在供應鏈的運作中，零售商往往需要在不確定性下進行需求預測，以制定最有利的決策。本研究以報童模型(newsvendor model)中零售商的角度，以條件風險價值評估市場風險，並根據其風險規避的程度不同，探討如何在需求不確定性之下訂定存貨與售價策略，以達到最大化利潤的目標。然而，過往文獻較少探討風險規避的報童模型，同時針對商品售價與訂購數量策略研究者更是稀有；另外，條件風險價值也較常被應用於金融商品的投資組合風險評估，而本研究則應用於供應鏈的決策之中。本研究使用穩健最佳化方法，可以解決在現實情況下難以預測的需求分配不確定問題；此外，也根據不同決策者對風險厭惡程度的不同，以參數的方式將其量化，使得決策者可根據自身的狀況進行調整。透過穩健最佳化，針對條件風險價值的目標函式進行求解，再以該結果針對零售商的商品售價與訂購數量問題求解，並同時更貼近真實情況。本研究提出的方法顯示以穩健最佳化方法來取代傳統條件風險價值求解方法是可行的，並且可以根據不同情境調整風險規避零售商的訂價與存貨策略，使得不同決策者可根據各自的情境來擬定策略；因此，本研究的結果使得風險規避零售商可以避免因預測偏差而造成損失，藉此將期望利潤極大化。

This study approaches the perspective of retailers in the newsvendor model and assesses market risk using conditional value at risk (CVaR). Depending on the degree of risk aversion, it explores how to determine inventory and pricing strategies under demand uncertainty to achieve the goal of maximizing profit. However, there has been limited research on the risk-averse newsvendor model, particularly concerning pricing and order quantity strategies. Additionally, while conditional value at risk is commonly applied in assessing risk for financial investment portfolios, this study applies it to supply chain decision-making.
This research employs robust optimization methods to address the issue of unpredictable demand distribution in realistic scenarios. Furthermore, it quantifies risk aversion levels of decision-makers using parameters tailored to different degrees of risk aversion, allowing adjustments based on individual situations. Through robust optimization, the objective function related to conditional value at risk is solved, followed by solving the retail pricing and ordering quantity problem based on the obtained results, leading to a more realistic approach.
The proposed method in this study demonstrates the feasibility of replacing traditional approaches for solving conditional value at risk with robust optimization methods. It allows for the adjustment of pricing and inventory strategies for risk-averse retailers based on various contexts, accommodating different decision-makers to formulate strategies according to their respective circumstances. As a result, the findings of this study enable risk-averse retailers to mitigate losses due to forecasting errors, ultimately maximizing expected profits.

Agrawal, V., & Seshadri, S. (2000). Impact of Uncertainty and Risk Aversion on Price and Order Quantity in the Newsvendor Problem. Manufacturing & Service Operations Management, 2(4), 410–423.

Alexander, G. J., & Baptista, A. M. (2003). Portfolio Performance Evaluation Using Value at Risk. The Journal of Portfolio Management, 29(4), 93–102.

Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203–228.

Ben-Tal, A., & Nemirovski, A. (1998). Robust Convex Optimization. Mathematics of Operations Research, 23(4), 769–805.

Bertsimas, D., & Sim, M. (2004). The Price of Robustness. Operations Research, 52(1), 35–53.

Chen, F., & Federgruen, A. (2000). Mean-variance analysis of basic inventory models. Tech. rep., Working paper, Columbia University.

Chen, F. Y., Yan, H., & Yao, L. (2004). A Newsvendor Pricing Game. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 34(4), 450–456.

Chen, Y., Xu, M., & Zhang, Z. G. (2009). A Risk-Averse Newsvendor Model Under the CVaR Criterion. Operations Research, 57(4), 1040–1044.

Dantzig, G. B. (1955). Linear Programming Under Uncertainty. Management Science, 1(3-4), 197–206.

