Sensitivity analysis for stochastic user equilibrium with elastic demand assignment model

This paper puts forward a rigorous approach for a sensitivity analysis of stochastic user equilibrium with the elastic demand （SUEED） model. First, proof is given for the existence of derivatives of output variables with respect to the perturbation parameters for the SUEED model. Then by taking advantage of the gradient-based method for sensitivity analysis of a general nonlinear program, detailed formulae are developed for calculating the derivatives of designed variables with respect to perturbation parameters at the equilibrium state of the SUEED model. This method is not only applicable for a sensitivity analysis of the logit-type SUEED problem, but also for the probit-type SUEED problem. The application of the proposed method in a numerical example shows that the proposed method can be used to approximate the equilibrium link flow solutions for both logit-type SUEED and probit-type SUEED problems when small perturbations are introduced in the input parameters.

Supply Chain Network Equilibrium with Revenue Sharing Contract under Demand Disruptions

Contract is a common and effective mechanism for supply chain coordination,which has been studied extensively in recent years.For a supply chain network model,contracts can be used to coordinate it because it is too ideal to obtain the network equilibrium state in practical market competition.In order to achieve equilibrium,we introduce revenue sharing contract into a supply chain network equilibrium model with random demand in this paper.Then,we investigate the influence on this network equilibrium state from demand disruptions caused by unexpected emergencies.When demand disruptions happen,the supply chain network equilibrium state will be broken and change to a new one,so the decision makers need to adjust the contract parameters to achieve the new coordinated state through bargaining.Finally,a numerical example with a sudden demand increase as a result of emergent event is provided for illustrative purposes.

A super-network equilibrium optimization method for operation architecture with fuzzy demands

From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepower level. Firstly, the optimized conditions of the perceptive level, command level and firepower level are analyzed respectively based on the demand of information relation,and then the information supply-and-demand equilibrium model of the operation architecture super-network is established. Secondly,a variational inequality transformation(VIT) model for equilibrium optimization of the operation architecture is given. Thirdly, the contraction projection algorithm for solving the operation architecture super-network equilibrium optimization model with fuzzy demands is designed. Finally, numerical examples are given to prove the validity and rationality of the proposed method, and the influence of fuzzy demands on the super-network equilibrium solution of operation architecture is discussed.

A Novel Stackelberg-Game-Based Energy Storage Sharing Scheme Under Demand Charge

Demand response(DR)using shared energy storage systems(ESSs)is an appealing method to save electricity bills for users under demand charge and time-of-use(TOU)price.A novel Stackelberg-game-based ESS sharing scheme is proposed and analyzed in this study.In this scheme,the interactions between selfish users and an operator are characterized as a Stackelberg game.Operator holds a large-scale ESS that is shared among users in the form of energy transactions.It sells energy to users and sets the selling price first.It maximizes its profit through optimal pricing and ESS dispatching.Users purchase some energy from operator for the reduction of their demand charges after operator's selling price is announced.This game-theoretic ESS sharing scheme is characterized and analyzed by formulating and solving a bi-level optimization model.The upper-level optimization maximizes operator's profit and the lower-level optimization minimizes users'costs.The bi-level model is transformed and linearized into a mixed-integer linear programming(MILP)model using the mathematical programming with equilibrium constraints(MPEC)method and model linearizing techniques.Case studies with actual data are carried out to explore the economic performances of the proposed ESS sharing scheme.

Properties of Nash Equilibrium Retail Prices in Contract Model with a Supplier, Multiple Retailers and Price-Dependent Demand

Recently, price contract models between suppliers and retailers, with stochastic demand have been analyzed based on well-known newsvendor problems. In Bernstein and Federgruen [6], they have analyzed a contract model with single supplier and multiples retailers and price dependent demand, where retailers compete on retail prices. Each retailer decides a number of products he procures from the supplier and his retail price to maximize his own profit. This is achieved after giving the wholesale and buy-back prices, which are determined by the supplier as the supplier’s profit is maximized. Bernstein and Federgruen have proved that the retail prices become a unique Nash equilibrium solution under weak conditions on the price dependent distribution of demand. The authors, however, have not mentioned the numerical values and proprieties on these retail prices, the number of products and their individual and overall profits. In this paper, we analyze the model numerically. We first indicate some numerical problems with respect to theorem of Nash equilibrium solutions, which Bernstein and Federgruen proved, and we show their modified results. Then, we compute numerically Nash equilibrium prices, optimal wholesale and buy-back prices for the supplier’s and retailers’ profits, and supply chain optimal retailers’ prices. We also discuss properties on relation between these values and the demand distribution.

