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1.
线性规划无穷多最优解的讨论   总被引:7,自引:1,他引:6  
李军 《运筹与管理》1999,8(1):87-92
利用线性规划单纯形表对线性规划原问题存在无穷多最优解和对偶问题存在无穷多最优解的情况进行了讨论,并分析了对偶问题存在无穷多最优解情况下的影子价格的方向性。最后以实例说明了各种情况。对初学者加深理解及决策者决策参考有一定帮助  相似文献   

2.
针对线性规划对偶问题最优解不唯一时,在已有文献提出的对偶最优解不唯一的充要条件定理基础上,结合线性规划灵敏度分析,提出影子价格的求解判断的简单准则及其命题,并进行证明.最后,用算例加以分析,指出该判断方法简单易行,也可作为通过计算软件求解影子价格的准确判断方法.  相似文献   

3.
影子价格与影子成本   总被引:2,自引:0,他引:2  
本文根据线性规划问题对偶变量和影子价格的经济意义,给出了影子成本的概念,讨论了影子成本与对偶价格的关系.通过灵敏度分析给出了影子成本的动态表示,并进一步阐明了影子价格和影子成本的惟一性以及影子成本在经济管理中的应用.  相似文献   

4.
本文探讨了线性规划的原问题与对偶问题理论,并在此基础上可开发出一种用于在线求解线性规划的递归神经网络和应用于冗余机器手臂逆运动学的求解问题上.如,Tang等人开展的原对偶神经网络.但鉴于对偶理论的复杂性和多样性,该原对偶神经网络模型仅可以得到线性规划问题的可行解,而本文对该网络模型改进后可得到线性规划问题的最优解.仿真结果证实了这种改进模型在解决线性规划问题上的有效性、正确性和高效率.  相似文献   

5.
多种资源灵敏度分析和影子价格的探讨   总被引:1,自引:0,他引:1  
徐一萍 《运筹与管理》2002,11(4):111-116
本在原有的线性规划灵敏度分析和影子价格理论的基础上,讨论了多种资源变化的灵敏度分析中影子价格的调节作用,提出资源最佳数量的LP模型,指出在多种资源变化的情况下,影子价格的应用可以而且应该超越传统的观点,以统筹调配各种资源,追求总的目标函数值达到最优。  相似文献   

6.
在一个带有非负和不等式约束的优化问题有最优解的情形下,存在着广义拉格朗日乘子即资源的影子价格.本文探索给出马克思两大部类扩大再生产中的影子价格,为经典的马克思扩大再生产理论增添新的重要内容.首先使用“价值系数法”替代单纯形法,简便地求得了扩大再生产优化问题的最优解.然后运用库恩一塔克条件,确立了关于最优解与广义拉格朗日乘子的互补松弛条件的三个不等式组.进而利用这些不等式组和已知的最优解,简便地解出广义拉格朗日乘子,即两大部类扩大再生产中的影子价格.最后引用和借鉴《资本论》中的两个举例,对所获得的影子价格和目标函数最优值做了计算验证.  相似文献   

7.
为了使政府给予城市公共交通的财政补贴得到最优分配,应用经济学中的资源配置问题,把公交运营收入财政补贴和公交车辆改造财政补贴看作两种资源,将其分别分配到道路交通和轨道交通中.然后根据城市公共交通的两种主要补贴计算方法按客流量计算和按车公里计算,以政府的财政补贴资源和公交企业的利润目标分别构建城市公共交通财政补贴的非线性规划模型.并通过非线性规划的KuhnTucker条件揭示在两种不同的补贴方法下政府对道路交通和轨道交通进行补贴的补贴单价即为政府对其进行补贴的影子价格.最后以重庆市为例,验证模型的可行性.  相似文献   

8.
双层线性规划的一个全局优化方法   总被引:7,自引:0,他引:7  
用线性规划对偶理论分析了双层线性规划的最优解与下层问题的对偶问题可行域上极点之间的关系,通过求得下层问题的对偶问题可行域上的极点,将双层线性规划转化为有限个线性规划问题,从而用线性规划方法求得问题的全局最优解.由于下层对偶问题可行域上只有有限个极点,所以方法具有全局收敛性.  相似文献   

