Abstract
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.
Highlights
E definitions of the mechanism of how the inventory affects demand put forward by researches are quite different
Urban [5] discussed two distinct types of inventory control models, the demand rate was a function of the initial inventory level, and the demand rate was dependent on the instantaneous inventory level
Taking the aforementioned points into account, we establish a production-inventory model of a monopolistic firm which controls production and sales together and seek the optimal pricing, advertising, and production policies to maximize the total profit under the planning horizon, where the demand rate depends on the sales price and goodwill level. e goodwill level is accumulated by the advertising in the most available literature, while we consider that the inventory and backlog are goodwill-building factors, which is the focus and contribution of this study from the modeling viewpoint
Summary
Gupta and Vrat [4] Urban [5] Lu et al [10] Zhang et al [11] Baye and Morgan [25] SeyedEsfahania et al [26] Yue et al [27] Karray and Martin-Herran [28] He et al [31] Chutani and Sethi [32] Liu et al [33] Feng et al [34]. Taking the aforementioned points into account, we establish a production-inventory model of a monopolistic firm which controls production and sales together and seek the optimal pricing, advertising, and production policies to maximize the total profit under the planning horizon, where the demand rate depends on the sales price and goodwill level. E goodwill level is accumulated by the advertising in the most available literature, while we consider that the inventory and backlog are goodwill-building factors, which is the focus and contribution of this study from the modeling viewpoint. E questions we are concerned about are as follows: What are the optimal production, pricing, and advertising strategies of the firm when the inventory and backlog affect goodwill? E optimization problem (8) is an optimal control problem with two state variables, G(t), I(t), and three controls, p(t), a(t), u(t)
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