Duality and continuity

This paper fills the one remaining lacuna in (multiple-output) duality theory by provingjoint continuity (in input and output vectors) of cost, benefit, and (input and output) distance functions. Continuity is an important property where measurement error exists, for it provides assurance that small errors of measurement (of quantities or prices) result only in small errors in concepts like minimal cost. We consider continuity not only in prices and quantities, but also in technologies. Continuity in technologies might be more important than continjity in prices or quantities, because production technologies are almost certainly measured (or estimated) with error.     

Axiomatic foundations of efficiency measurement on data-generated technologies

We assess the ability of three well-known technical efficiency indexes, the Debreu-Farrell index, the Färe–Lovell index, and the Zieschang index, to satisfy the Färe–Lovell axioms and continuity axioms (for technologies as well as input quantities) on the class of technologies generated by standard mathematical-programming methods of measuring efficiency: data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Färe–Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu–Farrell index), but (b) none of the indexes satisfies all Färe–Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.     

Estimating demand with distance functions: Parameterization in the primal and dual

Our purpose is to investigate the ability of different parametric forms to ‘correctly’ estimate consumer demands based on distance functions using Monte Carlo methods. Our approach combines economic theory, econometrics and quadratic approximation. We begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property. Homogeneity is typical of Shephard distance functions and expenditure functions, whereas translation is characteristic of benefit/shortage or directional distance functions. The functional forms which satisfy these conditions and include both first- and second-order terms are the translog and quadratic forms, respectively. We then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic. We assess functional form performance by focusing on empirical violations of the regularity conditions. Our analysis corroborates results from earlier Monte Carlo studies on the production side suggesting that the quadratic form more closely approximates the ‘true’ technology or in our context consumer preferences than the translog.     

Mathematical methods of optimization for multi-objective transportation systems

Transportation systems have multi-objective functions and there are multi-factor decision situations. A general mathematical optimization model for such systems is developed which has broad applications for the planning, system design and evaluation of many transportation systems. Three types of solution techniques are discussed. For multi-objective linear programs, a solution is obtained which satisfies the decision maker's preferences and optimization from the decision maker's point of view is considered. A goal programming solution technique is given when goals for the system can be defined. If this is not possible, an overall utility function is defined on the various objective functions and a concept of additive utilities is explored and a parametric programming solution is given.     

A utility representation theorem with weaker continuity condition

We prove that a mixture continuous preference relation has a utility representation if its domain is a convex subset of a finite dimensional vector space. Our condition on the domain of a preference relation is stronger than Eilenberg (1941) and Debreu (1959, 1964), but our condition on the continuity of a preference relation is strictly weaker than the usual continuity assumed by them.     

Optimal investment models with vintage capital: Dynamic programming approach

The dynamic programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE’s with age structure that have been studied in various papers (12, 11, 33 and 35) either in cases when explicit solutions can be found or using Maximum Principle techniques.     

无穷区间上的几类一致连续函数

从一致连续性的定义出发，给出了无穷区间上一致连续函数的几种类型．     

The Importance of Experimental Control in Testing the Impact of Interviewer Continuity on Panel Survey Nonresponse

The conventional wisdom in survey research suggests that it is advisable to have the same interviewers return to the same respondents in order to maintain good response rates in longitudinal surveys. There has been, however, very little documented experimental research to support this. Work conducted by Campanelli and O'Muircheartaigh (1999) using a subsample of the British Household Panel Study (BHPS) at Wave 2 with experimental control of the allocation of respondents to interviewers showed no evidence of a positive continuity effect on nonresponse; more extensive analysis by Laurie et al. (1999) of the full BHPS sample using Waves 2 through 4 presents contradictory results. This paper extends the earlier analysis and shows that these differences in findings are due to the lack of experimental control for the inferences from the full BHPS sample in the Laurie et al. (1999) report rather than the shorter time frame considered in Campanelli and O'Muircheartaigh (1999). This paper also considers variation in interviewer continuity effects across areas through the use of multilevel statistical models.     

