In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The ...In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The value of risk control becomes more important especially for products with short life cycle. This is because, the profit implications of low yield might be unbearable in the short run. We apply Conditional Value at Risk （CVaR） to model the, risk. CVaR measure is a coherent risk measure and thereby having nice conceptual and mathematical underpinnings. It is also widely used in practice. We consider the problem under general demand function and general distribution function of yield and find sufficient conditions under which the problem has a unique local maximum. We also both analytically and numerically analyze the impact of parameter change on the optimal solution. Among our results, we analytically show that with increasing risk aversion, the optimal price increases. This relation is opposite to that of in Newsvendor problem where the uncertainty lies in demand side.展开更多
发电量的多期投标组合是一个动态的优化问题,决策过程中常常呈现多期风险,因而对风险的度量也应该是动态的。条件风险价值(conditional value at risk,CVaR)是一种静态一致性风险度量,不适用于对发电量的时间分解进行多期风险评估。该...发电量的多期投标组合是一个动态的优化问题,决策过程中常常呈现多期风险,因而对风险的度量也应该是动态的。条件风险价值(conditional value at risk,CVaR)是一种静态一致性风险度量,不适用于对发电量的时间分解进行多期风险评估。该文提出一种动态一致性风险度量,考虑风险对未来投资收益波动的长期影响,将分位数作用于静态一致性风险度量来表征多期风险的动态特征,并采用分位数回归的方法,以各期CVaR的绝对偏差加权和最小为目标函数建立数学模型,该模型可同时应用于计及风险的发电量时间分解和空间分配计算。以水电厂短期优化调度为例,说明该风险度量指标的可行性和实用性。展开更多
文摘In this paper, we address a basic production planning problem with price dependent demand and stochastic yield of production. We use price and target quantity as decision variables to lower the risk of low yield. The value of risk control becomes more important especially for products with short life cycle. This is because, the profit implications of low yield might be unbearable in the short run. We apply Conditional Value at Risk （CVaR） to model the, risk. CVaR measure is a coherent risk measure and thereby having nice conceptual and mathematical underpinnings. It is also widely used in practice. We consider the problem under general demand function and general distribution function of yield and find sufficient conditions under which the problem has a unique local maximum. We also both analytically and numerically analyze the impact of parameter change on the optimal solution. Among our results, we analytically show that with increasing risk aversion, the optimal price increases. This relation is opposite to that of in Newsvendor problem where the uncertainty lies in demand side.
文摘发电量的多期投标组合是一个动态的优化问题,决策过程中常常呈现多期风险,因而对风险的度量也应该是动态的。条件风险价值(conditional value at risk,CVaR)是一种静态一致性风险度量,不适用于对发电量的时间分解进行多期风险评估。该文提出一种动态一致性风险度量,考虑风险对未来投资收益波动的长期影响,将分位数作用于静态一致性风险度量来表征多期风险的动态特征,并采用分位数回归的方法,以各期CVaR的绝对偏差加权和最小为目标函数建立数学模型,该模型可同时应用于计及风险的发电量时间分解和空间分配计算。以水电厂短期优化调度为例,说明该风险度量指标的可行性和实用性。
