Optimal purchase and inventory retrieval policies for perishable seasonal agricultural products

Many agricultural products or produce (e.g., apple, pear, potato, etc.) are perishable. Wholesalers purchase and store these products in a well-controlled environment in the harvest season, and then retrieve select amounts to sell in the market. The amount to purchase in the harvest season as well as how much to retrieve for each selling period strongly impact the profit for a wholesaler. This paper addresses the decisions for optimal purchase and inventory retrieval quantities for a perishable seasonal agricultural product considering the costs of storage, underage and overage, prospects of future prices and demands, and product deterioration. Specifically, we consider a single-product finite-period inventory model in which a wholesaler purchases the product in the first period and sells it in the subsequent periods where the prices fluctuate and are uncertain. The demands are influenced by the prices in the current and previous periods. The objective is to maximize the total expected profit. We characterize the structure of the optimal purchase and inventory retrieval policies, and perform numerical experiments to study sensitivity to various parameters and gain managerial insights. We also compare the performance of the optimal policy with two approximate policies in a case study to demonstrate the value of our model. The results show that the optimal policy can raise the expected profit by 22.4 percent in 2014 and reduce the expected loss by 10.2 percent in 2015 in the case.