Part of the Intelligent Systems Reference Library book series (ISRL, volume 87)

# Fuzzy Inventory Models for Deteriorating Items Under Different Types of Lead-Time Distributions

Chapter

## Abstract

In this chapter, a fuzzy inventory model for deteriorating items with shortages under fully backlogged condition is formulated by utilizing uncertain, vague and imprecise data. Fuzzy set theory has been used for handling the uncertainty in the data and hence the corresponding inventory parameters are assumed to be triangular fuzzy numbers. The main purpose of this work is to find out the quantity lot size (Q) and reorder point (R) level, which minimize the total annual inventory cost function in fuzzy environment. During the formulation of the model, the lead time is considered to be zero and the reorder level follows the different types of distribution namely uniform, exponential and Laplace distribution. Graded mean representation is used to defuzzify the total cost function and results obtained by these methods are compared with the crisp and the numerical results. A numerical example is given in order to show the applicability of the proposed model for different values of defective rate $$\left( \theta \right)$$ and the backorder ratio $$\left( \beta \right)$$. Finally, sensitivity analysis is carried out to explore the effect of changes in the values of some of the system parameters.

### Keywords

Fuzzy sets Inventory models Lead time Probability

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