Determining the Optimal Order Quantity for Perishable Products Affected by Stochastic Transportation Delays

Abstract

Background: Transportation delays pose significant challenges for perishable products by reducing freshness, shortening selling duration, and causing lost sales during the delay. Methods: Motivated by the growing importance of transportation delays on perishable products, this study develops a single-period analytical expected profit expression to determine the optimal order quantity that maximizes expected profit. The model incorporates deterioration-driven price reductions, lost sales opportunities occurring during the delay, and the shortened selling duration resulting from delayed delivery, without imposing a specific probability distribution on the transportation delay duration. Results: Numerical experiments illustrate how key parameters influence the optimal order quantity and the corresponding expected profit. Deterioration reduces expected profit by primarily reducing the selling price. In addition, a higher disruption probability reduces both the optimal order quantity and the expected profit, while longer selling durations result in larger order quantities and yield higher expected profits. A low initial selling price can result in negative expected profit, indicating cases where placing the order is inappropriate. Conclusions: The findings offer managerial implications for determining optimal order quantities that maximize profit under transportation delays for perishable products.