Numerical Calculation Of Multi-period Optimal Inventory Model With Conditional Value At Risk Constraints

The inventory problem is a typical problem in optimal decision-making problems. Such problem is focused by mathematicians and economistes, and a lot of research has been obtained in theoretical research and practical applications.This thesis addresses multi-period inventory control models with Conditional Value-at-Risk (CVaR) and solution method.On the assumption of the randomness of the market demand,we consider the CVaR management during the decision-making process, and minimize the expectation.Then,we extend the single period inventory decision to the multi-period one. Finally, we establish a class of convex stochastic optimization model with CVaR constraint.For the computation of the model, we study two types of optimization algorithms in this thesis.Taking into account of the non-smoothness lead by CVaR,and the penal function technology,we propose a smoothing method.Based on the piecewise linear property of the model,a Level Function Method (LFM) is proposed.We use Monte Carlo method for the smaple points.Numerical experiments show that the two algorithms have nice computing performance.The main content of this thesis is as follows:Chapter1introduces research background and significance of inventory problem and three kinds of risk measure. Then we present two kinds of algorithms for stochastic optimal problems. At last, the researching works are drowed in this thesis.Chapter2introduces the single period inventory model and Multi-period inventory model. The single period and Multi-period inventory problems with VaR constraints and CVaR constraints are modeled respectively.Chapter3addresses the solution process of sample average approximation method with penalty and smoothing technology and level function method, combining with the penal function technology.We use the Monte Carlo simulation method to choose the related points and a class of smoothing methods.Numerical examples also presented in this section by using Matlab software.Chapter4makes a calculation comparison between sample average approximation method and level function method. The convergence of the algorithm is analyzed. The last part of the thesis is a summary of the research work and further research problems.