Fuzzy periodic review system with fuzzy random variable demand

In this paper, a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously. A model has been developed with customer demand assumed to be a fuzzy random variable. The lead-time has been assumed to be a constant. The lead-time demand and the lead-time plus one period's demand have also been assumed to be fuzzy random variables. A methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized. A numerical example has been presented to illustrate the model.