风险厌恶供应链的定价与订货策略研究
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摘要
传统关于供应链管理的研究主要是建立在风险中性的基础上,即决策者的目标是最大化期望利润(或最小化期望成本)。然而,近年来关于供应链管理的研究和实践表明：决策者已不仅关注这种期望利润的最大化,而且更关注这种预期利润实现的可能性以及面临的各种风险。因此本文在决策者是风险厌恶的情况下,运用定量模型与定性分析相结合的方法,研究了供应链的定价与订货策略以及决策者的风险厌恶态度给供应链效益所带来的影响。论文的主要研究内容及研究成果如下：
1)在商品的市场零售价是外部给定时研究了二阶供应链的最佳策略：首先以条件价值风险CVaR作为风险厌恶零售商的风险度量,以期望利润和CVaR的加权平均为目标研究了零售商的订货策略,并在此基础上研究了上游供应商的定价策略,这样的“利润—CVaR "目标既反映了决策者追求高利润的愿望又反映了其对潜在风险的控制。由于在分散决策模式下,零售商独自承担随机需求的市场风险,因而选择通过紧缩订货量以规避风险,导致供应链失调,风险厌恶进一步恶化了这种情况。在这些研究的基础上,以共同分担市场风险为切入点,提出基于回购契约的供应链协调策略。最后,在供应商对零售商的风险厌恶程度并不知晓的情况下研究了供应链的最优策略,研究表明供应商不明确零售商的风险厌恶程度一定会导致其期望利润的下降,从而也体现了信息的价值。
2)在零售价是由决策者决定同时随机需求依赖于价格的情况下研究了供应链的最佳策略：这里主要研究了依赖于价格的平均需求和不依赖于价格的随机因素的两种组合：一种是乘积型需求,另一种是加型需求,分别在风险中性和风险厌恶两种背景下对决策者的最佳策略进行了研究。考虑到许多“滞销”商品都存在一定的残值,提出一个相对残值的需求价格弹性(PES)概念,在单调增加的相对残值的需求价格弹性(IPES)的假设下,证明了决策者最优策略的存在唯一性,从而为寻求最优解的一维搜索方法提供了理论依据。研究表明：在分散决策模式下零售商选择的最优订货量会低于在集中决策模式下的最优订货量,同时选择的零售价会比集中决策模式下更高。最后,基于这种价格依赖的随机需求的“价格依赖性”和“随机性”,提出了零售商与供应商的利润分配取决于由“价格依赖性”所引起零售商的“后动优势”与由“随机性”所引起供应商的“先动优势”的较量结果,并通过算例分析对此进行了实证。
3)首先考虑了一个企业的两周期生产决策,分别在风险中性和在风险厌恶下以CVaR为风险度量的情况下进行了研究,并通过算例分析考察了风险态度给企业所带来的影响,结果表明,当企业的风险厌恶程度在增加的时候,即越来越关注企业在“低赢利”时候的利润的期望值,对最坏的情况顾忌太多,导致在选择订货量时变得越来越保守,期望利润也跟着越来越少。然后基于贝叶斯信息更新研究了一个企业的多周期订货策略,研究表明,在以负指数效用函数为目标的情况下,最佳贝叶斯库存水平总会高于短视(myopic)零售商的最佳库存水平。
4)研究了一个由供应商和零售商组成的二阶供应链的多周期决策问题,每个决策者既要考虑到结构维度上供应链上下游之间的博弈,又要考虑到时间维度上面临的多周期决策问题。结合动态规划的方法和动态博弈的逆向归纳法,分别在零售商为风险中性和风险厌恶的两种情形下对供应商与零售商的最佳策略进行了研究。并把基于供应商与零售商合作的集中决策模式与基于非合作的分散决策模式下供应链的最佳决策进行了比较分析。最后通过算例分析,研究了零售商的风险厌恶态度给供应链效益所带来的影响。
论文的创新点主要表现在以下四个方面：
1)在供应链的环境下以“利润—CVaR "作为风险厌恶零售商的目标,研究了其订货策略以及给上游供应商的决策所带来的影响,结果表明,供应链效益随零售商的风险厌恶因子和CVaR权重的增加而减少；并在供应商不知晓零售商风险厌恶程度的情况下研究了供应链的最佳策略并得到：供应商对零售商风险厌恶程度的不确定一定会导致其期望利润的下降,且引起对期望利润的“预测失真”。
2)提出一个相对残值的需求价格弹性(PES)概念,在单调增加的相对残值的需求价格弹性(IPES)的假设下,证明了决策者最优策略的存在唯一性,从而为寻求最优解的一维搜索方法提供了理论依据。
3)基于价格依赖的随机需求的“价格依赖性”和“随机性”,提出了零售商与供应商的利润分配取决于由“价格依赖性”所引起零售商的“后动优势”与由“随机性”所引起供应商的“先动优势”的强弱较量。
4)在决策者为风险厌恶的情况下研究多周期供应链决策问题,并考虑了决策者的风险态度给供应链带来的影响,结果表明,在多周期的情况下,分散决策模式的供应链效益明显低于集中决策模式下的供应链效益,并且随零售商风险厌恶因子的增加而减少。
Tradtional research on supply chain management mainly focuses on the risk-neutral case, that is, the objective of the decision-maker is to maximize the expected profit (or minimize the expected cost). However, the research and practice on supply chain management in recent years shows that, the decision-maker conerns not only the maximization of the expected profit, but the possibility of realizing the expected profit and the risk that may occurs. So, under the assumption that the decision-maker is risk averse, through an approach combining the quantitative model and qualitative analysis, this dissertation studies the pricing and ordering policies of the supply chain and the effect of the risk aversion on the supply chain. The main research contents and results are as following:
