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

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.

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A Robust Data-Driven Approach for the Newsvendor Problem with Nonparametric Information

Manufacturing & Service Operations Management ◽

10.1287/msom.2020.0961 ◽

2021 ◽

Author(s):

Liang Xu ◽

Yi Zheng ◽

Li Jiang

Keyword(s):

Robust Optimization ◽

Real Data ◽

Newsvendor Problem ◽

Problem Definition ◽

Data Driven ◽

Optimization Approach ◽

Worst Case ◽

Demand Distribution ◽

Robust Decisions ◽

True Distribution

Problem definition: For the standard newsvendor problem with an unknown demand distribution, we develop an approach that uses data input to construct a distribution ambiguity set with the nonparametric characteristics of the true distribution, and we use it to make robust decisions. Academic/practical relevance: Empirical approach relies on historical data to estimate the true distribution. Although the estimated distribution converges to the true distribution, its performance with limited data is not guaranteed. Our approach generates robust decisions from a distribution ambiguity set that is constructed by data-driven estimators for nonparametric characteristics and includes the true distribution with the desired probability. It fits situations where data size is small. Methodology: We apply a robust optimization approach with nonparametric information. Results: Under a fixed method to partition the support of the demand, we construct a distribution ambiguity set, build a protection curve as a proxy for the worst-case distribution in the set, and use it to obtain a robust stocking quantity in closed form. Implementation-wise, we develop an adaptive method to continuously feed data to update partitions with a prespecified confidence level in their unbiasedness and adjust the protection curve to obtain robust decisions. We theoretically and experimentally compare the proposed approach with existing approaches. Managerial implications: Our nonparametric approach under adaptive partitioning guarantees that the realized average profit exceeds the worst-case expected profit with a high probability. Using real data sets from Kaggle.com, it can outperform existing approaches in yielding profit rate and stabilizing the generated profits, and the advantages are more prominent as the service ratio decreases. Nonparametric information is more valuable than parametric information in profit generation provided that the service requirement is not too high. Moreover, our proposed approach provides a means of combining nonparametric and parametric information in a robust optimization framework.

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Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

10.36227/techrxiv.12771257 ◽

2020 ◽

Author(s):

Ahmed Abdelmoaty ◽

Wessam Mesbah ◽

Mohammad A. M. Abdel-Aal ◽

Ali T. Alawami

Keyword(s):

Robust Optimization ◽

Electricity Market ◽

Real Life ◽

Optimization Approach ◽

Case Scenario ◽

Worst Case ◽

Bidding Strategies ◽

Wind Generators ◽

Proposed Model ◽

Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.

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