Continuous Review Inventory Model with Normally Distributed Fuzzy Random Variable Demand

A fuzzy random continuous review inventory model is developed in this paper in order to illustrate a means of quantifying both imprecision and stochastic uncertainty simultaneously when there is significant information (imprecise and/or otherwise) available. Here the annual customer demand is assumed to be continuous fuzzy random variable following normal distribution, because in real life inventory situations, normal distribution is most often used to quantify customer demand information. The associated probability density function of the annual demand is also taken to be fuzzy in nature. The lead-time demand is also taken to be a normally distributed continuous fuzzy random variable by connecting it to the annual demand through the length of the constant lead-time. Under these assumptions, a methodology is proposed to minimize the crisp equivalent of the expected total annual cost and determine the optimal values of the re-order point and order quantity in the process. A numerical example is also presented to illustrate the proposed model and provide managerial insights.