On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}

The research is focused on the question of proportional development in economic growth modeling. A multilevel dynamic optimization model is developed for the construction of balanced proportions for production factors and investments in a situation of changing prices. At the first level, models with production functions of different types are examined within the classical static optimization approach. It is shown that all these models possess the property of proportionality: in the solution of product maximization and cost minimization problems, production factor levels are directly proportional to each other with coefficients of proportionality depending on prices and elasticities of production functions. At the second level, proportional solutions of the first level are transferred to an economic growth model to solve the problem of dynamic optimization for the investments in production factors. Due to proportionality conditions and the homogeneity condition of degree 1 for the macroeconomic production functions, the original nonlinear dynamics is converted to a linear system of differential equations that describe the dynamics of production factors. In the conversion, all peculiarities of the nonlinear model are hidden in a time-dependent scale factor (total factor productivity) of the linear model, which is determined by proportions between prices and elasticities of the production functions. For a control problem with linear dynamics, analytic formulas are obtained for optimal development trajectories within the Pontryagin maximum principle for statements with finite and infinite horizons. It is shown that solutions of these two problems differ crucially from each other: in finite horizon problems the optimal investment strategy inevitably has the zero regime at the final stage, whereas the infinite horizon problem always has a strictly positive solution. A remarkable result of the proposed model consists in constructive analytical solutions for optimal investments in production factors, which depend on the price dynamics and other economic parameters such as elasticities of production functions, total factor productivity, and depreciation factors. This feature serves as a background for the productive fusion of optimization models for investments in production factors in the framework of a multilevel structure and provides a solid basis for constructing optimal trajectories of economic development.     

Bayes estimation in linear models: A coordinate-free approach

The unified theory of Bayes estimation in linear models is presented, using a coordinate-free approach. The results are applied to the problem of linear and quadratic estimation in linear regression model.     

Seemingly unrelated regression models

The cross-covariance matrix of observation vectors in two linear statistical models need not be zero matrix. In such a case the problem is to find explicit expressions for the best linear unbiased estimators of both model parameters and estimators of variance components in the simplest structure of the covariance matrix. Univariate and multivariate forms of linear models are dealt with.     

An additive utility mixed integer programming model for nonlinear discriminant analysis

Mathematical programming (MP) discriminant analysis models can be used to develop classification models for assigning observations of unknown class membership to one of a number of specified classes using values of a set of features associated with each observation. Since most MP discriminant analysis models generate linear discriminant functions, these MP models are generally used to develop linear classification models. Nonlinear classifiers may, however, have better classification performance than linear classifiers. In this paper, a mixed integer programming model is developed to generate nonlinear discriminant functions composed of monotone piecewise-linear marginal utility functions for each feature and the cut-off value for class membership. It is also shown that this model can be extended for feature selection. The performance of this new MP model for two-group discriminant analysis is compared with statistical discriminant analysis and other MP discriminant analysis models using a real problem and a number of simulated problem sets.     

Assignment problems with changeover cost

We consider some variant models, having changeover cost, of the assignment problem. In these models, multiple assignments to an operator are allowed. In addition to assignment costs, a changeover cost is incurred if an operator does one job after another is completed. Two different types of changeover costs and related two models are considered. Mathematical programming formulations are given for the models. When changeover costs are dependent on the operator but independent of the jobs and are non-negative, a linear programming model is obtained. For the case when changeover costs are dependent on the jobs, a linear integer programming formulation is obtained. We also show that, this problem is strongly NP-hard. A heuristic solution method is suggested for it. Numerical findings on the performance of the method are given.     

关于输电阻塞管理问题的思考

对"电力市场的输电阻塞管理"这道竞赛题进行了研究,首先对问题背景进行了说明,然后就建模过程的关键点进行了详细的阐述,同时建立了简明合理的非线性优化模型.通过适当的数学处理,将非线性模型巧妙地转化为线性模型.     

