| Many scholars have considered inventory systems, however, most of them assume demand is homogeneous. Recently, with the development of economy and society, the sources of demand are of diversity, and due to’distinct service level requirements, the arrival rate and shortage cost, they have different priorities. According to Pareto’s law, in the production and business activities, companies should provide differentiated services based on different priorities and pricing differentiation is a common strategy. This article is exactly based on the background, and studies the inventory control and pricing strategies of a system in which a single product is produced to fulfill several classes of demands.In the first place, under the assumption of without taking fixed ordering cost into account, the paper expand research on centralized decision-making of inventory control and pricing from single-cycle and multi-cycle respectively. In the study of single-cycle issues, the paper adopts differential pricing in deterministic demand and stochastic demand, then calculates the optimal order quantity through model and verifies the optimal order quantity is sufficient to meet the deterministic demand. Then the paper extends research from single-cycle to multi-cycle, and assumes the price of stochastic demand directly influence its amount, and finally draw the conclusion that the base stock list price strategy composed by base stock yt*and price pt*is optimal and show the higher the inventory level before ordering exceeds base stock, the greater the discount should be in order to reduce the backlog of inventory.At last, the paper further generalizes assumptions and takes fixed ordering cost into consideration to research optimal strategy of inventory control and pricing. Due to the particularity of fixed ordering cost, this paper utilizes the concept of k-convex function and show the k-concave of profit function Vt(x) and get the conclusion that improved (s, S, p) strategy is optimal. |
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