On the relationship between entropy, demand uncertainty, and expected loss

Fleischhacker, Adam; Fok, Pak-Wing

doi:10.1016/j.ejor.2015.03.014

Cited by 14 publications

(9 citation statements)

References 25 publications

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“…The optimal decision under the absolute loss (symmetric linear loss function

) is the median, so the minimum risk ME problem includes a moment and a quantile; this case will be extended to the asymmetric linear loss function in Section 3.3 . ( Fleishhacker & Folk (2015) studied the ME model with the expected loss under the loss function

where

is a probability vector (discrete distribution on N point), A is a nonnegative N × N matrix, and

.)…”

Section: Preliminariesmentioning

confidence: 99%

Maximum entropy distributions with quantile information

Bajgiran

Mardikoraem

Soofi

2021

European Journal of Operational Research

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HighLights Explore maximum entropy minimum elaborations of simpler maximum entropy models. Compare maximum entropy priors with parametric models fitted to elicited quantiles. Measure uncertainty and disagreement of forecasters based on their probability forecasts. Include the maximizing profit quantile in the newsvendor’s demand distribution.

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“…The optimal decision under the absolute loss (symmetric linear loss function

where

is a probability vector (discrete distribution on N point), A is a nonnegative N × N matrix, and

.)…”

Section: Preliminariesmentioning

confidence: 99%

Maximum entropy distributions with quantile information

Bajgiran

Mardikoraem

Soofi

2021

European Journal of Operational Research

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“…For probability assignment, the maximum entropy principle for the differential (or continuous) form of entropy is used in this article (see Abbas, , for introductory material). In contrast, Fleischhacker and Fok () analyze the use of discrete entropy to model uncertainty in demand outcome; our use of differential entropy models uncertainty as to which demand distributions are more plausible. Over the domain, [1, N ] differential entropy is defined as:

H (x) = - \int_{1}^{N} f (x) log (f (x)) d x

, where

f (\cdot)

is a probability density function.…”

Section: Literature Reviewmentioning

confidence: 99%

An Entropy‐Based Methodology for Valuation of Demand Uncertainty Reduction

Fleischhacker

Fok

2015

Decision Sciences

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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.

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“…Motivated by this observation, we regenerate the demand distributions (called ME distributions ) following the principle of maximum entropy (ME). This principle determines the demand distribution that maximizes the entropy defined over a set of demand distributions that have the same partial demand (i.e., support and moment) information (Fleischhacker & Fok, 2015a,b; Maglaras & Eren, 2015). Based on the ME distributions, we solve the stochastic models to obtain robust inventory decisions. (iii)As an extension to the prescriptive analtics, we incorporate tax risk into the proposed model, and investigate the effect of such risk on inventory decisions.…”

Section: Introductionmentioning

confidence: 99%

“…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).…”

Section: Introductionmentioning

confidence: 99%

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

Shi

Alwan

2020

Decision Sciences

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Problem statement: We present a data‐driven analytics study of a Chinese fashion retailer. The retailer fulfills cross‐border orders using online platforms, but faces inventory problems in its overseas warehouses, owing to operational complexities, such as extensive product offerings, high demand risks, and tax risks in cross‐border trade. Traditional approaches (e.g., model‐driven approaches) often fail to provide effective solutions. Therefore, this study proposes a new data‐driven approach to manage inventory in overseas warehouses. Methodology: A two‐stage predictive analytics approach is implemented, as follows: (i) all items are classified into one of two classes, where scriptA‐items are profitable to store in overseas warehouses, but scriptB‐items are not; (ii) the demand levels of SKUs of scriptA‐items are predicted. In the subsequent prescriptive analytics, models are proposed for optimizing inventory decisions related to scriptA‐items. These include a deterministic model that uses the predicted demand as the true demand, and a stochastic model that treats the true demand as a random variable. Results: (i) Using a variety of machine learning techniques in the predictive analytics phase, we find the random forest outperforms other methods. (ii) The deterministic model can be solved as a linear program, and the stochastic model with maximum entropy distributions can be solved using Karush–Kuhn–Tucker conditions. (iii) An application of our results shows that the predictive classification reduces costs (an average cost reduction of up to 20%) by avoid shipping unprofitable items to overseas warehouses. Furthermore, the stochastic model provides near‐optimal solutions (the smallest performance loss is just 0.00%).

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On the relationship between entropy, demand uncertainty, and expected loss

Cited by 14 publications

References 25 publications

Maximum entropy distributions with quantile information

Maximum entropy distributions with quantile information

An Entropy‐Based Methodology for Valuation of Demand Uncertainty Reduction

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

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