Joint dynamic pricing and freshness-keeping effort strategy for perishable products with price-, freshness-, and stock-dependent demand

In this paper, we formulate a joint dynamic pricing and freshness-keeping effort strategy for perishable products in a finite horizon. Based on the perishable nature of perishable products, this paper considers the product demand influenced by selling price, product freshness and stock level. Since the freshness level decreases with time, we assume that the freshness deteriorates exponentially. Besides, a freshness-keeping effort is introduced to reduce the deterioration rate of freshness. Our purpose is to determine the optimal joint dynamic pricing and freshness-keeping effort strategy to maximize profits. To solve the problem, the Pontryagin's maximum principle is applied. We present a numerical example in support to the theoretical results and propose the sensitivity analysis of the main parameters. In the end, some managerial guidelines are also provided. When the cost of freshness-keeping effort is high or the effect of freshness-keeping effort is low, not to adopt freshness-keeping effort is the optimal decision. However, if the cost of freshness-keeping effort is small or the effect of freshness-keeping effort is significant, adopting freshness-keeping effort is the best. In addition, managers can gain more profits by expanding market size and restraining inventory decay rate and freshness deterioration rate.