Research On The Extended Model Of Classical Newsvendor Based On Copula-CVaR

Newsvendor model is one of the basic models of supply chain management.Traditionally,the newsvendor model for single product,single cycle,only consider the optimal order quantity decision under demands uncertainty.But in practice,except demands,costs and prices can also be random exogenous variables.Moreover,because of the risk attitude of the decision maker,the actual order quantity is always deviated from the optimal order quantity.Therefore,in this paper,we consider the impact of two random variables and the risk attitude of decision makers on the final decision.And Copula function is used to describe the correlation of random variables,Conditional Value at Risk(CVaR)to measure the risk attitude.This paper established the Copula-CVaR newsvendor model with two kinds of stochastic situations,one is costs and prices,the other is cost and demands.Actually,the Copula-CVaR model is the stochastic programming problem,considering the reality of the random variable is discrete,we transformed the nonlinear programming model into a linear programming model to solve.In the simulation model,mainly considering the volatility for the costs and the prices,and taking the fluctuation of bulk commodity prices as the background,we construct a discrete model with Monte Carlo simulation,and we use Cplex to solve the model.The main contents and conclusions of this paper are as follows:(1)Under the premise of risk neutral,the expected payoff function is established under the joint distribution function of two random variables.We found that the optimal order quantity has nothing to do with the joint distribution function of random variables.So in this paper,the Conditional Value at Risk(CVaR)is used to construct the objective function.Meanwhile,the joint distribution function is used to describe the correlation of random variables.(2)We established the Copula-CVaR model under the double fluctuation of costs and prices,costs and demands.It has been proved that when the Copula function and the marginal distribution function of random variables are continuous functions,there is a unique optimal solution.The model under continuous function is actually a stochastic programming problem,therefore,we transformed the nonlinear programming model through discretization into a linear programming model to solve.(3)In the stage of simulation model,in the context of volatility in bulk commodity prices,mainly discussing the randomness and relevance of the costs and the prices,through the selection method of Copula function model and Monte Carlo simulation method,we analyzed the effects of the operational period of the products and changes in risk attitudes of decision makers on decision-making behavior,finding that under the same level of risk,for the price increase channel,the longer the operating cycle,the optimal decision is gradually reduced;while in the price decline channel,the longer the operating cycle,the optimal decision is gradually increased.And in the two price channels,the policy makers' tolerance for risk is not the same.For the randomness and relevance of the prices and the demands,this paper discussed the optimal order quantity and profit target of decision makers under the change of the two random factors of positive correlation,the volatility of the costs and demands on different levels of risk.When decision makers are risk neutral and under lower risk aversion level,the correlation and volatility have no effect on the optimal decision-making;when the risk aversion level is higher,under the influence of correlation or volatility,the optimal order quantity and profit target changes both vary regularly.