A fuzzy multi objective inventory model of demand dependent deterioration including lead time

Abstract

In this article, we have developed a deteriorated multi-item inventory model in a fuzzy environment. Here the demand rate is constant. Production cost and set-up cost are the most vital issue in the inventory system of the market world. Here production cost and set-up- cost are continuous functions of demand. Set-up-cost is also dependent on average inventory level. Deterioration cost is the most challenging issue in the business world. So here deterioration cost is dependent on inventory level and demand. Lead time crashing cost is considered the continuous function of leading time. In the real world all cost are not fixed. Due to uncertainty all cost parameters of the proposed model are taken as Generalized Triangular Fuzzy Number (GTFN). The formulated multi objective inventory problem has been solved by various techniques like as Geometric Programming (GP) technique, Fuzzy Programming Technique with Hyperbolic Membership Function (FPTHMF), Fuzzy Non-Linear Programming (FNLP) technique. Numerical example is taken to illustrate the model. Sensitivity analysis and graphical representation have been shown to test the parameters of the model.

Keywords

• inventory
• deterioration
• multi-item
• leading time
• generalized triangular fuzzy number
• fuzzy and gp techniques