Fuzzy Random Periodic Review Mixture Inventory Model With Shortage Dependent Backorder Rate

In most real-life inventory situations, it is observed that, during stock out period, an increase in the amount of shortage results in a decrease in the rate of backorder incurred. Therefore, backorder rate is dependent on shortages, and it may be assumed to be inversely proportional to the shortages. The present research describes a periodic review inventory model with a mixture of backorder and lost sales where the backorder rate is a control parameter. Furthermore, to incorporate two different types of uncertainties i.e., fuzziness and randomness, here the annual customer demand, lead-time demand and the lead-time plus one period's demand have been assumed to be continuous fuzzy random variable following the normal distribution with associated fuzzy probability density functions. An algorithm has been proposed to find the optimal backorder rate, the optimal period of review along with the target inventory level so that the crisp equivalent of the fuzzy random total annual inventory cost is a minimum.