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Optimization of stochastic, (Q, R) inventory system in multi-product, multi-echelon, distributive supply chain

Author

Listed:
  • Debabrata Das

    (Asansol Engineering College
    National Institute of Technology)

  • Nirmal Baran Hui

    (National Institute of Technology)

  • Vipul Jain

    (Victoria University of Wellington)

Abstract

The key idea of the paper is the development of a probabilistic model for optimum inventory policy for a three-product, four-echelon, distributive system. The mathematical model is built based on integer policy of ordering in the deterministic part with continuous review inventory policy. It is found to be a non-linear multi-variable constrained optimization problem. For illustration purpose, demand is taken as stationery random one and lead time is normally distributed. A MATLAB program is generated to derive the solution based on exhaustive search method. Optimum lot sizes, safety stocks, reorder points, and service levels for each product at each stage are found out in accordance with continuous review inventory system. Further inventory turnover ratio computed is found to be reasonable and bubble plot of chosen service levels of different products with annual sales, profit margin, variability in demand, and lead time is obtained with expected characteristics. The proposed model along with the applied method of solving can find the best possible order quantity and ROP of a stochastic inventory system efficiently.

Suggested Citation

  • Debabrata Das & Nirmal Baran Hui & Vipul Jain, 2019. "Optimization of stochastic, (Q, R) inventory system in multi-product, multi-echelon, distributive supply chain," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(5), pages 405-418, October.
  • Handle: RePEc:pal:jorapm:v:18:y:2019:i:5:d:10.1057_s41272-019-00204-7
    DOI: 10.1057/s41272-019-00204-7
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    References listed on IDEAS

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    1. Kevin H. Shang & Jing-Sheng Song, 2003. "Newsvendor Bounds and Heuristic for Optimal Policies in Serial Supply Chains," Management Science, INFORMS, vol. 49(5), pages 618-638, May.
    2. Fangruo Chen & Yu-Sheng Zheng, 1994. "Lower Bounds for Multi-Echelon Stochastic Inventory Systems," Management Science, INFORMS, vol. 40(11), pages 1426-1443, November.
    3. Mark Daskin & Collette Coullard & Zuo-Jun Shen, 2002. "An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results," Annals of Operations Research, Springer, vol. 110(1), pages 83-106, February.
    4. Stephen C. Graves, 1985. "A Multi-Echelon Inventory Model for a Repairable Item with One-for-One Replenishment," Management Science, INFORMS, vol. 31(10), pages 1247-1256, October.
    5. Funaki, Kenichi, 2012. "Strategic safety stock placement in supply chain design with due-date based demand," International Journal of Production Economics, Elsevier, vol. 135(1), pages 4-13.
    6. Inderfurth, Karl, 1991. "Safety stock optimization in multi-stage inventory systems," International Journal of Production Economics, Elsevier, vol. 24(1-2), pages 103-113, November.
    7. Tsan-Ming Choi & Kannan Govindan & Xiang Li & Yongjian Li, 2017. "Innovative supply chain optimization models with multiple uncertainty factors," Annals of Operations Research, Springer, vol. 257(1), pages 1-14, October.
    8. Graves, Stephen C., 1987. "Safety stocks in manufacturing systems," Working papers 1894-87., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    9. Tempelmeier, Horst, 1993. "Safety stock allocation in a two-echelon distribution system," European Journal of Operational Research, Elsevier, vol. 65(1), pages 96-117, February.
    10. Zhou, Li & Grubbstrom, R.W.Robert W., 2004. "Analysis of the effect of commonality in multi-level inventory systems applying MRP theory," International Journal of Production Economics, Elsevier, vol. 90(2), pages 251-263, July.
    11. Diks, E. B. & de Kok, A. G. & Lagodimos, A. G., 1996. "Multi-echelon systems: A service measure perspective," European Journal of Operational Research, Elsevier, vol. 95(2), pages 241-263, December.
    12. Gérard P. Cachon & Marshall Fisher, 2000. "Supply Chain Inventory Management and the Value of Shared Information," Management Science, INFORMS, vol. 46(8), pages 1032-1048, August.
    13. Axsater, Sven, 2003. "Approximate optimization of a two-level distribution inventory system," International Journal of Production Economics, Elsevier, vol. 81(1), pages 545-553, January.
    14. Kevin Glazebrook & Colin Paterson & Sandra Rauscher & Thomas Archibald, 2015. "Benefits of Hybrid Lateral Transshipments in Multi-Item Inventory Systems under Periodic Replenishment," Production and Operations Management, Production and Operations Management Society, vol. 24(2), pages 311-324, February.
    15. Diks, E. B. & de Kok, A. G., 1998. "Optimal control of a divergent multi-echelon inventory system," European Journal of Operational Research, Elsevier, vol. 111(1), pages 75-97, November.
    16. Yu-Sheng Zheng, 1992. "On Properties of Stochastic Inventory Systems," Management Science, INFORMS, vol. 38(1), pages 87-103, January.
    17. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.
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