Random utility demand models and service location

This paper considers the problem of the optimal location of facilities when the demand behavior is described by a random utility choice model. By means of duality theory of mathematical programming, it is shown how a wide family of such problems can be mapped into an entropy maximizing problem, which is usually easy to solve numerically. Theory and methods are discussed in details for the problem of locating a single type of facilities, and the extension to some kinds of systems with many types of facilities is outlined.     

Dini derivatives in optimization — Part I

This paper, published in two parts, is mainly concerned with general properties of Dini derivatives of functions of one and several variables and with some applications of this topic to the study of generalized convexity and generalized optimality conditions for mathematical programming problems.In part I the basic definitions and properties are given, with reference both to functions of one real variable and to functions of several real variables. In this part special attention is given to the restatement of the basic theorems of the classical analysis to nondifferentiable functions, in terms of Dini derivatives.In part II we use these derivatives in order to define some classes of nondifferentiable generalized convex functions and the class of generalized upper quasidifferentiable functions. This part concludes with the development of optimality conditions for a nonsmooth programming problem, expressed in terms of the tools prevously introduced.

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Riassunto Il presente lavoro, pubblicato in due parti, riguarda le principali proprietà dei numeri derivati di Dini (o derivate direzioni di Dini), sia di funzioni di una variablile che di più variabili, nonché alcune loro applicazioni allo studio della convessità generalizzata ed a problemi di ottimizzazione vincolata.Nella prima parte del lavoro si forniscono le definizioni e le proprietà fondamentali dei numeri derivati di Dini e vengono riformulati alcuni classici teoremi dell'an alisi, con riferimento a funzioni non differenziabili.Nella seconda parte tali derivate direzionali vengono applicate nello studio di alcune classi di funzioni convesse generalizzate non differenziabili e nell'ottenimento di condizioni di ottimalità per problemi (non differenziabili) di programmazione matematica.

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This research was supported by the Italian Ministry of University and Scientific Research and by the National Science Foundation of the Hungarian Academy of Sciences and Arts (grant OTKA 354/86). The authors have shared their work as follows: Chapters 1 and 3 are attributed to the first author, whereas Chapters 2 and 4 are attributed to the second author. The Introduction and Chapter 5 is common.     

Theorems related to symmetric nonlinear decomposition

Decomposition methods can provide the rescue from the curse of dimensionality, which often prevents the successful numerical solution of large scale nonlinear mathematical programming problems. A symmetric nonlinear decomposition theory has been elaborated by T.O.M. Kronsjö (4) as an extension of a theory by the same author (3). The stringent proof of the convergence of this decomposition algorithm requires some results on necessary optimality conditions for certain mathematical programming problems. In this paper we state and prove some theorems providing these results.     

Dini derivatives in optimization — Part II

This paper, published in two parts, is mainly concerned with general properties of Dini derivatives of functions of one and several variables and with some applications of this topic to the study of generalized convexity and generalized optimality conditions for mathematical programming problems.In part I the basic definitions and properties are given, with reference both to functions of one real variable and to functions of several real variables. In this part special attention is given to the restatement of the basic theorems of the classical analysis to nondifferentiable functions, in terms of Dini derivatives.In part II we use these derivatives in order to define some classes of nondifferentiable generalized convex functions and the class of generalized upper quasidifferentiable functions. This part concludes with the development of optimality conditions for a nonsmooth programming problem, expressed in terms of the tools prevously introduced.

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Riassunto presente lavoro, pubblicato in due parti, riguarda le principali proprietà dei numeri derivati di Dini (o derivate direzioni di Dini), sia di funzioni di una variabile che di più variabili, nonché alcune loro applicazioni allo studio della convessità generalizzata ed a problemi di ottimizzazione vincolata.Nella prima parte del lavoro si formiscono le definizioni e le proprietà fondamentali dei numeri derivati di Dini e vengono riformulati alcuni classici teoremi dell'analisi, con riferimento a funzioni non differenziabili.Nella seconda parte tali derivate direzionali vengono applicate nello studio di alcune classi di funzioni convesse generalizzate non differenziabili e nell'ottenimento di condizioni di ottimalità per problemi (non differenziabili) di programmazione matematica.

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This research was supported by the Italian Ministry of University and Scientific Research and by the National Science Foundation of the Hungarian Academy of Sciences and Arts (grant OTKA 354/86). The authors have shared their work as follows: Chapters 1 and 3 are attributed to the first author, whereas Chapters 2 and 4 are attributed to the second author. The Introduction and Chapter 5 is common.     