锥优化模型在Robust桁架拓扑设计实例中的应用

本文讨论Robust桁架拓扑设计(TTD)问题，即桁架结构设计问题，使其在固定重量的情况下，具有最佳的承载能力．本文陈述了几种应用锥优化解Robust TTD问题的方法，并简介了锥优化最新的领域．同时，本文给出了一个单负荷的线性模型和一个多负荷的半正定优化模型以及Robust TTD问题．文中所有的模型均有例证．例证显示通过应用对偶性这些模型的规模能被充分的减小．     

Linear programming with triangular fuzzy numbers—A case study in a finance and credit institute

The objective of this paper is to deal with a kind of fuzzy linear programming problem involving triangular fuzzy numbers. Then some interesting and fundamental results are achieved which in turn lead to a solution of fuzzy linear programming models without converting the problems to the crisp linear programming models. Finally, the theoretical results are also supported by a real case study in a banking system. The same idea is emphasized to be also useful when a general LR fuzzy numbers is given.     

Multiobjective data envelopment analysis

Data envelopment analysis (DEA) is popularly used to evaluate relative efficiency among public or private firms. Most DEA models are established by individually maximizing each firm's efficiency according to its advantageous expectation by a ratio. Some scholars have pointed out the interesting relationship between the multiobjective linear programming (MOLP) problem and the DEA problem. They also introduced the common weight approach to DEA based on MOLP. This paper proposes a new linear programming problem for computing the efficiency of a decision-making unit (DMU). The proposed model differs from traditional and existing multiobjective DEA models in that its objective function is the difference between inputs and outputs instead of the outputs/inputs ratio. Then an MOLP problem, based on the introduced linear programming problem, is formulated for the computation of common weights for all DMUs. To be precise, the modified Chebychev distance and the ideal point of MOLP are used to generate common weights. The dual problem of this model is also investigated. Finally, this study presents an actual case study analysing R&D efficiency of 10 TFT-LCD companies in Taiwan to illustrate this new approach. Our model demonstrates better performance than the traditional DEA model as well as some of the most important existing multiobjective DEA models.     

Stochastic fractional differential equations: Modeling,method and analysis

By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model described by a system of multi-time scale stochastic differential equations is formulated. The classical Picard–Lindelöf successive approximations scheme is applied to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this leads to the problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations of Itô–Doob type. Finally, to illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are outlined.     

Fuzzy programming and linear programming with several objective functions

In the recent past numerous models and methods have been suggested to solve the vectormaximum problem. Most of these approaches center their attention on linear programming problems with several objective functions. Apart from these approaches the theory of fuzzy sets has been employed to formulate and solve fuzzy linear programming problems. This paper presents the application of fuzzy linear programming approaches to the linear vectormaximum problem. It shows that solutions obtained by fuzzy linear programming are always efficient solutions. It also shows the consequences of using different ways of combining individual objective functions in order to determine an “optimal” compromise solution.     

Using an economics model for teaching linear algebra

We present an approach for teaching linear algebra using models. In particular, we are interested in analyzing the modeling process under an APOS perspective. We will present a short illustration of the analysis of an economics problem related to production in a set of industries. This problem elicits the use of the concepts of linear combination, linear independence, among other linear algebra concepts related to vector space. We describe cycles of students’ work on the problem, present an analysis of the learning trajectory with emphasis on the constructions they develop, and discuss the advantages of this approach in terms of students’ learning.     

Bounds of redundant multicast routing problem with SRLG-diverse constraints: edge,path and tree models

This paper proposes three classes of alternative mathematical programming models (i.e., edge-based, path-based, and tree-based) for redundant multicast routing problem with shared risk link group (SRLG)-diverse constraints (RMR-SRLGD). The goal of RMR-SRLGD problem is to find two redundant multicast trees, each from one of the two sources to every destination, at a minimum cost while ensuring the paths from the two sources to a destination do not share any common risks. Such risk could cause the failures of multiple links simultaneously. Therefore, the RMR-SRLGD problem ensures the availability and reliability of multicast services. We investigated and compared the theoretical bounds of the linear programming (LP) relaxation for all models. We also summarized a hierarchy relationship of the tightness of LP bounds for the proposed models.     

