A Joint Dynamic Pricing, Advertising, and Production Model with Inventory-Level-Dependent Goodwill

Inventory level has a significant impact on the goodwill of products to customers, which seldom becomes the focus of previous studies. In this paper, joint dynamic pricing, advertising, and production decision-making problem is investigated, where the demand rate depends on sales price and goodwill. The inventory and backlog as well as advertisement are considered as goodwill-building factors. The optimal dynamic pricing, advertising, and production policies are derived by using Pontryagin’s maximum principle. Numerical examples are provided to demonstrate the obtained results, and sensitivity analysis of main system parameters is carried out to obtain some managerial insights. We find that when the initial goodwill is relatively high, the firm’s profit first decreases and then increases with respect to the impact intensity of inventory on goodwill; otherwise, the firm always benefits from a higher impact intensity of inventory on goodwill. Furthermore, the optimal production and advertising policies are complementary caused by the feature of inventory-dependent goodwill.