Newsvendor Problems with VaR and CVaR Consideration

In this chapter, we consider approaches to express the risk preferences of a newsvendor by means of the risk measures value at risk (VaR), conditional value at risk (CVaR), and the mean-CVaR rule, which usually is defined as a convex combination of expected profit and CVaR. With these risk measures the decision maker can exploit risk-averse or risk-neutral behavior. In addition, we introduce a more general mean-CVaR measure where also risk- taking behavior can be expressed. The overall goal of the paper is a comparative analysis of these risk measures in the newsvendor framework. On the one hand VaR, CVaR and the (general) mean-CVaR, measures are used as objective functions to derive the respective optimal order quantity. Extensions of the basic models are reviewed. On the other hand the risk measures, especially VaR, are constraints of the model. We first review models with the expected profit as objective. Then the general mean-CVaR measure is taken as objective function and a service constraint and a loss constraint are added. In this framework, the risk attitudes of the newsvendor can be deduced from the characteristics of a product together with the specified service target and loss target.

[1]  Lei Yang,et al.  Supply Chain Coordination with CVaR Criterion , 2009, Asia Pac. J. Oper. Res..

[2]  T. Choi,et al.  Mean-downside-risk and mean-variance newsvendor models: Implications for sustainable fashion retailing , 2012 .

[3]  B. Chen,et al.  Pareto-optimal contracts for a supply chain with satisficing objectives , 2007, J. Oper. Res. Soc..

[4]  Fikri Karaesmen,et al.  Multi-product newsvendor problem with value-at-risk considerations , 2009 .

[5]  M. Fisher.  What is the Right Supply Chain for Your Product , 1997 .

[6]  Jun-ya Gotoh,et al.  Newsvendor solutions via conditional value-at-risk minimization , 2007, Eur. J. Oper. Res..

[7]  D. Tasche,et al.  On the coherence of expected shortfall , 2001, cond-mat/0104295.

[8]  ChenYouhua,et al.  Technical Note---A Risk-Averse Newsvendor Model Under the CVaR Criterion , 2009 .

[9]  Suresh P. Sethi,et al.  A Supply Chain with a Service Requirement for Each Market Signal , 2009 .

[10]  Hon-Shiang Lau.  The Newsboy Problem under Alternative Optimization Objectives , 1980 .

[11]  L. Eeckhoudt,et al.  The Risk-Averse and Prudent Newsboy , 1995 .

[12]  Mahmut Parlar,et al.  Balancing desirable but conflicting objectives in the newsvendor problem , 2003 .

[13]  Yimin Wang,et al.  On the Value of Mix Flexibility and Dual Sourcing in Unreliable Newsvendor Networks , 2005, Manuf. Serv. Oper. Manag..

[14]  Minghui Xu,et al.  Tradeoff between expected reward and conditional value-at-risk criterion in newsvendor models , 2007, 2007 IEEE International Conference on Industrial Engineering and Engineering Management.

[15]  Tsan-Ming Choi,et al.  Optimal Pricing and Stocking Decisions for Newsvendor Problem With Value-at-Risk Consideration , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[16]  Alexander Shapiro,et al.  Coherent risk measures in inventory problems , 2007, Eur. J. Oper. Res..

[17]  Peter Kischka,et al.  A Decision Rule Based on the Conditional Value at Risk , 2005 .

[18]  Yue Wu,et al.  Single and multi-period optimal inventory control models with risk-averse constraints , 2009, Eur. J. Oper. Res..

[19]  Peter Kischka,et al.  Risk-averse and risk-taking newsvendors: a conditional expected value approach , 2007 .

[20]  Jianbin Li,et al.  Downside risk-aversion analysis for a single-stage newsvendor problem , 2006, Wuhan University Journal of Natural Sciences.

[21]  Shouyang Wang,et al.  Risk Management of Supply and Cash Flows in Supply Chains , 2011 .

[22]  M. Yaari.  The Dual Theory of Choice under Risk , 1987 .

[23]  R. Rockafellar,et al.  Optimization of conditional value-at risk , 2000 .

[24]  J. Fichtinger.  The Single-Period Inventory Model with Spectral Risk Measures , 2011 .

[25]  C. Acerbi.  Spectral measures of risk: A coherent representation of subjective risk aversion , 2002 .

[26]  Xuan Zhao,et al.  Optimal ordering and pricing decisions for a target oriented newsvendor , 2011 .

[27]  Yao Zhao,et al.  A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk , 2011, Oper. Res..

[28]  Peter Kischka,et al.  Risk preferences of a newsvendor with service and loss constraints , 2013 .

[29]  Minghui Xu.  A price-setting newsvendor model under CVaR decision criterion with emergency procurement , 2010 .

[30]  Charles S. Tapiero,et al.  Value at risk and inventory control , 2005, Eur. J. Oper. Res..

[31]  Xiuli Chao,et al.  Joint optimal ordering and weather hedging decisions: mean-CVaR model , 2011 .

[32]  Alexander Schied,et al.  Convex measures of risk and trading constraints , 2002, Finance Stochastics.

[33]  Yuwen Chen,et al.  The newsvendor problem: Review and directions for future research , 2011, Eur. J. Oper. Res..

[34]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[35]  Zhe George Zhang,et al.  Technical Note - A Risk-Averse Newsvendor Model Under the CVaR Criterion , 2009, Oper. Res..

[36]  Houmin Yan,et al.  Channel Coordination with a Risk‐Neutral Supplier and a Downside‐Risk‐Averse Retailer , 2005 .