backorders," European Journal of Operational Research, Elsevier, vol. 152(1), pages 289-295, January.
    11. Borgonovo, E. & Peccati, L., 2011. "Finite change comparative statics for risk-coherent inventories," International Journal of Production Economics, Elsevier, vol. 131(1), pages 52-62, May.
    12. Borgonovo, E. & Peccati, L., 2007. "Global sensitivity analysis in inventory management," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 302-313, July.
    13. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    14. Butler, John & Jia, Jianmin & Dyer, James, 1997. "Simulation techniques for the sensitivity analysis of multi-criteria decision models," European Journal of Operational Research, Elsevier, vol. 103(3), pages 531-546, December.
    15. Paul Glasserman & Sridhar Tayur, 1995. "Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems," Management Science, INFORMS, vol. 41(2), pages 263-281, February.
    16. Borgonovo, E., 2010. "Sensitivity analysis with finite changes: An application to modified EOQ models," European Journal of Operational Research, Elsevier, vol. 200(1), pages 127-138, January.
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