Economy Equilibrium and Sustainable Development

The structure of technological mappings is studied and it is shown that for an important class of technological mappings there exists a continuous strategy of the behavior of firms as arbitrarily close in terms of profit. The latter is important for building the theory of economic equilibrium, which is an important tool for building the theory of sustainable economic development. Theorems of the existence of economic equilibrium under conditions of uncertainty and under general assumptions about the structure of supply and demand have been proved.

以有效需求牵引供给以高水平供给创造需求——学习习近平宏观经济治理供求关系良性互动的论述

学习和领会习近平宏观经济治理思想尤其是关于供求关系良性互动的论述,有助于梳理我国宏观经济治理与宏观调控政策的发展脉络,进一步深化认识和自觉遵循新时代客观经济规律,对于加快构建新发展格局和实现高质量发展具有非常重要的理论与实践意义。面对经济发展有效需求不足等失衡特点,“深化供给侧结构性改革和扩大有效需求协同发力”已成为新时代做好经济工作需要认识和遵循的重要规律。当前实现需求与供给两端协同发力,在政策目标和政策导向上必须追求以有效需求牵引供给、以高水平供给创造需求,还要从政策制定和传导机制、治理机制和体制基础等方面持续发力以切实提升宏观经济治理和政策调控的有效性。

A closed-loop Supply Chain Network Equilibrium Model with Fuzzy Demand under Production Capacity Constraints and Price Rigidities

A closed-loop supply chain network equilibrium problem is examined,which consists of mutual competitive manufacturers with production capacity constraints and retailers with fuzzy market demands,mutual competitive collectors as well as a binding price ceiling of the commodities.By utilizing the credibility measure of fuzzy event,variational inequality and Lagrange dual theory,the optimum behaviors of manufactures,retailers,collectors and consumers are described.Therefore,the supply chain network equilibrium model is established.Numerical examples were given to illustrate the impact of production capacity constraints and price ceiling on the network equilibrium pattern.The results show that the shortage of commodities in consumer market will be more serious,the wholesale price of product and purchase price of waste products rise,the profits of retailers decrease,the profits of manufacturers and collectors increase as the government gradually reduce the binding price ceiling on competitive markets,and the trend will be more obvious in the existence of production capacity constraints at same time.

多周期农产品废弃物供应链网络均衡模型构建

目的研究农产品废弃物可持续利用问题,既实现供应链整体利润最优,又减轻对环境的污染。方法在随机需求的背景下,考虑生产合作社对零售商的不同激励度,分析生产合作社、零售商、需求市场的最优状态,利用变分不等式建立相应的多周期供应链网络均衡模型。结果从多周期角度,实现了农产品废弃物供应链网络均衡利益最优化,可为合作社与零售商在较长时间达到一种均衡状态提供有效解决方案。结论既实现了多周期农产品废弃物的持续利用,又促进了循环经济的发展,同时还实现了供应链网络均衡、供应链整体利润最优和减轻环境污染等目标。

面向系统灵活性提升的大用户激励型需求响应优化策略

针对大规模可再生能源接入电力系统所导致的灵活爬坡产品(FRP)需求激增问题,提出一种大用户激励型需求响应(DR)策略,为独立系统运营商(ISO)获取需求侧灵活性资源提供有效途径。采用用户需求管理行为模型(CDMBM),估计能够反映DR行为差异化的用户响应成本函数;构建ISO与多个大用户之间的激励型DR主从博弈模型,以ISO为决策主体的电能与FRP联合出清优化模型作为上层模型,以大用户参与联合市场DR决策的优化模型作为下层模型,通过将主从博弈问题转换为带均衡约束的数学优化问题,求解博弈均衡解进而得到具有差异化的用户DR单位补偿费用。通过算例分析,验证了所提策略的有效性。

