Single and multi-period optimal inventory control models with risk-averse constraints

European Journal of Operational Research

Volumn 199, Issue 2, 2009, Pages 420-434

  Zhang, Dali ^a   Xu, Huifu ^a   Wu, Yue ^a  

^a UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Conditional value at risk constraints; Convex programming; Inventory control; Sample average approximation; Stochastic programming

Indexed keywords

CONDITIONAL VALUE AT RISK CONSTRAINTS; CONVERGENCE ANALYSIS; CONVEX PROGRAMMING; INVENTORY CONTROL PROBLEMS; MARKET DEMANDS; NUMERICAL EXAMPLES; OPTIMAL SOLUTIONS; ORDER QUANTITIES; RISK AVERSIONS; RISK MEASURES; SAMPLE AVERAGE APPROXIMATION; STOCHASTIC PROGRAMMING MODELS; VALUE AT RISKS;

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; INVENTORY CONTROL; RANDOM PROCESSES; STOCHASTIC MODELS; STOCHASTIC PROGRAMMING; VALUE ENGINEERING;

RISK ASSESSMENT;

EID: 67349135215     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2008.11.047     Document Type: Article

References (28)

1. Ahmed S., Cakmak U., and Shapiro A. Coherent risk measures in inventory problems. European Journal of Operational Research 182 (2007) 226-238
2. Alexander S., Coleman T., and Li Y. Minimizing CVaR and VaR for a portfolio of derivatives. Journal of banking and finance 30 (2006) 583-605
3. Arrow K., Harris T., and Marschak T. Optimal inventory policy. Econometrica 19 (1951) 250-272
4. Artstein Z., and Wets R.J.-B. Consistency of minimizers and the SLLN for stochastic programs. Journal of Convex Analysis 2 (1995) 1-17
5. Artzner P., Delbaen F., Eber J.-M., and Heath D. Conherent measures of risk. Mathematical Finance 9 (1999) 203-228
6. Aumann R.J. Integrals of set-valued functions. Journal of Mathematical Analysis and Applications 12 (1965) 1-12
7. Basak S., and Shapiro A. Value-at-Risk-based risk management: Optimal policies and asset prices. Review of Financial Studies 14 (2001) 371-405
8. Chen F., and Song J.-S. Optimal policies for multi-echelon inventory problems with Markov modulated demand. Operations Research 49 (2001) 226-234
9. Choi T., Li D., and Yan H. Mean-variance analysis of a single supplier and retailer supply chain under a returns policy. European Journal of Operational Research (2007) Available online
10. Dvoretzky A., Keefer K., and Walfowitz J. The inventory problem: Case of known distribution of demand. Econometrica 20 (1952) 187-222
11. Markowitz H. Portfolio Selection: Efficient Diversification of Investment (1959), John Wiley & Sons, New York
12. W. Jammernegg, P. Kischka, Performance measurement for inventory models with risk preferences, Friedrich-Schiller-Universität Jena, Wirtschaftswissenschaftliche Fakultät, series Jenaer Schriften zur Wirtschaftswissenschaft, No. 26, 2004.
13. P. Jorion, Value at Risk: The New Benchmark for Controlling Derivatives Risk, Irwin, Chicago, 1997.
14. Krokhmal P., Palmquist J., and Uryasev S. Portfolio optimization with conditional Value-at-Risk objective and constraints. Journal of Risk 4 (2002) 43-68
15. Lejeune M.A., and Ruszczynski A. An efficient trajectory method for probabilistic production-inventory-distribution problems. Operations Research 55 (2007) 378-394
16. Robinson S.M. Analysis of sample-path optimization. Mathematics of Operations Research 21 (1996) 513-528
17. Rockafellar R.T. Convex Analysis (1970), Princeton University Press, Princeton
18. Rockafellar R.T., and Uryasev S. Optimization of conditional value-of-risk. Journal of Risk 2 (2000) 21-41
19. Rockafellar R.T., and Uryasev S. Conditional Value-at-Risk for general cost distributions. Journal of Banking and Finance 26 (2002) 1443-1471
20. Rubinstein R.Y., and Shapiro A. Discrete Events Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Methods (1993), John Wiley and Sons, New York
21. Scarf H. The optimality of (s, S) policies in dynamic inventory problems. In: Arrow K., Karlin S., and Suppes P. (Eds). Mathematical Methods in the Social Sciences (1960), Standford University Press, Standford, CA
22. Sethi S.P., and Cheng F. Optimality of (s, S) policies in inventory models with Markovian demand. Operations Research 45 (1997) 931-939
23. Shapiro A., and Xu H. Uniform laws of large numbers for set-valued mappings and subdifferentials of random functions. Journal of Mathematical Analysis and Applications 325 (2007) 1390-1399
24. Song J.-S., and Zipkin P. Inventory control in a fluctuating demand environment. Operations Research 41 (1993) 351-370
25. Tapiero C. Value-at-Risk and inventory control. European Journal of Operational Research 163 (2005) 769-775
26. R. Wets, Stochastic Programming, Handbooks in OR & MS, Vol. 1, G.L. Nemhauser et al eds, 1989, pp. 573-629.
27. Xu H., and Meng F. Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints. Mathematics of Operations Research 32 (2007) 648-668
28. H. Xu, D. Zhang, Smooth sample average approximation of stationary points in nonsmooth stochastic optimization and applications, Mathematical Programming Series A, in press. Available from: .