# AN OPTIMIZATION OF FEOQ MODEL FOR WEIBULL DETERIORATING ITEMS WITH INFLATIONARY CONDITION

• Anu Sayal Department of Mathematics, Uttarakhand Technical University, Dehradun, India
• A. P. Singh Department of Mathematics S.G.R.R.(Pg) College. Dehradun, India
• Deepak Aggarwal Department of Mathematics, GRD IMT, Dehradun, India
Keywords: Fuzzy Economic Order Quantity (FEOQ) Model, Deterioration, Weibull Distribution Function, Inflation, Time Value of Money

### Abstract

The economic instability is a haunting situation in the present era for the economy. There is a monetary depreciation due to the tremendous increase in the price of the commodities. Present study basically deals with the investigation of the inventory system considering the case of perishable products under inflationary environment under condition of partial backorder. The rate of demand is a function which exponentially increases with increase in inflation and deterioration is taken as a Weibull distributed two parameter function. In the state of shortage when the inventory system runs out of stock an assumption is made that the demands are backlogged or lost. There is a variation in the rate of backlogging which shows this variation as a consequence of lead time required for the arrival of the next replenishment. The deterioration of commodities begins after a fixed interval of time. Present model aims at minimizing the average total cost considering both the crisp and fuzzy environments considering both inflationary effect as well as the time value of money. For the fuzzy economic order quantity (FEOQ) model of the inventory system fuzzification has been done by the use of fuzzy number of the trapezoidal nature. Defuzzification has been done by the use of centroid method. The primary motive of this work is to determine and compare the cost in total of the system of inventory in both crisp and fuzzy environments. The main inference that we can draw from this study is that fuzzy economic order quantity (FEOQ) model has more accuracy as in this model the total cost has been reduced as compared to the crisp model. Thus fuzzy economic order quantity (FEOQ) model is highly beneficial to any sort of inventory system and this result can be further generalized to any sector for enhancing the total profit of the system. Appropriate example has been provided for the illustration of both the models.

Published
2019-10-22
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