1) The optimal policy of a two-echelon supply chain is considered when the retail price of the commodity is exogenously given. Firstly, with conditionally risk-at-value(CVaR) as a risk measure of the risk averse retailer, we consider the ordering policy of the retailer, and therefore the pricing policy of the upstream supplier, under the objective of maximizing a combination of the expected profit and CVaR, which reflects the desire of the risk-averse decision maker to maximize the profit on one hand, and minimize the downside risk of his profit on the other hand. In a decentralized mode, the retailer faces solely the market risk of the stochastic demand, therefore chooses to decrease the ordering quantity to avoid the risk, which leads to an incoordination of the supply chain, moreover, the risk aversion aggravates the inefficiency. Based on the above research, with sharing risk of the retailer as a breakthrough point, we propose a buy-back contract to coordinate the supply chain. At last, in the event that the supplier is uncertain about the degree of the retailer's risk aversion, we study the optimal policy of the supply chain and get that the supplier's expected profit must be less than that in the certain case, which implies the value of information.
2) When the retail price is an endogenous variable and the stochastic demand is price-dependent, the optimal policy of a two-echelon supply chain is considered. Here we study two kind of combination of the mean demand depending on the retail price and the stochastic factor independent on the retail price:one is multiplicative mode, the other is additive mode, in the background of risk neutral and risk averse respectively. For many unsold commodities still own its salvage value, we propose a concept of price elasticity with respect to salvage value(PES) of the demand and demonstrate the existence and uniqueness of the optimal strategy under the condition of increasing price elasticity with respect to salvage value(IPES), which provides a theoretical foundation for one dimensional search for the optimal solution. The research shows that the optimal ordering quantity of the retailer in the decentralized mode will be less than that in the centralized case, while charges a higher retail price in the decentralized model than in the centralized case. Lastly, based on the price-dependent nature and stochastic nature of the price-dependent stochastic demand, we propose the allocation of the profit of the supply chain depending on the contest of the second-move advantage of the retailer resulting from the price-dependent nature and the first-move advantage of the supplier resulting from the stochastic nature, and demonstrate it through a numerical analysis.
