The value of information for price dependent demand
The value of information for price dependent demand
复制标题
DOI：
10.1016/j.ejor.2020.05.057
复制
发表时间：
2021-01
期刊：
影响因子：
--
通讯作者：
Zhengwei Sun;Andrea C. Hupman;A. Abbas
中科院分区：
文献类型：
--
作者：
Zhengwei Sun;Andrea C. Hupman;A. Abbas
预测需求和确定最优定价是运营管理的重要组成部分。在推理需求曲线时，考虑需求的价格弹性通常是有用的。希望投资于需求预测和信息收集的企业应该考虑需求的完全信息期望值（EVPI）与需求弹性之间的关系。如果弹性是高还是低，企业应该为需求信息支付更多还是更少的费用？此外，当考虑不同的产品价格时，不同价格下的需求之间可能存在相关性。如果不同价格下的需求之间的相关性是高还是低，企业应该为信息支付更多还是更少？本文推导了解析和数值结果来回答这些问题。我们首先假设需求是不确定的，并遵循一个均匀分布的带周围的确定性需求曲线的需求分布的上限和下限随价格而变化。该公式使EVPI的封闭形式表达成为可能，提供了有用的基准。我们发现EVPI的微妙行为取决于弹性和初始价格偏好。对于最初偏好低（高）价格的公司，随着弹性的增加（减少），EVPI接近于零。使用截断正态分布和贝塔分布的数值结果放松了对均匀分布的假设，并显示当分布方差相似时，EVPI是相似的。最后，我们放松了完美信息的假设，并显示不完美信息的期望值（EVOI）遵循类似的模式，EVPI的需求弹性。
Predicting demand and determining optimal pricing are essential components of operations management. It is often useful to think in terms of the price elasticity of demand when reasoning about the demand curve. Firms wishing to invest in demand prediction and information gathering should reason about the relationship between the expected value of perfect information (EVPI) on demand and demand elasticity. Should firms pay more/less for information on demand if elasticity is high/low? Furthermore, when considering different product prices, correlation may exist between demand at different prices. Should firms pay more/less for information if the correlation between demand at different prices is high or low? This paper derives analytic and numeric results to answer these questions. We start with the assumption that demand is uncertain and follows a uniformly distributed band around a deterministic demand curve where the upper and lower bounds of the demand distribution vary with price. This formulation enables a closed form expression for EVPI that provides a useful benchmark. We find nuanced behavior of EVPI that depends on both the elasticity and the initial price preference. The EVPI approaches zero as elasticity increases (decreases) for a firm that initially prefers the low (high) price. Numerical results using the truncated normal and beta distributions relax assumptions about the uniform distribution and show EVPI is similar when the distribution variances are similar. Finally, we relax the assumption of perfect information and show the expected value of imperfect information (EVOI) follows similar patterns as EVPI with respect to demand elasticity.