We consider a distribution system with one supplier and two retailers. For the two retailers, they face different demand and are both risk averse. We study a single period model which the supplier has ample goods and ...We consider a distribution system with one supplier and two retailers. For the two retailers, they face different demand and are both risk averse. We study a single period model which the supplier has ample goods and the retailers order goods separately. Market search is measured as the fraction of customers who unsatisfied with their ＂local＂ retailer due to stock-out, and search for the goods at the other retailer before leaving the system. We investigate how the retailers game for order quantity in a Conditional Value-at-Risk framework and study how risk averse degree, market search level, holding cost and backorder cost influence the optimal order strategies. Furthermore, we use uniform distribution to illustrate these results and obtain Nash equilibrium of order strategies.展开更多
We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional va...We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.展开更多
The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or schedu...The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.展开更多
A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC...A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.展开更多
为进一步提升综合能源系统环境效益,减少新能源出力不确定性所带来的潜在风险,提出了计及条件风险价值(conditional value at risk,CVaR)以及阶梯碳交易的综合能源系统优化调度模型。考虑到系统风电和光伏出力不确定性可能带来的影响,...为进一步提升综合能源系统环境效益,减少新能源出力不确定性所带来的潜在风险,提出了计及条件风险价值(conditional value at risk,CVaR)以及阶梯碳交易的综合能源系统优化调度模型。考虑到系统风电和光伏出力不确定性可能带来的影响,采用条件风险价值量度不确定性带来的潜在风险,并将碳捕获技术、电转气设备以及阶梯式碳交易机制引入系统调度模型,构建了综合考虑系统运行成本和碳交易成本的优化调度目标函数,由于所建立模型为混合整数规划问题,采用CPLEX求解器进行求解,设置4种场景进行验证分析,算例表明所提模型可有效减少二氧化碳排放,在兼顾经济性和环境性的同时引入CVaR,可避免由于忽略风光不确定性所带来的较为乐观的调度结果,使系统最终调度结果更为合理。展开更多
考虑到海上风电出力的随机性以及日益突出的生态环境问题,以含柔性直流输电技术(voltagesource converter high voltage direct current,VSC-HVDC)的交直流系统为研究对象,提出了考虑条件风险价值(conditional valueatrisk,CVaR)的两阶...考虑到海上风电出力的随机性以及日益突出的生态环境问题,以含柔性直流输电技术(voltagesource converter high voltage direct current,VSC-HVDC)的交直流系统为研究对象,提出了考虑条件风险价值(conditional valueatrisk,CVaR)的两阶段分布鲁棒低碳经济优化模型,构建了基于Kullback-Leibler(KL)散度的概率分布模糊集,同时利用条件风险价值量化了极端场景下的尾部风险,使得模型能够同时考虑概率分布不确定性以及处于最坏概率分布中极端场景下的尾部损失;此外,将阶梯型碳交易机制并入所提分布鲁棒模型中,通过合理利用柔性资源和储能装置,增强系统运行的灵活性,在兼顾运行风险的前提下,降低碳排放量的目标。再者,为了提高计算效率,在列和约束生成算法(column-and-constraint generation method,C&CG)和Multi-cut Benders分解算法的基础上提出了双循环分解算法。最后,在基于改进的IEEE RTS 79测试系统中验证了所提模型及算法的有效性。展开更多
基金Supported by the National Natural Science Foundation of China (70471034, A0324666)
文摘We consider a distribution system with one supplier and two retailers. For the two retailers, they face different demand and are both risk averse. We study a single period model which the supplier has ample goods and the retailers order goods separately. Market search is measured as the fraction of customers who unsatisfied with their ＂local＂ retailer due to stock-out, and search for the goods at the other retailer before leaving the system. We investigate how the retailers game for order quantity in a Conditional Value-at-Risk framework and study how risk averse degree, market search level, holding cost and backorder cost influence the optimal order strategies. Furthermore, we use uniform distribution to illustrate these results and obtain Nash equilibrium of order strategies.
文摘We consider risk minimization problems for Markov decision processes. From a standpoint of making the risk of random reward variable at each time as small as possible, a risk measure is introduced using conditional value-at-risk for random immediate reward variables in Markov decision processes, under whose risk measure criteria the risk-optimal policies are characterized by the optimality equations for the discounted or average case. As an application, the inventory models are considered.
基金supported by the National Key R&D Program of China(Grant No.2019YFA0308700)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0301500)。
文摘The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)class.This problem is widely used in encryption,planning or scheduling,and integer partitions.An accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical computers.To effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at risk.The proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum resources.The model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum era.We investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the model.Moreover,we also discuss the performance of the model under different conditional values at risk.Through computer simulation,the scale can reach more than nine qubits.By selecting the noise type,we construct simulators with different QVs and study the performance of the model with them.In addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum problem.This model provides a new perspective for solving the subset sum problem.
基金Sponsored by the National Natural Science Foundation of China(70571010)
文摘A new stochastic volatility（SV）method to estimate the conditional value at risk（CVaR）is put forward.Firstly,it makes use of SV model to forecast the volatility of return.Secondly,the Markov chain Monte Carlo（MCMC）simulation and Gibbs sampling have been used to estimate the parameters in the SV model.Thirdly,in this model,CVaR calculation is immediate.In this way,the SV-CVaR model overcomes the drawbacks of the generalized autoregressive conditional heteroscedasticity value at risk（GARCH-VaR）model.Empirical study suggests that this model is better than GARCH-VaR model in this field.
文摘为进一步提升综合能源系统环境效益,减少新能源出力不确定性所带来的潜在风险,提出了计及条件风险价值(conditional value at risk,CVaR)以及阶梯碳交易的综合能源系统优化调度模型。考虑到系统风电和光伏出力不确定性可能带来的影响,采用条件风险价值量度不确定性带来的潜在风险,并将碳捕获技术、电转气设备以及阶梯式碳交易机制引入系统调度模型,构建了综合考虑系统运行成本和碳交易成本的优化调度目标函数,由于所建立模型为混合整数规划问题,采用CPLEX求解器进行求解,设置4种场景进行验证分析,算例表明所提模型可有效减少二氧化碳排放,在兼顾经济性和环境性的同时引入CVaR,可避免由于忽略风光不确定性所带来的较为乐观的调度结果,使系统最终调度结果更为合理。
基金This research was supported by the Social Science Foundation of the Ministry of Education of China under Grant No. 07JA630015, the National Natural Science Foundation of China under Grant Nos. 70901059 and 70901029, and the Fundamental Research Funds for the Central Universities under Grant No. 105-275171.
文摘考虑到海上风电出力的随机性以及日益突出的生态环境问题,以含柔性直流输电技术(voltagesource converter high voltage direct current,VSC-HVDC)的交直流系统为研究对象,提出了考虑条件风险价值(conditional valueatrisk,CVaR)的两阶段分布鲁棒低碳经济优化模型,构建了基于Kullback-Leibler(KL)散度的概率分布模糊集,同时利用条件风险价值量化了极端场景下的尾部风险,使得模型能够同时考虑概率分布不确定性以及处于最坏概率分布中极端场景下的尾部损失;此外,将阶梯型碳交易机制并入所提分布鲁棒模型中,通过合理利用柔性资源和储能装置,增强系统运行的灵活性,在兼顾运行风险的前提下,降低碳排放量的目标。再者,为了提高计算效率,在列和约束生成算法(column-and-constraint generation method,C&CG)和Multi-cut Benders分解算法的基础上提出了双循环分解算法。最后,在基于改进的IEEE RTS 79测试系统中验证了所提模型及算法的有效性。