利用建筑虚拟储能提升风电消纳能力的电热联合系统优化调度方法

利用建筑虚拟储能能提升电热联合系统的风电消纳能力,但若只考虑建筑结构储能而不考虑室内空气储能会导致虚拟储能利用不足。针对此问题,在奖惩阶梯碳交易背景下提出一种利用建筑虚拟储能提升风电消纳能力的电热联合系统优化调度方法。首先,以室内空气和建筑结构热平衡模型为基础建立精细化建筑虚拟储能模型;其次,在系统中引入奖惩阶梯碳交易机制及需求响应机制;再次,考虑电、热功率平衡以及室内温度等约束,以电热联合系统总成本最低为目标函数,并提出改进型平衡器优化算法对目标函数进行优化求解;最后,对不同场景下电热联合系统对风电的消纳、CO_(2)排放及经济性进行分析,结果表明:所提方法不仅提高了电热联合系统的风电消纳率,降低了CO_(2)的排放量,且提升了经济性。

新常态下超大型城市干线路网发展思路——以深圳市为例

新常态下,经济增速放缓,传统发展方式难以为继,需要创新动力机制,加强供给侧改革。城市干线路网作为支撑城市空间结构优化调整的主动脉,新阶段,理应聚焦城市发展新趋势,从“高速度增长”向“高质量发展”转变。本文剖析当前深圳干线路网存在的问题,研判未来发展态势,提出未来深圳干线路网应该实现“四大升级”,引导人口、用地、建筑结构同步优化升级,促进区域供给侧的生产要素合理和有序流动,提高资源配置效率和质量,促进区域产业升级和经济发展。

随机用户均衡准动态交通分配模型

动态交通分配问题是交通科学研究的热点和难点,将动态交通分配方法应用于大规模网络往往产生过高的计算成本。通过研究准动态交通分配问题,降低动态交通分配中时间的连续性和动态交通分配模型的复杂性。采用路段行程时间计算公式定义一种新的剩余交通需求计算方法;然后考虑剩余交通需求在时段之间的传播过程和出行者对路网的熟悉程度差异,建立基于Logit的随机用户均衡准动态交通分配模型,基于逐次平均法设计模型的求解算法。最后通过Braess网络和九节点网络说明模型的应用情况,并分析模型参数的敏感度,验证模型的合理性与算法的有效性。本研究丰富了交通科学基础理论,为交通政策的制定提供参考依据。

路径选择准则对随机供需路网运行效率的影响

为研究不同路径选择准则对随机供需路网运行效率的影响,在假定需求服从对数正态分布、容量服从Beta分布的前提下,构建了三种路径选择准则:期望行程时间最短、行程时间预算最短以及超预算期望行程时间最短。基于这三种准则,分别构建了相应的交通分配变分不等式模型,并设计了求解算法。从交通周转角度出发,提出了路网运行效率的测算方法。通过算例分析,探讨了三种路径选择准则以及路段容量降级程度、需求结构、需求总量和行程时间可靠度对路网运行效率的影响。研究结果表明:期望行程时间最短择路准则下的路网运行效率最高,而超预算期望行程时间最短准则下的路网运行效率最低;无论采用哪种择路准则,路网运行效率均随路段容量降级程度的增加而显著下降;当路段容量降级程度与需求的“均值-方差比”一定时,在三种路径选择准则下,均存在一种特定的需求结构与总量,使运行效率达到最大值;在行程时间预算和超预算期望行程时间最短准则下,路网运行效率随行程时间可靠度的增加而显著下降。

Non-Cooperative Differential Game Based Energy Consumption Control for Dynamic Demand Response in Smart Grid

In this paper, we conduct research on the dynamic demand response problem in smart grid to control the energy consumption. The objective of the energy consumption control is constructed based on differential game, as the dynamic of each users’ energy state in smart gird can be described based on a differential equation. Concept of electricity sharing is introduced to achieve load shift of main users from the high price hours to the low price hours. Nash equilibrium is given based on the Hamilton equation and the effectiveness of the proposed model is verified based on the numerical simulation results.

Analysis on the situation and countermeasures of water resources supply and demand in the cities of small and medium-sized river basins along southeast coast of China-taking Xiamen City as an example

The small and medium-sized river basins along southeast coast of China hold comparatively abundant water resources.However,the rapid resources urbanization in recent years has produced a series of water problems such as deterioration of river water quality,water shortage and exacerbated floods,which have constrained urban economic development.By applying the principle of triple supply-demand equilibrium,this paper focuses on the estimation of levels of water supply and demand in 2030 at different guarantee probabilities,with a case study of Xiamen city.The results show that water shortage and inefficient utilization are main problems in the city,as the future water supply looks daunting,and a water shortage may hit nearly 2×10^(8)m^(3)in an extraordinarily dry year.Based on current water supply-demand gap and its trend,this paper proposes countermeasures and suggestions for developing and utilizing groundwater resources and improving the utilization rate of water resources,which can supply as a reference for other southeast middle-to-small-sized basin cities in terms of sustainable water resources and water environment protection.

