OPTIMIZATION OF A FUZZY INVENTORY MODEL WITH PENTAGONAL FUZZY NUMBERS

Abstract

This paper explores an optimal replenishment strategy for a two-echelon inventory model which has been considered and analyzed in a fuzzy environment. In fuzzy environment, carrying cost, ordering cost and the replenishment processing cost are assumed to be pentagonal fuzzy numbers. The purpose of this model is to minimize the total inventory cost in fuzzy scenario. There are two inventory models proposed in this paper. Crisp models are developed with fuzzy total inventory cost but crisp optimal order quantity. Fuzzy model is also formulated with fuzzy total inventory cost and fuzzy optimal order quantity. Graded mean integration formula is employed to defuzzify the total inventory cost and the Kuhn–tucker condition is used to determine the optimal order quantity. Finally, we develop an algorithm to obtain the optimal order quantity. A comparison of fuzzy model with classical inventory model is being made. Numerical results highlighting the sensitivity of various parameters are also elucidated. The result illustrates that this fuzzy model can be quite useful in determining the optimal order quantity and minimum total inventory cost.