3) Firstly, we consider a two-period optimal producing policy of a firm in the background of risk neutral and risk averse respectively, where the risk is measured by CVaR, and therefore the effect of the risk aversion on the firm through numerical analysis. The result shows that, when the degree of the risk aversion is increasing, that is the firm pay more attention on the "low profit", the firm becomes too conservative and order less quantity which leads to less expected profit. Then, based on the Bayesian information updating, we consider a multi-period ordering strategy, which shows that the optimal bayesian inventory level will be always higher than the optimal myopic inventory level, when the firm's objective is maximizing the negative exponential utility function.
4) A multi-period two-echelon supply chain consisting of a supplier and a retailer is considered, where every decision maker concerns not only the game between the upstream and downstream of the supply chain on the structure dimension, but also the multi-period dynamic decision on the time dimension. Combining the dynamic programming approach and the backward induction approach of the dynamic games, we study the optimal policy of the supplier and the retailer in the background of risk neutral and risk averse respectively. We make a comprison analysis for the corresponding policy of the centralized and the decentralized mode. At last, the effect of the risk aversion on the supply chain is considerd through numerical analysis.
In this dissertation, some innovations are made in the following four aspects:
1) Under the circumstances of a supply chain, with "profit-CVaR" as the objective of the risk averse retailer, we consider the ordering policy, and therefore the effect on the upstream supplier's pricing decision, which shows that the efficiency of the supply chain decreases with the increasing of the risk aversion factor of the retailer and the weight of CVaR. And as the supplier is uncertain about the degree of the retailer's risk aversion, the optimal policy of the supply chain is considered. The research shows that the uncertainty of the supplier about the degree of the retailer's risk aversion will results in the decreasing of the supplier's expected profit and "unbiased forecast" on the. expected profit.
2) A new concept of the price elasticity with respect to salvage value(PES) is proposed. Under the condition of increasing price elasticity with respect to salvage value (IPES), we demonstrate the existence and uniqueness of the optimal strategy which provides a theoretical foundation for one dimensional search for the optimal solution.
3) Based on the price-dependent nature and stochastic nature of the price-dependent stochastic demand, we propose the allocation of the profit of the supply chain depending on the contest of the second-move advantage of the retailer resulting from the price-dependence nature and the first-move advantage of the supplier resulting from the stochastic nature.
4) A multi-period supply chain problem with risk averse decision maker, and therefore the effect of the risk aversion on the supply chain is studied, which shows that in the background of multi-period, the efficiency of the supply chain in decentralized mode must be less than that in centralized mode, and decreases with the increasing of the retailer's risk aversion factor.
1)在商品的市场零售价是外部给定时研究了二阶供应链的最佳策略：首先以条件价值风险CVaR作为风险厌恶零售商的风险度量,以期望利润和CVaR的加权平均为目标研究了零售商的订货策略,并在此基础上研究了上游供应商的定价策略,这样的“利润—CVaR "目标既反映了决策者追求高利润的愿望又反映了其对潜在风险的控制。由于在分散决策模式下,零售商独自承担随机需求的市场风险,因而选择通过紧缩订货量以规避风险,导致供应链失调,风险厌恶进一步恶化了这种情况。在这些研究的基础上,以共同分担市场风险为切入点,提出基于回购契约的供应链协调策略。最后,在供应商对零售商的风险厌恶程度并不知晓的情况下研究了供应链的最优策略,研究表明供应商不明确零售商的风险厌恶程度一定会导致其期望利润的下降,从而也体现了信息的价值。
