本文關(guān)鍵詞： 報(bào)童模型 Copula函數(shù) 條件風(fēng)險(xiǎn)價(jià)值(Conditional Value at Risk CVa R) 線性規(guī)劃 蒙特卡洛模擬　出處：《東華大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：報(bào)童模型是供應(yīng)鏈管理問(wèn)題研究的基礎(chǔ)模型之一。傳統(tǒng)上,報(bào)童模型針對(duì)單一產(chǎn)品、單周期,僅考慮需求不確定性下的最優(yōu)訂貨量決策。但實(shí)際中,除了需求,成本和價(jià)格也可以是隨機(jī)的外生變量,而且由于決策主體可能具有的風(fēng)險(xiǎn)態(tài)度,實(shí)際中的訂貨量也常偏離理論上報(bào)童模型的最優(yōu)訂貨量。因此,本文考慮兩個(gè)隨機(jī)變量的相關(guān)性和決策者的風(fēng)險(xiǎn)態(tài)度對(duì)最終決策的影響。并分別用Copula函數(shù)描述隨機(jī)變量的相關(guān)性,條件風(fēng)險(xiǎn)價(jià)值(Conditional Value at Risk,CVaR)度量風(fēng)險(xiǎn)態(tài)度。建立了成本和價(jià)格相關(guān)、成本與需求相關(guān)兩種隨機(jī)情形下的Copula-CVaR報(bào)童模型。本質(zhì)上所構(gòu)建的兩種情形下的Copula-CVaR模型是隨機(jī)規(guī)劃問(wèn)題,通過(guò)離散化將其轉(zhuǎn)化為線性規(guī)劃模型并予以求解。在模型的仿真階段,主要針對(duì)成本和價(jià)格為隨機(jī)變量的情形,以大宗商品的價(jià)格波動(dòng)為背景,借助蒙特卡洛模擬構(gòu)建了離散下的線性規(guī)劃模型,并利用Cplex予以求解。本文的主要研究?jī)?nèi)容和結(jié)論如下:(1)在不考慮決策主體風(fēng)險(xiǎn)態(tài)度的前提下,建立兩個(gè)隨機(jī)變量具有聯(lián)合分布函數(shù)時(shí)決策者的期望收益函數(shù),經(jīng)過(guò)推導(dǎo)發(fā)現(xiàn)最優(yōu)訂貨量與隨機(jī)變量的聯(lián)合分布函數(shù)無(wú)關(guān)。因此,在討論用聯(lián)合分布函數(shù)描述隨機(jī)變量的相關(guān)性時(shí)同時(shí),考慮決策者的風(fēng)險(xiǎn)態(tài)度,引入CVaR進(jìn)行目標(biāo)函數(shù)的構(gòu)建。(2)建立了成本和價(jià)格雙波動(dòng)、成本和需求雙波動(dòng)下的CopulaCVaR模型,并證明了模型存在唯一的最優(yōu)解。連續(xù)函數(shù)下的模型實(shí)際上為隨機(jī)規(guī)劃問(wèn)題,因此將本文所構(gòu)建的非線性規(guī)劃問(wèn)題通過(guò)離散化轉(zhuǎn)化成了線性規(guī)劃問(wèn)題進(jìn)行求解。(3)在模型的仿真階段,對(duì)于成本和價(jià)格雙波動(dòng)的情形,以大宗商品的價(jià)格波動(dòng)性為背景,通過(guò)Copula函數(shù)模型的選擇方法以及蒙特卡洛模擬的方式,分析了價(jià)格上漲通道和下跌通道下,產(chǎn)品運(yùn)營(yíng)周期以及決策者風(fēng)險(xiǎn)態(tài)度的變化對(duì)決策行為的影響。在同一風(fēng)險(xiǎn)水平下,對(duì)于價(jià)格上漲通道,運(yùn)營(yíng)周期越長(zhǎng),最優(yōu)決策是逐漸降低的;而在價(jià)格下跌通道下,運(yùn)營(yíng)周期越長(zhǎng),最優(yōu)決策是逐漸升高的。而且在兩種價(jià)格變化下,決策者對(duì)于風(fēng)險(xiǎn)的容忍程度不一樣。對(duì)于成本和需求雙波動(dòng)的情形,本文討論了兩個(gè)隨機(jī)因素的正相關(guān)性、成本和需求的波動(dòng)性在不同的風(fēng)險(xiǎn)水平下對(duì)最優(yōu)訂貨量的影響以及決策者目標(biāo)利潤(rùn)的變化。當(dāng)決策者為風(fēng)險(xiǎn)中性和風(fēng)險(xiǎn)規(guī)避水平較低時(shí),相關(guān)性的變化以及波動(dòng)性的變化對(duì)最優(yōu)決策沒(méi)有影響;當(dāng)風(fēng)險(xiǎn)規(guī)避水平較高時(shí),最優(yōu)訂貨量以及目標(biāo)利潤(rùn)的變化無(wú)論是在相關(guān)性或是波動(dòng)性的影響下,都是呈現(xiàn)規(guī)律性變化的。
[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.
【學(xué)位授予單位】：東華大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F274

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