对偶问题多重解时影子价格的方向性及算法

对偶问题最优解不唯一时这些最优解不全等同于原问题约束资源的影子价格。这时影子价格有了方向性,即资源增加时的增影子价格与资源减少时的减影子价格不相等。并且两者的关系有一定的规律,影子价格有方向性的必要条件是对偶问题有多重解。我们只要在通常的单纯形法的后面加一些计算步骤,就可能把各种影子价格都求出来,包括对其存在和方向的差别。影子价格有方向性时存在一个区间,资源的市场单价只要在这个区间内,增减资源就都不合算。     

资源影子价格不唯一情况的探讨

指出线性规划在最优基不唯一时出现的各种现象,重点讨论引起影子价格不唯一的原因及其后果,影子价格不唯一的性质、判定及应用.     

中国工业二氧化碳影子价格的稳健估计与减排政策

二氧化碳影子价格的稳健估计是评估边际减排成本、设定环境税框架以及评价碳排放权交易体系有效程度的基础性工作。本文在采用自体抽样方法(bootstrap method)的基础上,通过构建二氧化碳影子价格的稳健估计模型,测算了中国36个工业行业1998～2011年的二氧化碳影子价格。研究结果表明:(1)在参数线性规划模型下,忽视随机因素对生产前沿的影响,会低估二氧化碳影子价格。稳健估计得到中国工业行业二氧化碳影子价格平均值为5480元/吨,远低于现有研究估计结果。(2)二氧化碳影子价格在不同行业间存在较大差异并呈扩大趋势,表明行业间存在巨大的碳排放权交易空间,但是36个行业中有越来越多的行业已经向"清洁型"生产技术转变。(3)二氧化碳边际减排成本与碳排放强度之间具有显著的"倒U形"关系,行业碳排放强度的临界值为10.37吨/万元。行业的碳排放强度控制在临界值以下时,可以实现有效减排和生产技术清洁化。(4)我国未来二氧化碳减排政策应采取数量机制和价格机制相结合的策略,价格机制控制碳排放强度较高的行业,数量机制实现行业间边际减排成本的趋同。     

多拉格朗日乘子情形下影子价格的判别和计算北大核心CSCDCSSCI

非线性优化模型中经常出现多重Lagrange乘子现象,导致决策者错误地计算资源的影子价格.本文针对该问题指出最小欧几里得范数的Lagrange乘子是影子价格.同时,还提出了一个无约束优化模型用以求解最小欧几里得范数Lagrange乘子,该无约束优化模型可以通过经典的非光滑优化算法求解.最后,本文提出一个基于次梯度的算法求解影子价格,该算法是次线性收敛的,且计算时间与约束条件的个数及自变量的个数线性相关.     

多拉格朗日乘子情形下影子价格的判别和计算

非线性优化模型中经常出现多重Lagrange乘子现象,导致决策者错误地计算资源的影子价格.本文针对该问题指出最小欧几里得范数的Lagrange乘子是影子价格.同时,还提出了一个无约束优化模型用以求解最小欧几里得范数 Lagrange乘子,该无约束优化模型可以通过经典的非光滑优化算法求解.最后,本文提出一个基于次梯度的算法求解影子价格,该算法是次线性收敛的,且计算时间与约束条件的个数及自变量的个数线性相关.     

关于影子价格概念的几个误区

本文运用线性规划有关理论并结合具体实例,纠正了学术界存在的一些关于影子价格概念的不正确提法,并且从中得出一些有益的结论     

人民币均衡汇率估计——不同方法的比较

本文用购买力平价、外汇的影子价格和因素回归三种不同的方法。估计了人民币和美元的均衡汇率。购买力平价和因素回归两种方法估计的人民币均衡汇率，有相似之处。它们的估计结果都表明，1985年以前人民币汇率存在长期高估的现象，1985年以后则出现高估和低估交替出现的现象，并且人民币高估或低估的平均幅度有所缩小。影子价格方法包括关税和配额两种类型。估计结果表明，现实的人民币汇率介于用这两种类型估计的均衡汇率之间。     