Delage, E., & Ye, Y. (2010). Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems. Operations Research, 58(3), 595–612.

Dupuis, P., & Ellis, R. S. (2011). A weak convergence approach to the theory of large deviations. John Wiley & Sons.

Gabrel, V., Murat, C., & Thiele, A. (2014). Recent advances in robust optimization: An overview. European Journal of Operational Research, 235(3), 471–483.

Gotoh, J.-y., Kim, M. J., & Lim, A. E. (2018). Robust empirical optimization is almost the same as mean–variance optimization. Operations Research Letters, 46(4), 448–452.

Kim, M. J., & Lim, A. E. (2016). Robust Multiarmed Bandit Problems. Management Science, 62(1), 264–285.

Lariviere, M. A. (2006). A Note on Probability Distributions with Increasing Generalized Failure Rates. Operations Research, 54(3), 602–604.

Lim, A. E., & Shanthikumar, J. G. (2007). Relative Entropy, Exponential Utility, and Robust Dynamic Pricing. Operations Research, 55(2), 198–214.

Lim, A. E., Shanthikumar, J. G., & Shen, Z. M. (2006). Model Uncertainty, Robust Optimization, and Learning. In Models, Methods, and Applications for Innovative Decision Making, (pp. 66–94). INFORMS.

Lim, A. E., Shanthikumar, J. G., & Vahn, G.-Y. (2012). Robust Portfolio Choice with Learning in the Framework of Regret: Single-Period Case. Management Science, 58(9), 1732–1746.

Linsmeier, T. J., & Pearson, N. D. (2000). Value at Risk. Financial Analysts Journal, 56(2), 47–67.

Mausser, H., & Rosen, D. (1999). Beyond VaR: From measuring risk to managing risk. In Proceedings of the IEEE/IAFE 1999 Conference on Computational Intelligence for Financial Engineering (CIFEr)(IEEE Cat. No. 99TH8408), (pp. 163–178). IEEE.

McKay, R., & Keefer, T. E. (1996). VaR is a dangerous technique. Corporate Finance Searching for Systems Integration Supplement, 9, 30.

Ogryczak, W., & Ruszczynski, A. (2002). Dual Stochastic Dominance and Related MeanRisk Models. SIAM Journal on Optimization, 13(1), 60–78.

Petruzzi, N. C., & Dada, M. (1999). Pricing and the Newsvendor Problem: A Review with Extensions. Operations Research, 47(2), 183–194.

Pflug, G. C. (2000). Some Remarks On The Value-At-Risk And The Conditional Value At-Risk. In Probabilistic Constrained Optimization, (pp. 272–281). Springer.

Qin, Y., Wang, R., Vakharia, A. J., Chen, Y., & Seref, M. M. (2011). The newsvendor problem: Review and directions for future research. European Journal of Operational Research, 213(2), 361–374.

Rockafellar, R. T., Uryasev, S., et al. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk, 2, 21–42.

Sarykalin, S., Serraino, G., & Uryasev, S. (2008). Value-at-Risk vs. Conditional Value at-Risk in Risk Management and Optimization. In State-of-the-Art Decision-Making Tools in the Information-Intensive Age, (pp. 270–294). Informs.

Uryasev, S. (2000). Conditional Value-at-Risk: Optimization Algorithms and Applications. In proceedings of the IEEE/IAFE/INFORMS 2000 conference on computational intelligence for financial engineering (CIFEr)(Cat. No. 00TH8520), (pp. 49–57). IEEE.

Wald, A. (1945). Statistical Decision Functions Which Minimize the Maximum Risk. Annals of Mathematics, (pp. 265–280).

Whitin, T. M. (1955). Inventory Control and Price Theory. Management Science, 2(1), 61–68.

Yao, L., Chen, Y. F., & Yan, H. (2006). The newsvendor problem with pricing: Extensions. International Journal of Management Science and Engineering Management, 1(1), 3–16.