An optimal ordering and issuing policy for a two-stage inventory system for perishable products

This paper considers the problem of ordering and issuing policies arising in controlling finite-life-time fresh-meat-carcass inventories in supermarkets. A supermarket orders a product, which constitutes a set of sub-products of fixed proportion, from a vendor at the beginning of each time cycle. After it is received from the vendor, the product is stored in the cool-room, before being issued to the display shelves. The sub-products then satisfy random customer demand. After passing the life-time, sub-products are salvaged. In this system, the sub-products are issued to the display shelves according to the order-up-to level policies at the beginning of every period. The decisions to be taken to solve this problem are the product-ordering quantity from the outside vendor and the order-up-to issuing quantities for each sub-product. The objective function to be maximized is the expected profit per unit time, consisting of revenue from sales and salvage, and the cost of ordering, processing (or issuing), inventory holding, emergency issuing, and shortage. In this paper we first develop a mathematical model describing actual operations and then simplify the sub-product runout period so that optimal ordering and issuing policies are easily established. We then carry out extensive numerical experiments for a case of two sub-products in order to ascertain the properties and the behavior of the optimal solutions.