Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study

Adida, Elodie; Perakis, Georgia

doi:10.1007/s10479-010-0706-1

Cited by 45 publications

(20 citation statements)

References 49 publications

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“…utilized factor-based models in constructing uncertainty sets [22,11,10]. An alternate, and possibly less conservative, data-driven model of such a problem that employs a point estimate of the mean and covariance matrix requires the solution of two coupled problems: (1) A portfolio optimization problem parametrized by (θ * , Σ * ) representing the mean and covariance matrix of returns; and (2) A learning problem that utilizes data to obtain the best (θ * , Σ * ).…”

mentioning

confidence: 99%

On the Solution of Stochastic Optimization and Variational Problems in Imperfect Information Regimes

Jiang

Shanbhag

2016

SIAM J. Optim.

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Abstract. We consider the solution of a stochastic convex optimization problem E[f (x; θ * , ξ)] over a closed and convex set X in a regime where θ * is unavailable and ξ is a suitably defined random variable. Instead, θ * may be obtained through the solution of a learning problem that requires minimizing a metric E[g(θ; η)] in θ over a closed and convex set Θ. Traditional approaches have been either sequential or direct variational approaches. In the case of the former, this entails the following steps: (i) a solution to the learning problem, namely θ * , is obtained; and (ii) a solution is obtained to the associated computational problem which is parametrized by θ * . Such avenues prove difficult to adopt particularly since the learning process has to be terminated finitely and consequently, in large-scale instances, sequential approaches may often be corrupted by error. On the other hand, a variational approach requires that the problem may be recast as a possibly non-monotone stochastic variational inequality problem in the (x, θ) space; but there are no known first-order stochastic approximation schemes are currently available for the solution of this problem. To resolve the absence of convergent efficient schemes, we present a coupled stochastic approximation scheme which simultaneously solves both the computational and the learning problems. The obtained schemes are shown to be equipped with almost sure convergence properties in regimes when the function f is either strongly convex as well as merely convex. Importantly, the scheme displays the optimal rate for strongly convex problems while in merely convex regimes, through an averaging approach, we quantify the degradation associated with learning by noting that the error in function value after K steps is O ln(K)/K , rather than O 1/K when θ * is available. Notably, when the averaging window is modified suitably, it can be see that the originakl rate of O 1/K is recovered. Additionally, we consider an online counterpart of the misspecified optimization problem and provide a non-asymptotic bound on the average regret with respect to an offline counterpart. In the second part of the paper, we extend these statements to a class of stochastic variational inequality problems, an object that unifies stochastic convex optimization problems and a range of stochastic equilibrium problems. Analogous almost-sure convergence statements are provided in strongly monotone and merely monotone regimes, the latter facilitated by using an iterative Tikhonov regularization. In the merely monotone regime, under a weak-sharpness requirement, we quantify the degradation associated with learning and show that expected error associated with dist(x k , X * ) is O ln(K)/K . Preliminary numerics demonstrate the performance of the prescribed schemes.

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confidence: 99%

On the Solution of Stochastic Optimization and Variational Problems in Imperfect Information Regimes

Jiang

Shanbhag

2016

SIAM J. Optim.

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“…These authors assume that there is no demand noise, which means that the unknown parameters that determine the demand function are completely known once a demand realization is observed that does not lead to stock-out. Adida and Perakis (2010a) discuss several robust and stochastic optimization approaches to joint pricing and procurement under demand uncertainty, and compare these approaches with each other in a numerical study.…”

Section: Joint Pricing and Inventory Problemsmentioning

confidence: 99%

Dynamic pricing and learning: Historical origins, current research, and new directions

Boer

2015

Surveys in Operations Research and Management Science

305

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Dynamic pricing and learning is a research topic that has received a considerable amount of attention in recent years, from different scientific communities: operations research and management science, marketing, economics, econometrics, and computer science. We survey these literature streams: we provide a brief introduction to the historical origins of quantitative research on pricing and demand estimation, point to different subfields in the area of dynamic pricing, and provide an in-depth overview of the available literature on dynamic pricing and learning. We discuss relations with methodologically related research areas, and identify several important directions for future research.

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“…For instance, we can construct a budget of uncertainty across products, for a given parameter and at a given time, as suggested in Adida and Perakis [2]:…”

Section: Uncertainty In Demand Parametersmentioning

confidence: 99%

Production planning in furniture settings via robust optimization

Alem

Morábito

2012

Computers & Operations Research

144

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Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study

Cited by 45 publications

References 49 publications

On the Solution of Stochastic Optimization and Variational Problems in Imperfect Information Regimes

On the Solution of Stochastic Optimization and Variational Problems in Imperfect Information Regimes

Dynamic pricing and learning: Historical origins, current research, and new directions

Production planning in furniture settings via robust optimization

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