Periodic review inventory model with normally distributed fuzzy random variable demand

Abstract

ABSTRACTIn this article, a periodic review inventory model has been analysed in a fuzzy random framework. In order to incorporate the two different kind of uncertainties, namely fuzziness and randomness, that characterise any real-life inventory situation simultaneously, the model has been developed in the mixed fuzzy random environment. The amalgamation of these two uncertainties has been accomplished by assuming the annual customer demand to be a continuous fuzzy random variable following the normal distribution. The lead-time has been assumed to be constant. The lead-time demand and the lead-time plus one period's demand have also been assumed to be normally distributed fuzzy random variables by connecting them to the annual customer demand through the length of the lead-time and the lead-time plus one period's demand, respectively. An algorithm has been proposed to determine the optimal period of review and the optimal target inventory level so as to minimise the total expected annual inventory cost. The proposed methodology has been illustrated by way of a numerical example.