Economic Efficiency and Frontier Techniques

Abstract. Most of the literature related to the measurement of economic efficiency has based its analysis either on parametric or on non‐parametric frontier methods. The choice of estimation method has been an issue of debate, with some researchers preferring the parametric and others the non‐parametric approach. The aim of this paper is to provide a critical and detailed review of both core frontier methods. In our opinion, no approach is strictly preferable to any other. Moreover, a careful consideration of their main advantages and disadvantages, of the data set utilized, and of the intrinsic characteristics of the framework under analysis will help us in the correct implementation of these techniques. Recent developments in frontier techniques and economic efficiency measurement such as Bayesian techniques, bootstrapping, duality theory and the analysis of sampling asymptotic properties are also considered in this paper.     

Forecasting leadership transitions around the world

We use popular non-parametric (CART, TreeNet) and parametric (logit) techniques to identify robust economic, demographic and political conditions that lead to shifts in control in the executive branch of government in 162 countries during the period 1960–2004. We find that institutional aspects of the political system, executive characteristics, demographic variables, economic growth, and economic trade variables are all very important for predicting leadership turnover in the following year. Financial crises are not robustly useful for this purpose, but a vulnerability to currency crises in times of low economic growth implies very high conditional probabilities of job losses for democratic leaders in non-election years. In-sample, TreeNet predicts 78% of leadership transition events correctly, compared to CART’s 70%, and TreeNet also generally achieves higher overall prediction accuracies than either CART or the logit model out-of-sample.     

A new criterion for technical efficiency measures: non‐monotonicity across dimensions axioms

Based on non‐parametric deterministic production technologies radial and non‐radial measures of technical efficiency are evaluated using properties guaranteeing insensitivity to the dimensionality of technology. These new axioms are important in empirical research and may especially prevent manipulation of results when implementing these benchmark methodologies in private or public organizations. An empirical example illustrates to which extent a series of radial and non‐radial technical efficiency measures satisfies the proposed axioms. Copyright © 1999 John Wiley & Sons, Ltd.     

Double implementation of the Lindahl equilibrium by a continuous mechanism

We consider a class of economies with public goods that have the following properties: (i) The preferences of the agents are convex, interior, and strictly increasing. (ii) The technology for production of public goods is a closed convex cone that satisfies free disposal and an additional mild assumption. No assumptions are made on continuity, completeness or transitivity of preferences. We provide a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria, and has the following property: For every economy in our class every Nash equilibrium of the game induced by the mechanism is a strong Nash equilibrium.     

Design method evaluation—an experiment with corridor selection

The improvement of the process of design requires the evaluation of alternative design methods. A framework for evaluating graphically based, intuitive design methods is (1) solve a set of problems with a proven algorithm, (2) have a sample of designers solve the same set of problems, and (3) compare the results to identify the success of each designer or design method. A proto-typical experiment using the problem of corridor selection is used to illustrate the approach, with solutions obtained by twelve students being compared to solutions obtained by discrete dynamic programming for a set of three problems. An important distinction is drawn between measuring the success of the solution vs the success of the problem solving procedure. An extension to evaluate the handling of separately defined objectives is suggested, and questions concerning the stability of a solution with respect to minor changes in the algorithms identified.     

多维离散资源分配问题的模型转换及其Excel求解方法

离散资源分配问题是管理科学中的一个重要问题。对于一维资源问题,一般都采用动态规划方法求解,而对于多维离散资源问题,用逐次逼近法转化为一维资源问题求解,其计算量巨大,需要利用专门的优化软件计算。本文中,将多维离散资源问题转化为0-1规划问题,并利用大家熟悉的Excel软件进行求解,以利于分析利用。算例表明,该方法是简单、有效,而且实用。     

Expected utility theory on mixture spaces without the completeness axiom

A mixture preorder is a preorder on a mixture space (such as a convex set) that is compatible with the mixing operation. In decision theoretic terms, it satisfies the central expected utility axiom of strong independence. We consider when a mixture preorder has a multi-representation that consists of real-valued, mixture-preserving functions. If it does, it must satisfy the mixture continuity axiom of Herstein and Milnor (1953). Mixture continuity is sufficient for a mixture-preserving multi-representation when the dimension of the mixture space is countable, but not when it is uncountable. Our strongest positive result is that mixture continuity is sufficient in conjunction with a novel axiom we call countable domination, which constrains the order complexity of the mixture preorder in terms of its Archimedean structure. We also consider what happens when the mixture space is given its natural weak topology. Continuity (having closed upper and lower sets) and closedness (having a closed graph) are stronger than mixture continuity. We show that continuity is necessary but not sufficient for a mixture preorder to have a mixture-preserving multi-representation. Closedness is also necessary; we leave it as an open question whether it is sufficient. We end with results concerning the existence of mixture-preserving multi-representations that consist entirely of strictly increasing functions, and a uniqueness result.     

