OPTIMIZATION OF FUZZY INTEGRATED INVENTORY MODEL WITH ORDERING COST REDUCTION DEPENDENT ON LEAD TIME

[摘要] The intellectual and industrial design of a complex inventory system becomes a vital issue for the organizationof responsiveness to uncertainties. The parameters involved in inventory model are likely to be varied due to thefluctuating business environment. Therefore, it will be more realistic apply fuzzy model rather than crisp model. Thispaper derives a single-vendor and a single-buyer integrated inventory model with ordering cost reduction dependent onlead time in a fuzzy environment. In this model, buyer and vendor cost parameters are uncertainties which necessitatethe use of trapezoidal fuzzy numbers. The purpose of this model is to determine the minimum integrated total costand optimal order quantity in the fuzzy scenario. There are two mathematical inventory models proposed in this paper.Initially, a crisp model is developed with fuzzy total inventory cost along with crisp optimal order quantity. Next, thefuzzy model is formulated with fuzzy total inventory cost and fuzzy optimal order quantity. Graded mean integrationformula is employed to defuzzify the total inventory cost and the extension of the Lagrangian method is used todetermine the optimal order quantity. An algorithm is developed to obtain the optimal order quantity and minimumintegrated total cost. The comparison of a fuzzy inventory model with the conventional crisp inventory model is madethrough numerical examples. This proposed fuzzy model is also compared with some specific cases of the previousmodels. Finally, the graphical representation is presented to demonstrate the proposed model. The result illustratesthat this fuzzy model can be quite useful in determining the optimal order quantity and minimum integrated total costprocedure when the lead time is analysed.

[学科分类] 数学（综合）

[关键词] Optimal integrated total cost;Optimal order quantity;Graded mean integration representation method;Fuzzy inventory system;Lagrangian method.