A single period fuzzy production inventory control model with exponential time and stock dependent fuzzy demand

Abstract

In this paper, we construct a fuzzy inventory system with imperfect production control. Here we introduce the rate of change of inventory level as a fuzzy dynamical equation (FDE). We consider a exponentially time dependent initial demand function and the total demand function is advertisement dependent and depends also on the inventory level of the system. To make the system more realistic we consider the inventory level and the demand functions are fuzzy in nature. Here we use “e” and “g” operator to defuzing the fuzzy dynamical system (FDS) and to test the optimality condition of the system. Here we consider the effect of inflation rate on the objective function which is for economical profit function in maximizing form. In this model, we also consider a function for the carbon emission which is made by several reasons in inventory system. Here we introduce the imperfect rate is reliability and time dependent. In this article, we consider the production cost as reliability dependent. Further, some numerical experiments are performed and graphical representation of the results are also depicted to illustrate the model.