A Fuzzy Inventory Model with Shortages Using Different Fuzzy Numbers

Abstract

It is found from the literature that most of the authors have considered inventory problems without shortage in fuzzy environment and they also considered different costs as fuzzy numbers and defuzzified by using signed distance method. In our present investigation an attempt has been made to study inventory model with shortage by considering the associated costs involved as fuzzy numbers. In the present piece of work we have referred the work of Dutta and Kumar (2012). They have considered fuzzy inventory model without shortages using trapezoidal fuzzy number and for defuzzification signed distance method was used. Following their work we have extended it for purchasing inventory model with shortages using trapezoidal fuzzy number for different costs and signed distance method for defuzzification, and then for the same purchasing inventory model, the associated costs were considered as different fuzzy numbers like triangular fuzzy number, trapezoidal fuzzy number and parabolic fuzzy number and for defuzzification we have applied Graded Mean Integration Value of defuzzification. Finally numerical illustration has been given. It is observed from this study that the optimal values are improved in fuzzy environment as compared to that of in crisp environment.

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