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A collaborative strategy for a three echelon supply chain with ramp type demand, deterioration and inflation

Author

Listed:
  • Narayan Singh
  • Bindu Vaish
  • Shiv Ray Singh

Abstract

A supply chain system has been investigated in which a single manufacturer procures raw mate- rials from a single supplier, processes them to produce finished products, and then delivers the products to a single retailer. The customer’s demand rate is assumed to be time-sensitive in nature (ramp type) that allows two-phase variation in the demand and production rate. Our adoption of ramp type demand reflects a real market demand for a newly launched product. Shortages are allowed with partial backlogging of demand (only for the retailer), i.e. the rest represent lost sales. The effects of inflation of the cost parameters and deterioration are also considered separately. We show that the total cost function is convex. Using this convexity, a simple algorithm is presented to determine the optimal order quantity and optimal cycle time for the total cost function. The results are discussed with numerical examples and particular cases of the model discussed briefly. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.

Suggested Citation

  • Narayan Singh & Bindu Vaish & Shiv Ray Singh, 2014. "A collaborative strategy for a three echelon supply chain with ramp type demand, deterioration and inflation," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(3), pages 77-100.
    • Handle: RePEc:wut:journl:v:3:y:2014:p:77-100:id:1101
    DOI: 10.5277/ord140305
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    References listed on IDEAS

    as
    1. Chern, Maw-Sheng & Yang, Hui-Ling & Teng, Jinn-Tsair & Papachristos, Sotiris, 2008. "Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation," European Journal of Operational Research, Elsevier, vol. 191(1), pages 127-141, November.
    2. Lo, Sh-Tyan & Wee, Hui-Ming & Huang, Wen-Chang, 2007. "An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 106(1), pages 248-260, March.
    3. Michael Resh & Moshe Friedman & Lineu C. Barbosa, 1976. "On a General Solution of the Deterministic Lot Size Problem with Time-Proportional Demand," Operations Research, INFORMS, vol. 24(4), pages 718-725, August.
    4. Pritibhushan Sinha, 2013. "Solving some deterministic finite horizon inventory models," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 23(1), pages 63-74.
    5. Manna, S.K. & Chaudhuri, K.S., 2006. "An EOQ model with ramp type demand rate, time dependent deterioration rate, unit production cost and shortages," European Journal of Operational Research, Elsevier, vol. 171(2), pages 557-566, June.
    6. S.R. Singh & Chaman Singh, 2010. "Supply chain model with stochastic lead time under imprecise partially backlogging and fuzzy ramp-type demand for expiring items," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 8(4), pages 511-522.
    7. Chung, Kun-Jen & Eduardo Cárdenas-Barrón, Leopoldo & Ting, Pin-Shou, 2014. "An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit," International Journal of Production Economics, Elsevier, vol. 155(C), pages 310-317.
    8. Tadeusz Galanc & Wiktor Kołwzan & Jerzy Pieronek, 2012. "A quantitative management support model of a certain production-supply system - boundary conditions," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 22(2), pages 5-13.
    9. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    10. Yang, P. C. & Wee, H. M., 2002. "A single-vendor and multiple-buyers production-inventory policy for a deteriorating item," European Journal of Operational Research, Elsevier, vol. 143(3), pages 570-581, December.
    11. Narayan Singh & Bindu Vaish & S.R. Singh, 2012. "An economic production lot-size (EPLS) model with rework and flexibility under allowable shortages," International Journal of Procurement Management, Inderscience Enterprises Ltd, vol. 5(1), pages 104-122.
    12. Skouri, K. & Konstantaras, I. & Papachristos, S. & Ganas, I., 2009. "Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate," European Journal of Operational Research, Elsevier, vol. 192(1), pages 79-92, January.
    13. Lo, Sh-Tyan & Wee, Hui-Ming & Huang, Wen-Chang, 2007. "An integrated production-inventory model with imperfect production processes and Weibull distribution deterioration under inflation," International Journal of Production Economics, Elsevier, vol. 106(2), pages 493-505, April.
    14. Iida, Tetsuo, 2001. "The infinite horizon non-stationary stochastic multi-echelon inventory problem and near-myopic policies," European Journal of Operational Research, Elsevier, vol. 134(3), pages 525-539, November.
    15. repec:wut:journl:v:2:y:2012:id:1047 is not listed on IDEAS
    16. He, Yong & Wang, Shou-Yang & Lai, K.K., 2010. "An optimal production-inventory model for deteriorating items with multiple-market demand," European Journal of Operational Research, Elsevier, vol. 203(3), pages 593-600, June.
    17. S.K. Goyal & S.R. Singh & Himani Dem, 2013. "Production policy for ameliorating/deteriorating items with ramp type demand," International Journal of Procurement Management, Inderscience Enterprises Ltd, vol. 6(4), pages 444-465.
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