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Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index

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  • De, Sujit Kumar
  • Sana, Shib Sankar

Abstract

The article deals with a backorder EOQ (Economic Order Quantity) model with promotional index for fuzzy decision variables. Here, a profit function is developed where the function itself is the function of m-th power of promotional index (PI) and the order quantity, shortage quantity and the PI are the decision variables. The demand rate is operationally related to PI variables and the model has been split into two types for the multiplication and addition operation. First the crisp profit function is optimized, letting it free from fuzzy decision variable. Yager (1981) ranking index method is utilized here to have a best inventory policy for the fuzzy model. Finally, a graphical presentation of numerical illustrations and sensitivity analysis are done to justify the general model.

Suggested Citation

  • De, Sujit Kumar & Sana, Shib Sankar, 2013. "Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index," Economic Modelling, Elsevier, vol. 31(C), pages 351-358.
    • Handle: RePEc:eee:ecmode:v:31:y:2013:i:c:p:351-358
    DOI: 10.1016/j.econmod.2012.11.046
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    References listed on IDEAS

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    1. Ravi Shankar Kumar & S.K. De & A. Goswami, 2012. "Fuzzy EOQ models with ramp type demand rate, partial backlogging and time dependent deterioration rate," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 4(5), pages 473-502.
    2. Harish Krishnan & Roman Kapuscinski & David A. Butz, 2004. "Coordinating Contracts for Decentralized Supply Chains with Retailer Promotional Effort," Management Science, INFORMS, vol. 50(1), pages 48-63, January.
    3. Cárdenas-Barrón, Leopoldo Eduardo, 2007. "Optimizing inventory decisions in a multi-stage multi-customer supply chain: A note," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 647-654, September.
    4. Wu, Kweimei & Yao, Jing-Shing, 2003. "Fuzzy inventory with backorder for fuzzy order quantity and fuzzy shortage quantity," European Journal of Operational Research, Elsevier, vol. 150(2), pages 320-352, October.
    5. Vujosevic, Mirko & Petrovic, Dobrila & Petrovic, Radivoj, 1996. "EOQ formula when inventory cost is fuzzy," International Journal of Production Economics, Elsevier, vol. 45(1-3), pages 499-504, August.
    6. Xie, Jinxing & Wei, Jerry C., 2009. "Coordinating advertising and pricing in a manufacturer-retailer channel," European Journal of Operational Research, Elsevier, vol. 197(2), pages 785-791, September.
    7. Szmerekovsky, Joseph G. & Zhang, Jiang, 2009. "Pricing and two-tier advertising with one manufacturer and one retailer," European Journal of Operational Research, Elsevier, vol. 192(3), pages 904-917, February.
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    Citations

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    Cited by:

    1. Prasenjit Pramanik & Manas Kumar Maiti & Manoranjan Maiti, 2018. "An appropriate business strategy for a sale item," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 85-106, March.
    2. Hardik N. Soni & Dipali N. Suthar, 2020. "Optimal pricing and replenishment policy for non-instantaneous deteriorating items with varying rate of demand and partial backlogging," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 986-1021, September.
    3. Udayan Chanda & Alok Kumar, 2019. "Optimization of EOQ Model for New Products Under Multi-Stage Adoption Process," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 1-25, April.
    4. Pal, Shilpi & Mahapatra, G.S. & Samanta, G.P., 2015. "A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness," Economic Modelling, Elsevier, vol. 46(C), pages 334-345.
    5. Sujit Kumar De & Shib Sankar Sana, 2018. "The (p, q, r, l) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean," Journal of Intelligent Manufacturing, Springer, vol. 29(8), pages 1753-1771, December.
    6. Anushri Maji & Asoke Kumar Bhunia & Shyamal Kumar Mondal, 2022. "A production-reliability-inventory model for a series-parallel system with mixed strategy considering shortage, warranty period, credit period in crisp and stochastic sense," OPSEARCH, Springer;Operational Research Society of India, vol. 59(3), pages 862-907, September.

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