9.
线性规划消耗系数矩阵灵敏度分析的某些探讨   总被引:5,自引:0,他引:5  
讨论了线性规划模型中 ,消耗系数矩阵 A中某个基变量或某个约束方程的系数向量变化以及增减约束方程时 ,对最优基、最优解、目标函数值和影子价格的影响 .  相似文献   

10.
求线性规划对偶问题最优解的一种方法   总被引:2,自引:0,他引:2  
线性规划对偶问题的最优解有重要的经济意义,中给出了一种较为简捷的求对偶问题最优解的方法。  相似文献   

11.
The relationships between multiple optimal dual solutions of a convex programming problem and the corresponding primal optimal value function are established by straightforward arguments on known results in duality theory. The subsequent discussion includes a demonstration that one-sided shadow prices can be found by solving a linear programming problem, conditions for the uniqueness and validity of the classical shadow price interpretation and a specialization of the results to the linear programming case.  相似文献   

12.
The purpose of this paper is to demonstrate that when degeneracy is present in an optimal basic solution to a linear programming problem, the optimal values of the dual variables do not necessarily correspond to shadow prices. In such instances, major commercial L.P. packages (such as IBM's MPS and MPSX) may provide misleading information about the shadow prices. It will be shown how the actual values of the shadow prices may be determined, and the nature of the relationship between shadow prices and dual variables will be discussed.  相似文献   

13.
网格环境下制造资源优化配置的区间规划模型   总被引:1,自引:0,他引:1  
针对网格环境下影响制造资源优化配置的关键参数具有区间性的特点,基于区间数建立了资源优化配置模型,以任务完工的总成本最低为目标,将资源的价格及任务的成本限制转换为区间数,并充分考虑了资源工作时间限制以及任务时间要求,给出线性区间规划模型及其解法,并通过算例分析表明该方法的可行性与有效性.该模型在反映市场需求以及应对市场变化基础上,可得出合理的优化配置方案.  相似文献   

14.
The problem of efficiency vs fairness is considered in relation to the splitting of costs for shared facilities between users. This is considered as a result of a problem of sharing the cost of the provision of central computing facilities between different faculties in a large university, but the basic problem is widespread. A linear programming model is considered in order to minimise cost. The dual of this model is shown to correspond to an efficient allocation of costs. An alternative optimal dual solution is shown to give a ‘fair’ solution according to criteria resulting from cooperative game theory.  相似文献   

15.
This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.  相似文献   

16.
The return obtained from the allocation of resources to an activity is occasionally modelled by means of concave, strictly increasing functions. Exponential functions of a certain class conveniently lend themselves to such modelling. A nonlinear programming formulation of a multiresource allocation problem with return functions of the class appears to have Kuhn-Tucker conditions which in a sense are intrinsically linear. The paper shows how this fact can be utilised to save processing time in the execution of numerical algorithms for the solution of this mathematical programming problem.  相似文献   

17.
This paper describes the relationship between market prices and shadow prices when the economy has general types of institutional price constraints. We consider a decentralized linear economy where market prices quide the decentralized behavior of each activity and the shadow prices measure the social values of resources. To measure the social values, we introduce a social objective criterion. Hence, our approach could be regarded as a central economic price control with institutional price constraints for a decentralized economy. A simple example is employed to graphically illustrate the wedges between market prices and shadow prices. It has been shown that our problem can be solved through mixed integer linear programming techniques.  相似文献   

18.
We deal with the linear programming problem in which input data can vary in some given real compact intervals. The aim is to compute the exact range of the optimal value function. We present a general approach to the situation the feasible set is described by an arbitrary linear interval system. Moreover, certain dependencies between the constraint matrix coefficients can be involved. As long as we are able to characterize the primal and dual solution set (the set of all possible primal and dual feasible solutions, respectively), the bounds of the objective function result from two nonlinear programming problems. We demonstrate our approach on various cases of the interval linear programming problem (with and without dependencies).  相似文献   

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