Continuous review inventory model in mixed fuzzy and stochastic environment
In this paper, we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting. Since demand plays an important role in such type of inventory systems, we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand. After fuzzifying the random lead-time demand we consider the annual average demand as a fuzzy random variable. We provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value. Since the expected value of a fuzzy random variable is a fuzzy quantity, a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution. A numerical example is presented to illustrate the proposed model.