Dynamic inventory decisions for humanitarian aid materials considering budget limitations

In case of disaster, providing relief supplies to the affected people has vital importance. Governmental or non-governmental organizations (NGOs) prepare for disasters by purchasing and stockpiling these aid materials in appropriate quantities. They operate under a limited budget and this budget can either be used before the disaster for stocking decisions under uncertainty or it can be used after the disaster to satisfy the required demand at a higher cost when the uncertainty is resolved. If all the budget is used before the disaster, and if there is no disaster in a long term, there will be a high holding cost. On the other hand, if all the budget is reserved for use after the disaster, meeting the demand will be more costly or the demand may not be met within a certain period of time. Thus, NGOs need to decide how to allocate the budget for pre and post-disaster usage. In this system, the budget of NGOs may also change over time through donations or other incomes. In this point of view, NGOs need to make dynamic stock and budget allocation decisions, under the available budget at hand. In our study, we analyze the dynamic stocking decisions of NGOs using stochastic dynamic programming formulations under budget constraints. We develop infinite horizon stochastic dynamic programming models with and without budget considerations, and compare the results of these models via numerical analysis. Detailed numerical studies and results of the sensitivity analysis show the significance of budget considerations in inventory decisions and the effects of different parameters on the system results.     

有理Bézier曲线段的几何连续拼接

本文提出了通过调整权因子而不是改变控制顶点来修改有理三次Bézier样条曲线的形状,实现了相邻两段Bézier曲线间的G3连续拼接;实现了两段分离的Bézier曲线之间的G3连续过渡;在不改变给定控制顶点的情况下,能实现整体曲率连续的闭曲线造型;在仅仅修改或插入两点的情形下实现了整体G3连续的闭曲线造型。     

ANSYS二次开发在薄壁墩参数优化设计中的应用

介绍大型有限元分析软件ANSYS的二次开发及其在双支薄壁桥墩参数优化设计中的实现过程,最后给出具体的应用示例。     

Incentive compatibility constraints and dynamic programming in continuous time

This paper is devoted to the study of infinite horizon continuous time optimal control problems with incentive compatibility constraints that arise in many economic problems, for instance in defining the second best Pareto optimum for the joint exploitation of a common resource, as in Benhabib and Radner [Benhabib, J., Radner, R., 1992. The joint exploitation of a productive asset: a game theoretic approach. Economic Theory, 2: 155–190]. An incentive compatibility constraint is a constraint on the continuation of the payoff function at every time. We prove that the dynamic programming principle holds, the value function is a viscosity solution of the associated Hamilton–Jacobi–Bellman (HJB) equation, and that it is the minimal supersolution satisfying certain boundary conditions. When the incentive compatibility constraint only depends on the present value of the state variable, we prove existence of optimal strategies, and we show that the problem is equivalent to a state constraints problem in an endogenous state region which depends on the data of the problem. Some economic examples are analyzed.     

A nonsmooth approach to envelope theorems

We develop a nonsmooth approach to envelope theorems applicable to a broad class of parameterized constrained nonlinear optimization problems that arise typically in economic applications with nonconvexities and/or nonsmooth objectives. Our methods emphasize the role of the Strict Mangasarian–Fromovitz Constraint Qualification (SMFCQ), and include envelope theorems for both the convex and nonconvex case, allow for noninterior solutions as well as equality and inequality constraints. We give new sufficient conditions for the value function to be directionally differentiable, as well as continuously differentiable. We apply our results to stochastic growth models with Markov shocks and constrained lattice programming problems.