考虑马尔可夫决策的产消者P2P电能交易非合作博弈模型

随着电力市场改革的推进和分布式能源在用户端的大规模发展,基于产消者端对端(P2P)的电能交易逐渐成为促进分布式能源消纳的重要解决方案。为解决产消者多阶段P2P电能交易中互动行为的强不确定性、状态转移概率不明晰等问题,提出了一种考虑Markov决策过程的产消者P2P电能交易非合作博弈模型。首先,引入可将用户行为聚合的Markov决策过程,解决了产消者由阶段性交易决策随机性导致的用电行为不确定性问题。其次,针对产消者在P2P电能交易市场中相互竞争的角色地位,建立了考虑Markov决策过程的非合作博弈模型,以产消者收益最大化为目标,结合需求响应计算P2P交易的最优电价。再次,在证明非合作博弈Nash均衡解存在的基础上,采用Nikaido-Isoda函数将博弈问题等效转化为全局最优问题,并采用分布式算法进行求解,获取最优Nash均衡解,保障产消者最大收益。最后,通过算例证明了所提方法的有效性与可行性。

基于弹性需求的列车停站方案优化方法

为了更好地协调铁路运输能力分配和提升旅客出行服务质量、客观体现铁路企业和旅客间的博弈关系,提出一种弹性需求下的列车停站方案优化方法。首先,在考虑弹性需求和严格列车能力约束的基础上,分析列车停站方案、旅客出行成本和弹性需求三者间的相互影响关系,建立列车停站方案优化模型;其次,采用松弛和外近似技术等线性化方法,将模型重构为便于求解的线性规划模型;最后,通过小型算例和郑州—西安高速铁路实例,验证提出方法的有效性。结果表明:优化后的停站方案能够实现运输能力的合理分配;与真实的停站方案相比,优化方案在票价收益提高了0.30%的情况下,减少了22次停站,并使旅客总停站附加时间下降了76.14%,实现了对铁路运输效率和旅客服务质量的兼顾。

基于终点需求可变的市域旅游客流运输均衡分配模型

以旅游者到达目的地城市后的运输优化问题为研究对象,为减少旅游景点游客量和市域客运网运输量失衡的现象,提出了一种基于旅游终点需求可变的运输均衡分配模型。首先,基于旅游者的完整出行过程分析,构建了目的地城市内部旅游客流的交通运输网络;其次,基于市域内旅游出行起点需求固定但终点需求可变的旅游客流出行特征给出了旅游客流出行分布函数形式,建立了基于终点需求可变的市域旅游客流运输分配模型,通过其一阶最优化条件证明了在均衡状态下,旅游客运分布量能满足Logit形式的出行分布函数和出行发生量约束,旅游客流运输分配量能满足用户均衡条件;最后,基于凸组合法的思想设计了模型的求解算法,并在简化的黄山市旅游客流运输网络分配实例中验证了模型与算法的可行性。研究结果表明:旅游终点吸引度的变化和运输线路广义费用阻抗的变化可以同时影响旅游出行需求分布量,运输线路运能的增加可以提高旅游客流分配量,决策部门可通过调整运输网络节点的吸引度来平衡市域旅游资源,运输企业可通过调整运力配置,改善旅游客运服务能力。

基于用户均衡的双模式接驳公交一体化布局优化

接驳公交是城市公共交通系统的重要部分,用于解决轨道交通乘客“最后一公里”出行难题。针对固定线路接驳公交中边缘地区乘客步行前往公交站时间较长的问题,提出在固定线路公交服务范围边缘处布置需求响应公交,从而实现双模式接驳公交一体化布局。为科学且人性化地划分不同模式接驳公交的服务范围,基于用户均衡理论,提出以乘客出行时间均衡为目标的双模式接驳公交一体化布局模型;为在多个达到均衡条件的布局方案中进一步挑选出最优布局方案,建立以乘客出行时间最小为目标的优化模型,并设计遗传算法求解。最后,以重庆东站站前片区为研究案例验证模型与算法的可行性与有效性,求解结果证明双模式接驳公交一体化布局可以在不增加投入车辆数的前提下相比单一固定线路运营模式降低乘客出行时间成本32%;但需求响应模式的加入也会导致公交人均能耗上升83%。