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Regret in the Newsvendor Model with Partial Information
Georgia Perakis,Guillaume Roels +1 more
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This paper derives the order quantities that minimize the newsvendor's maximum regret of not acting optimally, which can be extended to a variety of problems that require a robust but not conservative solution.Abstract:
Traditional stochastic inventory models assume full knowledge of the demand probability distribution. However, in practice, it is often difficult to completely characterize the demand distribution, especially in fast-changing markets. In this paper, we study the newsvendor problem with partial information about the demand distribution (e.g., mean, variance, symmetry, unimodality). In particular, we derive the order quantities that minimize the newsvendor's maximum regret of not acting optimally. Most of our solutions are tractable, which makes them attractive for practical application. Our analysis also generates insights into the choice of the demand distribution as an input to the newsvendor model. In particular, the distributions that maximize the entropy perform well under the regret criterion. Our approach can be extended to a variety of problems that require a robust but not conservative solution.read more
Citations
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Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
TL;DR: Cachon et al. as mentioned in this paper studied robust linear optimization problems with uncertainty regions defined by φ-divergences and showed that the robust counterpart of a linear optimization problem with φ divergence uncertainty is tractable for most of the choices of φ typically considered in the literature.
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Robust Solutions of Optimization Problems Affected by Uncertain Probabilities
TL;DR: In this paper, robust linear optimization problems with uncertainty regions defined by o-divergences (for example, chi-squared, Hellinger, Kullback-Leibler) are studied.
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Distributionally Robust Optimization: A Review
Hamed Rahimian,Sanjay Mehrotra +1 more
TL;DR: Main concepts and contributions to DRO are surveyed, and its relationships with robust optimization, risk-aversion, chance-constrained optimization, and function regularization are surveyed.
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Games and Decisions. By R. Duncan Luce and Howard Raiffa. Pp. xi, 509. 70s. 1957. (J Wiley & Sons)
Journal ArticleDOI
Likelihood robust optimization for data-driven problems
TL;DR: The asymptotic behavior of the distribution set is proved and the relationship between the model and other distributionally robust models is established and to test the performance of the model, it is applied to the newsvendor problem and the portfolio selection problem.
References
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Book
Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
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Information Theory and Statistical Mechanics. II
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Probability theory : the logic of science
TL;DR: In this article, a survey of elementary applications of probability theory can be found, including the following: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Advanced applications: 11. Discrete prior probabilities, the entropy principle 12. Simple applications of decision theory 15.
Journal ArticleDOI
Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty
Graham Loomes,Robert Sugden +1 more
TL;DR: The main body of current economic analysis of choice under uncertainty is built upon a small number of basic axioms, formulated in slightly different ways by von Neumann and Morgenstern (I 947), Savage (1 954), and others.