基于Copula-CVaR的经典报童模型扩展研究

发布时间：2018-01-22 15:47

本文关键词： 报童模型 Copula函数条件风险价值(Conditional Value at Risk CVa R) 线性规划蒙特卡洛模拟　出处：《东华大学》2017年硕士论文　论文类型：学位论文

【摘要】：报童模型是供应链管理问题研究的基础模型之一。传统上,报童模型针对单一产品、单周期,仅考虑需求不确定性下的最优订货量决策。但实际中,除了需求,成本和价格也可以是随机的外生变量,而且由于决策主体可能具有的风险态度,实际中的订货量也常偏离理论上报童模型的最优订货量。因此,本文考虑两个随机变量的相关性和决策者的风险态度对最终决策的影响。并分别用Copula函数描述随机变量的相关性,条件风险价值(Conditional Value at Risk,CVaR)度量风险态度。建立了成本和价格相关、成本与需求相关两种随机情形下的Copula-CVaR报童模型。本质上所构建的两种情形下的Copula-CVaR模型是随机规划问题,通过离散化将其转化为线性规划模型并予以求解。在模型的仿真阶段,主要针对成本和价格为随机变量的情形,以大宗商品的价格波动为背景,借助蒙特卡洛模拟构建了离散下的线性规划模型,并利用Cplex予以求解。本文的主要研究内容和结论如下:(1)在不考虑决策主体风险态度的前提下,建立两个随机变量具有联合分布函数时决策者的期望收益函数,经过推导发现最优订货量与随机变量的联合分布函数无关。因此,在讨论用联合分布函数描述随机变量的相关性时同时,考虑决策者的风险态度,引入CVaR进行目标函数的构建。(2)建立了成本和价格双波动、成本和需求双波动下的CopulaCVaR模型,并证明了模型存在唯一的最优解。连续函数下的模型实际上为随机规划问题,因此将本文所构建的非线性规划问题通过离散化转化成了线性规划问题进行求解。(3)在模型的仿真阶段,对于成本和价格双波动的情形,以大宗商品的价格波动性为背景,通过Copula函数模型的选择方法以及蒙特卡洛模拟的方式,分析了价格上涨通道和下跌通道下,产品运营周期以及决策者风险态度的变化对决策行为的影响。在同一风险水平下,对于价格上涨通道,运营周期越长,最优决策是逐渐降低的;而在价格下跌通道下,运营周期越长,最优决策是逐渐升高的。而且在两种价格变化下,决策者对于风险的容忍程度不一样。对于成本和需求双波动的情形,本文讨论了两个随机因素的正相关性、成本和需求的波动性在不同的风险水平下对最优订货量的影响以及决策者目标利润的变化。当决策者为风险中性和风险规避水平较低时,相关性的变化以及波动性的变化对最优决策没有影响;当风险规避水平较高时,最优订货量以及目标利润的变化无论是在相关性或是波动性的影响下,都是呈现规律性变化的。
[Abstract]:The newsboy model is one of the basic models of supply chain management. Traditionally, the newsboy model only considers the optimal order quantity decision under the uncertainty of demand for a single product and a single period. But in practice, except demand. The cost and price can also be random exogenous variables, and because of the possible risk attitude of decision makers, the order volume in practice often deviates from the optimal order quantity of the newsboy model in theory. In this paper, the correlation of two random variables and the risk attitude of decision makers are considered, and the Copula function is used to describe the correlation of random variables. Conditional Value at RiskCvar) measures risk attitude and establishes cost and price correlation. The Copula-CVaR newsboy model based on cost and demand is a stochastic programming problem. In essence, the two Copula-CVaR models are stochastic programming problems. In the simulation stage of the model, the cost and price are random variables, with the commodity price fluctuation as the background. The discrete linear programming model is constructed by Monte Carlo simulation and solved by Cplex. The main contents and conclusions of this paper are as follows: 1) without considering the risk attitude of decision makers. When two random variables have the joint distribution function, the expected return function of the decision maker is established. It is found that the optimal order quantity has nothing to do with the joint distribution function of the random variable. When discussing the correlation of random variables with joint distribution function (JDF), taking into account the risk attitude of decision makers, CVaR is introduced to construct objective function.) the double fluctuation of cost and price is established. The CopulaCVaR model with double fluctuation of cost and demand is proved to have a unique optimal solution. The model under continuous function is actually a stochastic programming problem. Therefore, the nonlinear programming problem constructed in this paper is transformed into a linear programming problem by discretization to solve the linear programming problem. In the simulation stage of the model, the cost and price are both fluctuated. In the context of commodity price volatility, through the selection of Copula function model and Monte Carlo simulation, this paper analyzes the price rise channel and down channel. The influence of product operation cycle and the change of decision maker's risk attitude on the decision-making behavior. At the same risk level, the longer the operating cycle is, the lower the optimal decision is. However, the longer the operating cycle, the higher the optimal decision is, and under the two price changes, the degree of tolerance for risk is not the same. For the case of double fluctuation of cost and demand. In this paper, we discuss the positive correlation of two random factors. The impact of the volatility of cost and demand on the optimal order volume at different risk levels and the change of the decision-maker 's target profit. When the decision maker is risk-neutral and the risk aversion level is low. The change of correlation and volatility have no effect on the optimal decision. When the level of risk aversion is high, the change of optimal order quantity and target profit is regular, whether under the influence of correlation or volatility.
【学位授予单位】：东华大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F274

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