Convex and convex-like optimization over a range inclusion problem and first applications

The paper deals with the minimization of a function over the solution set of a range inclusion problem determined by a multifunction. A strong Lagrange duality is provided first in terms of a quasirelative interior condition and then under a so-called Assumption (S). When the function and the multifunction are convex, we improve this duality under a closed cone condition. The stability analysis is investigated. In addition, if the multifunction is a convex process, then the Fenchel dual is performed in terms of its conjugate. As a first application, we provide a unified approach to the optimization of general discrete inclusions systems; in particular, we improve several results on optimal control, strong Lagrange duality and Fenchel duality for some classes of convex controlled discrete processes.     

用Excel规划求解报亭选址问题

报亭的选址问题是一类目标优化问题,从采用精确重心方法来求解的数学模型来看,此目标问题是一个迭代型规划问题,不能直接用常规的Excel规划方法来求解。文中通过引入过渡变量来逐步进行迭代求解。在每一步通过比较前后2对坐标之间的误差,在有限的时间与迭代次数内,求解到了地址目标。求解结果与手工计算的相吻合。     

基于运筹优化的物流与设施规划课程教学研究

在传统教学中,物流与设施规划课程的物流分析、设施布局等内容的一些经典问题采用启发式方法或试验法来解决。为了更精确地解决这些问题,采用数学规划方法提供解决方案。主要围绕建模技巧、应用软件教学和解决物流与设施规划专业案例等方面培养学生运用优化原理与方法构建运筹优化模型的能力以及运用ILOG OPL优化软件解决实际优化问题的能力。以二次分配问题和多产品工艺过程图优化问题为案例阐述了数学规划建模和编程求解的过程。     

Utility indifference valuation for jump risky assets

We discuss utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to backward stochastic equations driven by the Poisson martingales. Via a duality result, the solution to the dual problems is derived. In particular, an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated non tradable asset.     

Using difference equations to find optimal tax structures on the SugarScape

The use of equations to describe agent-based model dynamics allows access to mathematical theory that is not otherwise available. In particular, equation models can be effective at solving optimization problems—that is, problems concerning how an agent-based model can be most effectively steered into a particular state. In order to illustrate this strategy, we describe a modified version of the well-known SugarScape model and implement taxation. The optimization problem is to determine tax structures that minimize deaths but maximize tax income. Tax rates are dependent upon the amount of sugar available in a particular region; the rates change over time. A system of discrete difference equations is built to capture agent-based model dynamics. The equations are shown to capture the dynamics very well both with and without taxation. A multi-objective optimization technique known as Pareto optimization is then used to solve the problem. Rather than focusing on a cost function in which the two objectives are assigned weights, Pareto optimization is a heuristic method that determines a suite of solutions, each of which is optimal depending on the priorities of the researcher. In this case, Pareto optimization allows analysis of the tradeoff between taxes collected and deaths caused by taxation. The strategies contained here serve as a framework for a broad class of models.     

Naar aseptische en realistische methoden in de toegepaste statistiek

Summary
Applied statistics is not pure mathematics but the application of suitable methods of mathematical statistics to practical problems.
In choosing the method one should be extremely suspicious in regard to septic methods and give strong preference to realistic methods.
Septic methods are those which by their very nature introduce properties alien to the magnitudes concerned e.g. addition of non-additive variables, differentiation of stochastic variables, stochastic treatment of indeterminate variables, etc. Realistic methods are those based on a preliminary analysis of the practical problem which should bring to light the essential mutually independent variables controlling the outcome of the problem. Undue simplification at the cost of the accuracy required in actual practice should be avoided; especially weak correlations between variables shown by the deductive analysis as being essentially mutually independent should be discarded.
On the other hand the mathematical treatment should be as simple and direct as possible.
The professional mathematician can become a real danger if he wants to guide the application of mathematical statistics to certain fields of applied science in which he is not sufficiently specialised and experienced. Contrariwise, if he acquires this knowledge in business, the highest positions are open to him.     