2)在零售价是由决策者决定同时随机需求依赖于价格的情况下研究了供应链的最佳策略：这里主要研究了依赖于价格的平均需求和不依赖于价格的随机因素的两种组合：一种是乘积型需求,另一种是加型需求,分别在风险中性和风险厌恶两种背景下对决策者的最佳策略进行了研究。考虑到许多“滞销”商品都存在一定的残值,提出一个相对残值的需求价格弹性(PES)概念,在单调增加的相对残值的需求价格弹性(IPES)的假设下,证明了决策者最优策略的存在唯一性,从而为寻求最优解的一维搜索方法提供了理论依据。研究表明：在分散决策模式下零售商选择的最优订货量会低于在集中决策模式下的最优订货量,同时选择的零售价会比集中决策模式下更高。最后,基于这种价格依赖的随机需求的“价格依赖性”和“随机性”,提出了零售商与供应商的利润分配取决于由“价格依赖性”所引起零售商的“后动优势”与由“随机性”所引起供应商的“先动优势”的较量结果,并通过算例分析对此进行了实证。
3)首先考虑了一个企业的两周期生产决策,分别在风险中性和在风险厌恶下以CVaR为风险度量的情况下进行了研究,并通过算例分析考察了风险态度给企业所带来的影响,结果表明,当企业的风险厌恶程度在增加的时候,即越来越关注企业在“低赢利”时候的利润的期望值,对最坏的情况顾忌太多,导致在选择订货量时变得越来越保守,期望利润也跟着越来越少。然后基于贝叶斯信息更新研究了一个企业的多周期订货策略,研究表明,在以负指数效用函数为目标的情况下,最佳贝叶斯库存水平总会高于短视(myopic)零售商的最佳库存水平。
4)研究了一个由供应商和零售商组成的二阶供应链的多周期决策问题,每个决策者既要考虑到结构维度上供应链上下游之间的博弈,又要考虑到时间维度上面临的多周期决策问题。结合动态规划的方法和动态博弈的逆向归纳法,分别在零售商为风险中性和风险厌恶的两种情形下对供应商与零售商的最佳策略进行了研究。并把基于供应商与零售商合作的集中决策模式与基于非合作的分散决策模式下供应链的最佳决策进行了比较分析。最后通过算例分析,研究了零售商的风险厌恶态度给供应链效益所带来的影响。
论文的创新点主要表现在以下四个方面：
1)在供应链的环境下以“利润—CVaR "作为风险厌恶零售商的目标,研究了其订货策略以及给上游供应商的决策所带来的影响,结果表明,供应链效益随零售商的风险厌恶因子和CVaR权重的增加而减少；并在供应商不知晓零售商风险厌恶程度的情况下研究了供应链的最佳策略并得到：供应商对零售商风险厌恶程度的不确定一定会导致其期望利润的下降,且引起对期望利润的“预测失真”。
2)提出一个相对残值的需求价格弹性(PES)概念,在单调增加的相对残值的需求价格弹性(IPES)的假设下,证明了决策者最优策略的存在唯一性,从而为寻求最优解的一维搜索方法提供了理论依据。
3)基于价格依赖的随机需求的“价格依赖性”和“随机性”,提出了零售商与供应商的利润分配取决于由“价格依赖性”所引起零售商的“后动优势”与由“随机性”所引起供应商的“先动优势”的强弱较量。
4)在决策者为风险厌恶的情况下研究多周期供应链决策问题,并考虑了决策者的风险态度给供应链带来的影响,结果表明,在多周期的情况下,分散决策模式的供应链效益明显低于集中决策模式下的供应链效益,并且随零售商风险厌恶因子的增加而减少。
Tradtional research on supply chain management mainly focuses on the risk-neutral case, that is, the objective of the decision-maker is to maximize the expected profit (or minimize the expected cost). However, the research and practice on supply chain management in recent years shows that, the decision-maker conerns not only the maximization of the expected profit, but the possibility of realizing the expected profit and the risk that may occurs. So, under the assumption that the decision-maker is risk averse, through an approach combining the quantitative model and qualitative analysis, this dissertation studies the pricing and ordering policies of the supply chain and the effect of the risk aversion on the supply chain. The main research contents and results are as following:
1) The optimal policy of a two-echelon supply chain is considered when the retail price of the commodity is exogenously given. Firstly, with conditionally risk-at-value(CVaR) as a risk measure of the risk averse retailer, we consider the ordering policy of the retailer, and therefore the pricing policy of the upstream supplier, under the objective of maximizing a combination of the expected profit and CVaR, which reflects the desire of the risk-averse decision maker to maximize the profit on one hand, and minimize the downside risk of his profit on the other hand. In a decentralized mode, the retailer faces solely the market risk of the stochastic demand, therefore chooses to decrease the ordering quantity to avoid the risk, which leads to an incoordination of the supply chain, moreover, the risk aversion aggravates the inefficiency. Based on the above research, with sharing risk of the retailer as a breakthrough point, we propose a buy-back contract to coordinate the supply chain. At last, in the event that the supplier is uncertain about the degree of the retailer's risk aversion, we study the optimal policy of the supply chain and get that the supplier's expected profit must be less than that in the certain case, which implies the value of information.