Global optimization of non-convex piecewise linear regression splines

Multivariate adaptive regression spline (MARS) is a statistical modeling method used to represent a complex system. More recently, a version of MARS was modified to be piecewise linear. This paper presents a mixed integer linear program, called MARSOPT, that optimizes a non-convex piecewise linear MARS model subject to constraints that include both linear regression models and piecewise linear MARS models. MARSOPT is customized for an automotive crash safety system design problem for a major US automaker and solved using branch and bound. The solutions from MARSOPT are compared with those from customized genetic algorithms.     

Analytical solution for a class of learning by doing models with multiplicative uncertainty

We find the closed form optimal solution for a class of learning by doing models, where multiplicative uncertainty is introduced in a piecewise linear cost reduction function. Previous literature does not find the closed form optimal solution for these models. We consider a monopolist, facing a linear demand function. The optimal policy for the resulting problem is shown to be piecewise linear and continuous. The optimal output increases with unit cost for certain values of the latter. Numerical examples are provided.     

城市道路交通信号实时控制的数学模型与算法研究

研究了交通信号的实时配时控制问题.建立了在已有交通设施条件下,控制信号具有线性约束的非线性实时配时系统优化模型,设计了与模型相适应的实时CLY系列算法.重点讨论了点控制问题,建立了相应的数学优化模型,设计了CLY-Point1算法求解.还对线控制问题和面控制问题,建立了多层优化控制模型,并设计CLY-Point2、CLY-Line和CLY-Area算法进行求解.数值模拟结果表明,CLY系列算法具有很强的实时性,车辆平均等待时间比固定配时减少了约20%.     

Optimal tactics for close support operations: Part IV,perfect intelligence and communications

A new generation ofC ³ (command, control, and communication) models for military cybernetics is developed. Recursive equations for the solution of theC ³ problem are derived for an amphibious campaign with linear, time-varying dynamics. Air and ground commanders are assumed to have perfect intelligence and perfect communications. Numerical results are given for the optimal decision rules.     

Lineare Verteilungsmodelle in der Betriebswirtschaft — Beispiele für den praktischen Einsatz der Linearplanung in Unternehmungen

Zusammenfassung Lineare Verteilungsmodelle eine spezielle Klasse linearer Planungsansätze. Transportproblem aus der Betriebspraxis. Allgemeine Eigenschaften linearer Verteilungsmodelle. Problem der Rohstoffverteilung mit Näherungslösung. Hinweise auf eine weiteres Verfahren der Konstruktion linearer Verteilungsmodelle.

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Summary Linear distribution models as a special class of the general linear programming problem. A transportation problem of bussiness economics. General features of linear distribution models. Problem of raw material allocation with approximate solution. Reference to a further method of constructing linear distribution models.

     

Comparative evaluation of MILP flowshop models

This paper investigates the performance of two families of mixed-integer linear programing (MILP) models for solving the regular permutation flowshop problem to minimize makespan. The three models of the Wagner family incorporate the assignment problem while the five members of the Manne family use pairs of dichotomous constraints, or their mathematical equivalents, to assign jobs to sequence positions. For both families, the problem size complexity and computational time required to optimally solve a common set of problems are investigated. In so doing, this paper extends the application of MILP approaches to larger problem sizes than those found in the existing literature. The Wagner models require more than twice the binary variables and more real variables than do the Manne models, while Manne models require more constraints for the same sized problems. All Wagner models require much less computational time than any of the Manne models for solving the common set of problems, and these differences increase dramatically with increasing number of jobs and machines. Wagner models can solve problems containing larger numbers of machines and jobs than the Manne models, and hence are preferable for finding optimal solutions to the permutation flowshop problem with makespan objective.