An Entropy‐Based Methodology for Valuation of Demand Uncertainty Reduction

Abstract

We propose a distribution-free entropy-based methodology to calculate the expected value of an uncertainty reduction effort and present our results within the context of reducing demand uncertainty. In contrast to existing techniques, the methodology does not require a priori assumptions regarding the underlying demand distribution, does not require sampled observations to be the mechanism by which uncertainty is reduced, and provides an expectation of information value as opposed to an upper bound. In our methodology, a decision maker uses his existing knowledge combined with the maximum entropy principle to model both his present and potential future states of uncertainty as probability densities over all possible demand distributions. Modeling uncertainty in this way provides for a theoretically justified and intuitively satisfying method of valuing an uncertainty reduction effort without knowing the information to be revealed. We demonstrate the methodology's use in three different settings: (i) a newsvendor valuing knowledge of expected demand, (ii) a short life cycle product supply manager considering the adoption of a quick response strategy, and (iii) a revenue manager making a pricing decision with limited knowledge of the market potential for his product.

Analytics for Cross‐Border E‐Commerce: Inventory Risk Management of an Online Fashion Retailer

“…As mentioned previously, we will regenerate the demand distribution following the principle of maximum entropy, which has been shown to be a powerful tool to estimate an unknown probability distribution from limited information (Andersson et al., 2013; Fleischhacker & Fok, 2015, 2015; Maglaras & Eren, 2015). Given a discrete random variable X over support , we regenerate a discrete distribution from a set of distributions subject to certain constraints (such as support and moment constraints) with the goal of maximizing the entropy over this set of distributions: where is the probability that happens.…”

“…Robust decision making is widely used in operations analytics because of the difficulty of extracting full distribution information from data. There are different ideas for incorporating robustness in decision models, such as minimax regret over ambiguity sets (Ben‐Tal, Golany, Nemirovski, & Vial, 2005; Bertsimas & Thiele, 2006; Bertsimas, Brown, & Caramanis, 2011; Natarajan, Sim, & Uichanco, 2017) and entropy maximization (Andersson, Jornsten, Nonas, Sandal, & Uboe, 2013; Fleischhacker & Fok, 2015, 2015; Maglaras & Eren, 2015). In this paper, we set up the model based on the principle of entropy maximization (EM).…”

Does Decision-Maker’s Intelligence Matter? Evidences From Distribution-Free Newsvendor Problem

“…Classical examples of entropy-maximizing distributions, listed in [37], [39], [40], and others, are the uniform distribution, when only the range of the distribution is known; the exponential distribution, when the distribution is known to be non-negative and has a certain mean; and the cases which is most relevant to our study, the normal distribution, when the distribution has known mean and variance. Further discussions about this approach can also be found in [38], [41], and [42].…”

Managing the complexity of new product development project from the perspectives of customer needs and entropy

“…Information entropy, proposed by Shannon, provides a solid foundation to measure the complexity and uncertainty of information exchange in a system (Fleischhacker and Fok, 2015; Smunt and Ghose, 2016). Information entropy provides a direct way to measure the unpredictability or uncertainty of information content, in that low information entropy represents a low level of complexity or disorder degree in a system.…”