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

• Published in: European journal of operational research Vol. 199; no. 2; pp. 420 - 434
• Main Authors: Zhang, Dali, Xu, Huifu, Wu, Yue
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2009; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Applied sciences; Approximation; Conditional value at risk constraints; Convex programming; Exact sciences and technology; Inventory control; Inventory control Conditional value at risk constraints Sample average approximation Stochastic programming Convex programming; Inventory control, production control. Distribution; Mathematical programming; Operational research and scientific management; Operational research. Management science; Order quantity; Portfolio theory; Risk aversion; Risk theory. Actuarial science; Sample average approximation; Stochastic models; Stochastic programming; Studies; Inventory control; Convex programming; Conditional value at risk constraints; Sample average approximation; Stochastic programming; Stochastic model; Probabilistic approach; Financial management; Risk analysis; Modeling; Risk aversion; Approximation method; Optimal control; Economic order quantity; Risk management; Portfolio management; Quantile; Convex analysis; Numerical convergence
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2008.11.047

This paper presents some convex stochastic programming models for single and multi-period inventory control problems where the market demand is random and order quantities need to be decided before demand is realized. Both models minimize the expected losses subject to risk aversion constraints expressed through Value at Risk (VaR) and Conditional Value at Risk (CVaR) as risk measures. A sample average approximation method is proposed for solving the models and convergence analysis of optimal solutions of the sample average approximation problem is presented. Finally, some numerical examples are given to illustrate the convergence of the algorithm.