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In this article we developed an inventory model for noninstantaneous decaying items is considered under crisp and fuzzy environment. In this study we have considered stock dependent demand rate and variable deterioration. It is supposed that shortages are allowed and partially backlogged with exponential backlogging rate. Holding cost follows the learning curve. The deterioration rate, ordering cost, shortage cost and deterioration cost are assumed as a triangular fuzzy numbers. The aim of our study is to defuzzify the total cost function by signed distance method. This model is developed in both crisp and fuzzy surroundings. A numerical experiment is given to demonstrate the developed crisp and fuzzy models. Sensitivity analysis is implemented to examine the effect of parameters. The convexity of the total cost function is shown by graphically.

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Deterioration of goods and learning is a realistic phenomenon in daily life. Therefore maintaining the stock of decaying items becomes an important factor for decision makers. In this study deterioration rate follows the Weibull distribution and holding cost is gradually decreases, therefore learning effect is incorporated on holding cost. Many researchers generally assumed that the shortages are either completely backlogged or lost. But in this paper shortage is allowed and partial backlogged. The backlogging rate is taken as exponential function of time. Numerical examples are provided to further illustrate the model. Sensitivity analysis has been carried out to analyze the impact of change in various parameters. The aim of this model is to minimize the total cost.

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