Two-level national-regional planning and mathematical programming decomposition applied to spatial price equilibrium models2

This paper is concerned with computation strategies related with the quantitative analysis of only a sector of a global economy (e.g. agriculture or energy). Under a ceteris paribus condition on the environment of the sector, and within the hypothetical context of the neoclassical economic theory, it is well known a type of partial equilibrium model that can be cast mathematically into an optimization framework. We attempt here to a typical specification which considers spatially separated markets, that has been called spatial price equilibrium model and that has contained within it many classical transportation problems (one for each commodity). The model is specially suitable for mathematical programming decomposition, resulting regional sybsystems whose coupling variables are the transportation flows. We explore here this structure, discussing two decomposition algorithms with economic interpretations that suggest decentralized procedures for planning. The first—of the price coordination type—is a variant of the Dantzig-Wolfe's principle which is expected to have a low number of cycles of information flow between the master level and the sub-problems (at each cycle it is calculated a series of regional production-consumption responses to alternative prices generated by transhipment problems at the central planning level). The second algorithm specializes the Geoffrion's projection/feasible directions technique, so interpreting the problem solution within the context of a net-output target coordination.     

基于自适应蚂蚁算法的房地产投资组合优化决策

房地产投资组合优化是降低投资风险的有效方法之一。现有的房地产投资组合理论及算法存在缺陷,本文利用熵作为风险衡量指标,并将蚂蚁算法引入房地产开发领域,且针对基本蚂蚁算法存在的计算复杂,易陷入局部最优等缺陷,提出了一种变系数的自适应蚂蚁算法,TSP问题的计算结果表明了该方法较之其他改进算法的优势。以各项目间的均值熵代替TSP中的各城市距离后的房地产投资组合计算实例表明,该方法具有较好的收敛性、稳定性和鲁棒性,是求解组合优化问题的一种较好的方法。     

基于最小费用最大流的集群式供应链库存优化

首先介绍了集群式供应链库存管理存在的问题,据此设计出系统优化的网络结构,引入最小费用最大流的方法并进行了实际的赋值计算,然后提出了集群式供应链库存的优化模型,结尾对建立在集群式供应链基础上的库存管理的实际意义进行了评价。     

基于局部搜索遗传算法的仓库车辆调度优化研究

针对仓库装卸搬运系统实际运行时设备资源冲突和搬运车辆任务分配问题,建立了具有多个复杂约束条件的车辆调度优化问题数学模型。提出了一种求解仓库车辆调度优化问题的局部搜索遗传算法,解决了局部搜索中寻找高效邻域结构的技术难题,并用实例进行了验证。     

Cost and Production Duality: The Case of the Regulated Firm

This paper examines a generalization of cost-production duality for regulated firms. It derives an equivalency between the production function and conditional factor demands for the case where the firm's optimization problem is subject to a set of additional (regulatory) constraints. This procedure is extended to an optimization problem within a dynamic framework which leads to the recovery of the firm's technology.     

中石化销售公司成品油物流运作优化问题初探

介绍了中石化成品油物流的管理现状和存在的问题,说明采用现行的物流操作模式对销售公司成品油物流运作优化的影响;提出了中石化销售公司成品油物流运作优化的解决方案,以及成立销售公司成品油物流总部的思路和方法,包括组织机构和管理体制,物流的优化和信息系统的建设,从而形成一个完整的销售公司成品油物流运作优化的方案。     

关于高层建筑暖通空调设计的研究

本文简要叙述了高层建筑在设计暖通空调时的基本原则,同时详细分析了在设计过程中应高度重视的问题,这对于我国高层建筑的暖通空调设计来说能起到至关重要的优化与推动作用。     

Optimal allocation of the sample size to strata under box constraints

In stratified random sampling without replacement boundary conditions, such as the sample sizes within strata shall not exceed the population sizes in the respective strata, have to be considered. Stenger and Gabler (Metrika, 61:137–156, 2005) have shown a solution that satisfies upper boundaries of sample fractions within the strata. However, in modern applications one may wish to guarantee also minimal sampling fractions within strata in order to allow for reasonable separate estimations. Within this paper, an optimal allocation in the Neyman-Tschuprov sense is developed which satisfies upper and lower bounds of the sample sizes within strata. Further, a stable algorithm is given which ensures optimality. The resulting sample allocation enables users to bound design weights within stratified random sampling while considering optimality in allocation.     

我国物流园区二元结构与物流园区发展

近几年我国物流园区如雨后春笋般出现,其发展规模、档次不一,运营过程中问题很多,其中自发性与规划性的相互交叉使得物流园区产生了二元结构（二元经济）。文章通过分析物流园区二元结构的现状、成因,并基于发展园区的目的提出了解决当前我国物流园区二元结构矛盾的方案。其基本结论是：通过主管部门政策性引导,由自发性向规划性有计划地转移;通过市场竞争,逐步淘汰园区的自发性经营活动。