2) When the retail price is an endogenous variable and the stochastic demand is price-dependent, the optimal policy of a two-echelon supply chain is considered. Here we study two kind of combination of the mean demand depending on the retail price and the stochastic factor independent on the retail price:one is multiplicative mode, the other is additive mode, in the background of risk neutral and risk averse respectively. For many unsold commodities still own its salvage value, we propose a concept of price elasticity with respect to salvage value(PES) of the demand and demonstrate the existence and uniqueness of the optimal strategy under the condition of increasing price elasticity with respect to salvage value(IPES), which provides a theoretical foundation for one dimensional search for the optimal solution. The research shows that the optimal ordering quantity of the retailer in the decentralized mode will be less than that in the centralized case, while charges a higher retail price in the decentralized model than in the centralized case. Lastly, based on the price-dependent nature and stochastic nature of the price-dependent stochastic demand, we propose the allocation of the profit of the supply chain depending on the contest of the second-move advantage of the retailer resulting from the price-dependent nature and the first-move advantage of the supplier resulting from the stochastic nature, and demonstrate it through a numerical analysis.
3) Firstly, we consider a two-period optimal producing policy of a firm in the background of risk neutral and risk averse respectively, where the risk is measured by CVaR, and therefore the effect of the risk aversion on the firm through numerical analysis. The result shows that, when the degree of the risk aversion is increasing, that is the firm pay more attention on the "low profit", the firm becomes too conservative and order less quantity which leads to less expected profit. Then, based on the Bayesian information updating, we consider a multi-period ordering strategy, which shows that the optimal bayesian inventory level will be always higher than the optimal myopic inventory level, when the firm's objective is maximizing the negative exponential utility function.
4) A multi-period two-echelon supply chain consisting of a supplier and a retailer is considered, where every decision maker concerns not only the game between the upstream and downstream of the supply chain on the structure dimension, but also the multi-period dynamic decision on the time dimension. Combining the dynamic programming approach and the backward induction approach of the dynamic games, we study the optimal policy of the supplier and the retailer in the background of risk neutral and risk averse respectively. We make a comprison analysis for the corresponding policy of the centralized and the decentralized mode. At last, the effect of the risk aversion on the supply chain is considerd through numerical analysis.
In this dissertation, some innovations are made in the following four aspects:
1) Under the circumstances of a supply chain, with "profit-CVaR" as the objective of the risk averse retailer, we consider the ordering policy, and therefore the effect on the upstream supplier's pricing decision, which shows that the efficiency of the supply chain decreases with the increasing of the risk aversion factor of the retailer and the weight of CVaR. And as the supplier is uncertain about the degree of the retailer's risk aversion, the optimal policy of the supply chain is considered. The research shows that the uncertainty of the supplier about the degree of the retailer's risk aversion will results in the decreasing of the supplier's expected profit and "unbiased forecast" on the. expected profit.
2) A new concept of the price elasticity with respect to salvage value(PES) is proposed. Under the condition of increasing price elasticity with respect to salvage value (IPES), we demonstrate the existence and uniqueness of the optimal strategy which provides a theoretical foundation for one dimensional search for the optimal solution.
3) Based on the price-dependent nature and stochastic nature of the price-dependent stochastic demand, we propose the allocation of the profit of the supply chain depending on the contest of the second-move advantage of the retailer resulting from the price-dependence nature and the first-move advantage of the supplier resulting from the stochastic nature.
4) A multi-period supply chain problem with risk averse decision maker, and therefore the effect of the risk aversion on the supply chain is studied, which shows that in the background of multi-period, the efficiency of the supply chain in decentralized mode must be less than that in centralized mode, and decreases with the increasing of the retailer's risk aversion factor.
引文
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