非期望产出、影子价格与无效决策单元的改进

本文首先建立考虑非期望产出的非参数DEA效率模型,从影子价格的视角论证DEA有效的充分必要条件,计算出无效DMU的可改进量,从而构建了一个考虑非期望产出、影子价格以及无效决策单元的改进的非参数DEA模型,然后通过一个算例进行实证分析,将这个新的模型和经典的SBM模型进行比较,结果显示两者的相关系数超过0.9,而且这一新模型还显示出一些SBM模型所没有的优良特性.这种新的非参数方法不仅能够对环境效率水平进行测度评价,而且相较于参数方法而言,它不需要事先设定规范的函数形式,对指标数据也不需要考虑计量单位问题,具有比较独特的优势.     

投入产出分析在我国九大流域水资源影子价格计算中的应用

本文在中国九大流域投入占用产出表的基础上，利用投入产出分析和线性规划相结合的方法，首次计算了中国九大流域生产用水和工业用水的影子价格，这对于制定合理水价，建立水市场很有参考价值。     

影子价格在产品生产决策中的应用

每个企业都为社会生产产品,追求利润最大化。在产品生产过程中,资源采购、生产计划和成本控制是其主要方面。本文就这些主要方面介绍了如何利用影子价格这一有效工具进行决策的问题,不仅做了定性研究,而且做了定量分析,以期对企业的产品生产决策提供帮助。     

THE EFFECTS OF DEGENERACY ON COST-COEFFICIENT RANGES AND AN ALGORITHM TO RESOLVE INTERPRETATION PROBLEMS

The problems of determining valid shadow prices and of performing a valid sensitivity analysis for managerial purposes are considered. For primal degenerate optima, earlier results on finding shadow prices are used to propose a clear and efficient method for finding valid cost-coefficient ranges. An example is used to demonstrate how managerial information can be obtained at degenerate optima.     

Duality of weakly disposable technology

The axiom of weak disposability is frequently imposed in data envelopment analysis (DEA) models involving undesirable outputs such as pollution. This paper sheds new light on the economic interpretation of weak disposability by developing dual formulations of the weakly disposable DEA technology. We find that the economic implications of weak disposability on the multiplier DEA problem are two-fold: (1) the shadow prices of the undesirable outputs can be positive or negative, and (2) the economic loss of the benchmark cannot exceed the suck cost of the inputs. We interpret the second implications as a limited liability condition. The dual formulations developed in this paper enable one to estimate shadow prices of the undesirable outputs using the weakly disposable technology. The insights gained are illustrated by a numerical example and an empirical application to the US power plants.     

储量不确定对可耗竭资源优化开采的影响研究

回采率是储量不确定的重要参数之一。利用回采率提高的概率、调整次数及调整幅度描述回采率不确定,给出回采率的调整方法,进而确定了有效可采储量,然后利用最优控制理论建立了可耗竭资源最优开采模型,确定了资源最优开采路径、影子价格和耗竭时间。结果表明:提高回采率,能增加企业资源供给量,延长采区的服务年限;回采率提高的越多,需要调整的次数也越多,回采率提高的概率较高时,相应调整次数可以减少些;在理论上验证了当前提高回采率政策的有效性。     

An Experimental Analysis of Capacity-Sensitive Setup Parameters for MRP Lot Sizing

Most material requirements planning (MRP) systems apply standard costing (absorption costing) approaches to define setup costs that are used as fixed (time invariant) setup parameters in single-level lot-sizing methods. This paper presents a computationally simple approach for estimating more appropriate setup parameters based on estimates of work-center shadow prices. These setup parameters then are used in traditional single-level MRP lot-sizing procedures. The shadow price of capacity at each work center is calculated as the increase in the overall inventory carrying cost for each additional hour of capacity lost to setups. The opportunity cost of a setup for an order subsequently is determined based on the routing information for each order and is used by traditional MRP lot-sizing procedures to calculate lot sizes. A simulation experiment compares the performance period order quantity lot sizing with capacity-sensitive setup parameters with the fixed accounting-based setup parameters. The simulation replicates the planning and control functions of a typical MRP system. The results of the experiment show that capacity-sensitive setup parameters can make significant reductions in both carrying cost and lateness and can achieve many of the benefits of optimized production technology in the context of an MRP system.     

