Optimal joint dynamic pricing, advertising and inventory control model for perishable items with psychic stock effect

Abstract

In this study, a joint pricing, advertising and inventory control problem will be investigated for a firm selling perishable products with psychic stock effect. The proposed problem is analyzed in the deterministic multi-period setting in which demand at each period depends on not only the amount of inventory displayed and advertising goodwill affected by the firm’s current and past advertising efforts but also selling price and freshness index. The objective is to determine the optimal pricing, advertising, and psychic stock strategies maximizing the discount total profit over the infinite planning horizon. Our theoretical results prove that the firm would adopt a static pricing strategy, and then demonstrate that the optimal paths of the advertising goodwill and psychic stock can be determined uniquely. We also show that the convergence of the advertising goodwill towards its equilibrium is from above or below, depending on the relative location of the initial stock of advertising goodwill with respect to the unique equilibrium stock of advertising goodwill. Moreover, a set of structural properties is developed to explore the relationships among the optimal decisions. Finally, the concluding remarks and suggestions will be provided for future studies.