An inventory model for perishable items with two retailers

Perishable products widely occur in daily production and life, such as vegetables, fruits, meats, seafood, whose freshness level are decreasing and inventory are losing by deterioration (damage, spoilage, dryness, vaporization, etc) as time elapsing. In this paper, an inventory model with two retailers is discussed, whose demands for perishable products are respectively constant and stock-dependent. Two retailers sell the same perishable product ordered from the single wholesaler. In the model, constant deteriorating rate is considered, shortages are allowed without backlogging, the total cost (including holding, purchasing, shortage and ordering costs) is analyzed, in which shortage cost rates are different for two retailers. The necessary conditions of the existence and uniqueness of the optimal solution are shown. An optimal solution procedure to find the optimal replenishment policy is presented, and convexity conditions discussed.