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The (p, q, r, l) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean


  • Sujit Kumar De

    () (Midnapore College (Autonomous))

  • Shib Sankar Sana

    () (Bhangar Mahavidyalaya)


Abstract This paper investigates a hill type economic production-inventory quantity (EPIQ) model with variable lead-time, order size and reorder point for uncertain demand. The average expected cost function is formulated by trading off costs of lead-time, inventory, lost sale and partial backordering. Due to the nature of the demand function, the frequent peak (maximum) and valley (minimum) of the expected cost function occur within a specific range of lead time. The aim of this paper is to search the lowest valley of all the valley points (minimum objective values) under fuzzy stochastic demand rate. We consider Intuitionistic fuzzy sets for the parameters and used Intuitionistic Fuzzy Aggregation Bonferroni mean for the defuzzification of the hill type EPIQ model. Finally, numerical examples and graphical illustrations are made to justify the model.

Suggested Citation

  • Sujit Kumar De & Shib Sankar Sana, 0. "The (p, q, r, l) model for stochastic demand under Intuitionistic fuzzy aggregation with Bonferroni mean," Journal of Intelligent Manufacturing, Springer, vol. 0, pages 1-19.
  • Handle: RePEc:spr:joinma:v::y::i::d:10.1007_s10845-016-1213-2
    DOI: 10.1007/s10845-016-1213-2

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    References listed on IDEAS

    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. 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.
    3. Fredrik Olsson, 2014. "Analysis of inventory policies for perishable items with fixed leadtimes and lifetimes," Annals of Operations Research, Springer, vol. 217(1), pages 399-423, June.
    4. Leopoldo Eduardo Cardenas-Barron & Neale R. Smith & Jose Luis Martinez-Flores & Marisela Rodriguez Salvador, 2010. "Modelling lead time effects on joint inventory and price optimisation," International Journal of Logistics Economics and Globalisation, Inderscience Enterprises Ltd, vol. 2(3), pages 270-291.
    5. Hsu, Shu-Lu & Lee, Chun Chen, 2009. "Replenishment and lead time decisions in manufacturer-retailer chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(3), pages 398-408, May.
    6. Sujit De & Shib Sana, 2015. "Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach," Annals of Operations Research, Springer, vol. 233(1), pages 57-76, October.
    7. Ouyang, Liang-Yuh & Wu, Kun-Shan, 1998. "A minimax distribution free procedure for mixed inventory model with variable lead time," International Journal of Production Economics, Elsevier, vol. 56(1), pages 511-516, September.
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