Managing Inventories for Agricultural Products: The Optimal Selling Policies

Abstract

The inventory control theory in the operations research and management literature is primarily concerned about manufactured products, for which, the typical assumptions are ample external supplies and predictable prices, and the decision is on how much to order or produce. Agricultural products, on the other hand, are rarely studied in this literature but deserve an attention long overdue because of their unique features, such as the limited and unpredictable supply, inelastic demand and thus highly unpredictable prices, and a decision of how much to sell. Such features are considered in the agricultural economics literature which provides insights and strategic guidelines but with limited structural results on the theory. Inspired by real-life practice in the Kenya coffee industry, we consider a class of stochastic and dynamic inventory models for storable agricultural products with random exogenous supply and price. We characterize the optimal inventory (selling) policies for a variety of cost functions relevant in practice. In the cases of linear cost functions, we derive closed-form expressions for the optimal policies and the optimal discounted profits. Our theoretical advancement reveals additional insights and deepens the understanding of inventory management for agricultural products. Applying the theory to practice, we show that making selling decisions judiciously can significantly outperform the prevailing practice of selling-all regardless.