服务水平约束下动态定价与库存管理

Dynamic Pricing and Inventory Management under Service Level Constraint

本文研究服务水平约束下的动态定价与库存管理问题。企业在有限期内销售某种产品,产品的需求为随机需求,且期望需求依赖于产品价格。在每一期期初,企业需要在满足服务水平约束的条件下同时决定订货量和产品价格。本文首先构建了动态定价和订购联合决策的随机动态规划模型,并证明了最优解的存在性。进一步,通过对最优解的结构进行刻画,将原问题的求解转化为若干子问题的求解,降低了问题求解的难度。通过对最优解的分析发现,当期初库存增大时,产品最优价格降低。通过分析目标服务水平对利润的影响,证明了服务水平与利润之间存在权衡,实现高的服务水平需要承受利润损失。数值模拟表明,相对于传统的静态定价策略,采用动态定价策略可以降低追求服务水平所带来的利润损失,验证了动态定价策略的有效性。

This paper studies a dynamic pricing and inventory management problem under service level constraint . Consider a firm who sells a product through finite planning horizon, then the demand of product is stochastic demand and the expect demand depends on the product price. At the beginning of each period, with the consideration of service level constraint, the firm needs to decide the price of the product and order quantity simultaneously. The problem is modeled through stochastic dynamic programming, and the existence of optimal solution is verified. Furthermore, by characterizing the structure of optimal solution, the original problem is divided into several sub-problems, which makes the problem easier to solve. Through the analysis of optimal solution , we prove that the optimal price of product decreases in initial inventory level. By analyzing the impact of target service level on firm’s profit, we find that there exists a tradeoff between service level and profit, where the pursing of high service level leads to profit loss. The numerical simulation shows that compared to the traditional static pricing strategy, the introduction of dynamic pricing strategy can alleviate this profit loss, and therefore verifies the effectiveness of dynamic pricing strategy.