Optimization Of Substitutable Perishable Inventory System With Partial Backlogging In Supply Chain

Abstract

 This article deals with the continuous review perishable inventory systems with two different substitutable items in stock. The demand for the products are independent of each other and follows an Poisson distribution with parameters ?₁ and ?₂ respectively for product A and B with partial backlogging. The demands, that occurred when the inventory is out of stock, are back logged. That means these demands are satisfied as soon as the replenishment is received. The common demand for both products at distributor follows Poisson distribution with rate ?_d. The operating policy is used at the lower echelon for the products. That is whenever the inventory level drops to s_i on order for Q_i =  items is placed, the ordered items are received after a random time which is distributed as exponential. The items are perishable in nature and the life time of items of each commodity is assumed to be exponentially distributed.  The retailer replenishes the stock of products from the supplier which adopts (0, M_i) policy. The joint probability distribution of the inventory levels of the products, at retailer and the products at supplier are obtained in the steady state case. We derive the system performance measures and calculate the long run total expected inventory cost using several instances of numerical examples.