含参考价格效应的定价与库存管理联合策略研究

Pricing and inventory control play the critical roles in the enterprise management. And their coordination significantly influences the profit that companies ought to achieve. Coordinated pricing and inventory models have enjoyed a rapid growth in the past decade. The academics in response developed and analyzed a variety of mathematical models that integrate the two kinds of decisions. Nevertheless, the major stream of revenue management literature and almost all existing inventory management models exclusively assume that the demand of a period only depends on the selling price at the current period. This assumption ignores that consumers may react to companies' pricing strategies hence is inappropriate to model customers' repeating purchasing behavior. Thanks to recent advances in sophisticated information technologies such as enterprise resource planning systems, companies are now able to effectively gather information from customers on their purchase behaviors with a relatively small amount of effort. Basing on such information, this project will aim to the associated coordinated pricing and inventory management decisions. Specifically, we will consider a so-called reference price model which assumes consumers may form a reference price through the observed historic prices to evaluate the selling price before purchasing in the current period: If the selling pirce is lower than the reference price, then consumers perceive this as a gain, and otherwise they perceive it as a loss. Therefore demand depends on not only the current selling price but also the reference price. In addition, we also focus on the loss-averse case, that is, consumers are more sensitive to losses than gains. Indeed, the loss averse assumption is consistent with the prospect theory in economics and has also been validated by many empirical studies. .Reference price effect is now accepted as an empirical generalization in the marketing and economic literature. ..The purpose of this project is to study how managers can take reference price effect into consideration to achieve a more accurate judgement on the aggregate demand and hence a more profitable decision. We hope the studying on characterizations of the optimal policy and associated topics on this problem can greatly promote companies' competitiveness through more effective management.

产品定价和库存控制是管理中两种非常核心的决策行为，对企业实现其最大化利润有着重要影响。目前，学术界和众多企业已经对于这两种决策的联动问题进行了广泛的研究工作。但这些研究工作通常简单假定产品需求只受到其当前定价的影响，其原因在于过去受到技术能力和成本的限制，无法对消费者的购买行为进行更全面的分析考量。近年来，随着信息技术的快速发展，企业可以低成本地获取和保存顾客的消费购买记录，有效地分析其行为模式。如何以此为基础进行更有效的产品定价-库存管理，则是本项目研究的重点。具体而言，我们将考虑一类具有参考价格效应的需求模型，并在假定消费者对收益的偏好不超过对同等数量损失的偏好的前提下，分析相应的最优定价-库存管理策略。值得一提的是，该需求模型已经在市场营销和经济学中得到了广泛的理论和实证支持，在运筹管理范畴中却还没有引起足够重视。本项目希望通过对此问题的研究，帮助企业更有效地进行供应链管理。

本项目研究了生产运作管理领域中一类多期定价和库存控制的联合决策问题，其中顾客的购买行为和企业的决策之间存在交互效应，导致产品的需求会受到过往决策的影响，因此，企业在进行决策时需仔细权衡当期收益和远期收益，以达到全计划期内整体最优利润。.本项目着重分析了一类所谓的含参考价格效用的需求模型。当需求不确定时，本研究针对损失厌恶型顾客的行为，建立了一个随机动态规划模型；在某些条件之下，得到了最优策略的一些结构性质，以及若干管理学上的启示，为实际决策提供指导性建议。当需求确定时，本研究同时考虑了损失厌恶型和收益偏好型顾客的行为，建立了确定性动态规划模型，不但分析得到了一些有意义的结构性质，而且以此为基础设计高效的求解算法。在一些常见的合理设定下，本项目实现若干强多项式时间算法，能够快速得到计划期内各期的最优决策；在最一般的设定之下，提出了一些启发示算法，并给出了理论上的误差界限。另外，本项目还通过大量的数值运算，对此类问题进行了广泛的讨论，得到了丰富的管理学洞见。另外，本项目还通过企业调查，提出并分析了一个与参考价格效应类似，同样基于顾客行为的新型需求模型，其中顾客的购买行为会受到降价决策的影响，导致当期需求有可能漂移到将来。研究结果表明，企业的最优库存控制决策具有所谓的“全或无” 结构，是一个在库存管理的相关文献中从未出现过的新结果。