DETERMINING THE APPROPRIATE DISCOUNT RATES IN PURE CAPITAL RATIONING

This paper proposes an interpretation of the pure capital rationing problem as it is faced by many managers in decentralized firms in which budgets serve as the principal means of control. It is argued that the appropriate objective for situations such as these is the maximization of either undiscounted earnings over the planning horizon or total value of the investments at the horizon. When either objective function is used in conjunction with the frequently encountered linear programming models for the capital rationing problem, shadow prices result which give rise to discount rates that will reproduce the optimal solution using discounted cash flow as a criterion. These results are then used as a means for clarifying several confusing and misleading statements that have appeared in the literature.     

The coordination of short-run decision-making with long-range planning

The dichotomy of short-run and long-run decision-making in economic enterprises has gained widespread acceptance, both in practice and in the related literature despite the inherent interdependence of these decisions. The problem addressed in this paper deals with the proper coordination of short- and long-run planning. Structuring the overall decision problem of the firm as a dynamic programming problem, we find that a natural decomposition into long- and short-range planning results. In this decomposition, all decisions which must be made in the first segment of the planning period are allocated to the short-run decision-makers and all subsequent decisions to the long-range planners. Though several formats have been suggested in the literature for linking short- and long-run plans, most notably the use of shadow prices and of targets or quotas, we find that from a conceptual viewpoint these are inadequate mechanisms and that the proper connection involves the dynamic programming return function.     

Inventory Positioning/Partitioning for Backorders Optimization for a Class of Multi-Echelon Inventory Problems*

Inventory management has undergone significant philosophical changes in recent decades such as the advent of the zero inventory concept. However, as attractive as the concept of minimal inventories may be, it is often unrealistic in application. Attention to basic features of inventory control systems such as order quantities, base stock levels, and reorder points remain crucial to ensure customer service at minimal cost. A nonlinear optimization model for determining base stock levels in a multi-echelon inventory network is presented. Lagrangian relaxation results in (1) newsboy-style relations that provide the optimal solutions, and (2) instantaneous shadow prices for the budget constraint. Sensitivity analysis of this model will facilitate making decisions concerning the desired investment in inventory for the entire system. This model may be solved on standard nonlinear programming software and is generalizable to problems in both production and distribution settings.     

Shadow Insurance

Life insurers use reinsurance to move liabilities from regulated and rated companies that sell policies to shadow reinsurers, which are less regulated and unrated off‐balance‐sheet entities within the same insurance group. U.S. life insurance and annuity liabilities ceded to shadow reinsurers grew from $11 billion in 2002 to $364 billion in 2012. Life insurers using shadow insurance, which capture half of the market share, ceded 25 cents of every dollar insured to shadow reinsurers in 2012, up from 2 cents in 2002. By relaxing capital requirements, shadow insurance could reduce the marginal cost of issuing policies and thereby improve retail market efficiency. However, shadow insurance could also reduce risk‐based capital and increase expected loss for the industry. We model and quantify these effects based on publicly available data and plausible assumptions.     

中国影子银行违约风险和防范机制研究——来自上市公司委托贷款数据的经验证据

本文运用中国上市公司披露的委托贷款公告数据，实证研究了影子银行的违约风险及其防范机制。数据显示，我国委托贷款的整体违约率为10.09%，远高于同期银行业金融机构的不良贷款率。进一步研究发现，与影子银行风险受信息因素影响的直觉一致，抵押条款和借贷距离会显著影响委托贷款违约率：其一，从抵押视角来看，抵押条款和贷款违约率显著正相关，这表明，为了防范事后的道德风险问题，贷款者会要求借款者提供抵押；其二，从借贷距离视角看，与近距离借贷（或同省借贷）相比，远距离借贷（或异省借贷）的违约风险相对较高，这揭示出，借贷距离越远，贷款者越难对借款者进行甄别和监督，从而推高了借款企业的违约概率。本文研究不仅为我国委托贷款这一影子银行机制的风险状况提供了直接的经验证据，而且对影子银行参与者如何有效防范风险和相关政府部门加强监管具有重要的借鉴意义。