Fuzzy Inventory Models for Crisp and Fuzzy Production Quantity With Trapezoidal Fuzzy Numbers

Abstract

ABSTRACT The main objective of inventory management is to get satisfactory levels of customer service while keeping inventory costs within reasonable bounds and that is why the subject of inventory control is a major consideration in economic situations. Inventory management and control in manufacturing environments involve various types of data, which may be deterministic or probalistic, however in real life situations in inventory management the data is uncertain and imprecise. Conventional inventory models that include uncertainty are based on the concept of randomness and on probability theory. However, in certain situations uncertainties are due to fuzziness and in these cases the fuzzy set theory is applicable only. In this study inventory models in fuzzy environment have been considered and the solution are obtained. The present thesis consists of five chapters. Chapter one is introductory in which basic inventory models and literature related to the work have been discussed. The fuzzy production inventory models with fuzzy parameters for crisp and fuzzy production quantity involves constant rate demand with uniform order replenishment have been considered by Hsieh and Extension of the lagrangean method used to solve the problem. In chapter two this problem has been reviewed in detail with instantaneous and uniform replenishment separately and in place of Extension of the lagrangean method, KT conditions has been used to solve inequality constraints problem for uniform and instantaneous replenishment. In chapter three, the fuzzy shortage cost has been introduced in existing fuzzy production inventory model with fuzzy parameters for crisp production quantity involve constant rate demand with instantaneous replenishment and solution has been obtained. In chapter Four, A fully fuzzy production inventory models with price breaks involving uniform and instantaneous replenishment is developed and the technique used in chapter two and three has been used to find the solution of the problem. In chapter Five, A Multi-item fuzzy production inventory model with fuzzy parameters for crisp production quantity involving uniform and instantaneous replenishment has been considered and solution is obtained.