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Application of Generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment

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  • Majumder, Pinki
  • Mondal, Sankar Prasad
  • Bera, Uttam Kumar
  • Maiti, Manoranjan

Abstract

In this present study, a production inventory model with partial trade credit is formulated and solved in fuzzy environment via Generalized Hukuhara derivative approach. To capture the market, a supplier offers a trade credit period to its retailers. Due to this facility, retailer also offers a partial trade credit period to his/her customer to boost the demand of the item. In practical life situation, demands are generally dependent upon time. Constant demand of an item varies time to time. In this vague situation, demands are taken as time dependent, where its constant part is taken as Left Right - type fuzzy number. In this paper, Generalized Hukuhara derivative approach is used to solve the fuzzy inventory model. Four different cases are considered by using Generalized Hukuhara-(i) differentiability and Generalized Hukuhara-(ii) differentiability. The objective of this paper is to find out the optimal time so as the total inventory cost is minimum. Finally the model is solved by generalized reduced gradient method. The proposed model and technique are illustrated by numerical examples. Some sensitivity analyses both in tabular and graphical forms are presented and the effects of minimum cost with respect to various inventory parameters are discussed.

Suggested Citation

  • Majumder, Pinki & Mondal, Sankar Prasad & Bera, Uttam Kumar & Maiti, Manoranjan, 2016. "Application of Generalized Hukuhara derivative approach in an economic production quantity model with partial trade credit policy under fuzzy environment," Operations Research Perspectives, Elsevier, vol. 3(C), pages 77-91.
    • Handle: RePEc:eee:oprepe:v:3:y:2016:i:c:p:77-91
    DOI: 10.1016/j.orp.2016.08.002
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    References listed on IDEAS

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    1. Wee, Hui-Ming & Lo, Chien-Chung & Hsu, Ping-Hui, 2009. "A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment," European Journal of Operational Research, Elsevier, vol. 197(2), pages 620-631, September.
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    3. Kumar Maiti, Manas, 2011. "A fuzzy genetic algorithm with varying population size to solve an inventory model with credit-linked promotional demand in an imprecise planning horizon," European Journal of Operational Research, Elsevier, vol. 213(1), pages 96-106, August.
    4. Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
    5. Javad Sadeghi & Seyed Taghi Akhavan Niaki & Mohammad Reza Malekian & Saeid Sadeghi, 2016. "Optimising multi-item economic production quantity model with trapezoidal fuzzy demand and backordering: two tuned meta-heuristics," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 10(2), pages 170-195.
    6. Yan, Nina & Sun, Baowen & Zhang, Hui & Liu, Chongqing, 2016. "A partial credit guarantee contract in a capital-constrained supply chain: Financing equilibrium and coordinating strategy," International Journal of Production Economics, Elsevier, vol. 173(C), pages 122-133.
    7. Majumder, P. & Bera, U.K. & Maiti, M., 2016. "An EPQ model for two-warehouse in unremitting release pattern with two-level trade credit period concerning both supplier and retailer," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 430-458.
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