Robust stochastic optimization with convex risk measures: A discretized subgradient scheme

Yu, Haodong; Sun, Jie

doi:10.3934/jimo.2019100

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…However, these robust optimization models are often over-conservative in reality [16]. Since a method of data-driven uncertainty set recently proposed in [21] can handle relevance of the multi-item demands by principal component analysis, and give the bounds of the demands by kernel density estimation technique, we attempt to extend such a method to treat the newsboy problem (3) in this paper, which is different from the existing models available in the literature [28,30,38].…”

Section: 2mentioning

confidence: 99%

A new data-driven robust optimization approach to multi-item newsboy problems

Kou

Wan

2023

JIMO

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<p style='text-indent:20px;'>A newsboy problem is a typical stochastic inventory management problem and has extensive applications in the fields of operational research, management sciences and marketing sciences. One of the challenges underlying such problems is to handle the uncertainty of demands. In the existing results, it is often to assume that the demand distribution is given to facilitate solution of the problems. In this paper, a novel data-driven robust optimization model for solving multi-item newsboy problems is proposed by combining the absolute robust optimization with a data-driven uncertainty set, and the latter is leveraged to address the uncertainty of demands. For the single-item situation, a closed-form solution is obtained and influences of parameters on the optimal solutions are analyzed. Owing to complexity of the multi-item situation, a uniform smoothing function is leveraged to smooth the proposed model. Then, an algorithm, called a modified Frank-Wolfe feasible direction algorithm, is developed to solve a series of smooth subproblems. Numerical simulation demonstrates that the proposed model in this paper can reduce over-conservation of robust optimization methods and is more robust than other similar well-established methods in the literature. By numerical simulation and sensitivity analysis, it is concluded that: (1) The proposed method can provide more stable optimal order policy and profits than the existing ones; (2) For a product with a higher unit purchase price, the optimal order quantities are more sensitive to its change; (3) In view of profitability, the newsboy should not to be too risk-averse.</p>

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Section: 2mentioning

confidence: 99%

A new data-driven robust optimization approach to multi-item newsboy problems

Kou

Wan

2023

JIMO

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“…The entropic value‐at‐risk (EVaR) (Ahmadi‐Javid, 2012) is a widely used risk measure owing to its analytical tractability and close relationship with other existing risk measures. Applications of EVaR include economics (Chen et al, 2019), mechanical engineering (Wasserburger et al, 2020; Watanabe et al, 2022), and portfolio optimization (Yu & Sun, 2021).…”

Section: Introductionmentioning

confidence: 99%

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

Yoshioka,

Yoshioka

2023

Environmetrics

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The modeling and identification of time series data with a long memory are important in various fields. The streamflow discharge is one such example that can be reasonably described as an aggregated stochastic process of randomized affine processes where the probability measure, we call it reversion measure, for the randomization is not directly observable. Accurate identification of the reversion measure is critical because of its omnipresence in the aggregated stochastic process. However, the modeling accuracy is commonly limited by the available real‐world data. We resolve this issue by proposing the novel upper and lower bounds of a statistic of interest subject to ambiguity of the reversion measure. Here, we use the Tsallis value‐at‐risk (TsVaR) as a convex risk functional to generalize the widely used entropic value‐at‐risk (EVaR) as a sharp statistical indicator. We demonstrate that the EVaR cannot be used for evaluating key statistics, such as mean and variance, of the streamflow discharge due to the blowup of some exponential integrand. We theoretically show that the TsVaR can avoid this issue because it requires only the existence of some polynomial moment, not exponential moment. As a demonstration, we apply the semi‐implicit gradient descent method to calculate the TsVaR and corresponding Radon–Nikodym derivative for time series data of actual streamflow discharges in mountainous river environments.

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Robust stochastic optimization with convex risk measures: A discretized subgradient scheme

Cited by 2 publications

References 27 publications

A new data-driven robust optimization approach to multi-item newsboy problems

A new data-driven robust optimization approach to multi-item newsboy problems

Statistical evaluation of a long‐memory process using the generalized entropic value‐at‐risk

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