An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.     

Antieigenvalue techniques in statistics

In a number of his recent papers Karl Gustafson has outlined the similarities between the Antieigenvalue Theory he founded and several finite dimensional matrix optimization theorems for positive matrices arising in statistics. In this paper, we will show how the techniques that the author and Karl Gustafson have used for computation of Antieigenvalues can also be applied to prove and generalize these matrix optimization theorems in statistics. We will primarily focus on two techniques which we have used in Antieigenvalue computations in recent years. These two techniques are a two nonzero component property for certain class of functionals, and converting the matrix optimization problems in statistics to a convex programing problem. Indeed, these two techniques allow us to generalize some of the matrix optimization problems arising in statistics to strongly accretive operators on finite or infinite dimensional Hilbert spaces.     

Parallel computing in nonconvex programming

In this paper, we are concerned with the development of parallel algorithms for solving some classes of nonconvex optimization problems. We present an introductory survey of parallel algorithms that have been used to solve structured problems (partially separable, and large-scale block structured problems), and algorithms based on parallel local searches for solving general nonconvex problems. Indefinite quadratic programming posynomial optimization, and the general global concave minimization problem can be solved using these approaches. In addition, for the minimum concave cost network flow problem, we are going to present new parallel search algorithms for large-scale problems. Computational results of an efficient implementation on a multi-transputer system will be presented.     

A brief survey on numerical methods for solving singularly perturbed problems

In the present paper, a brief survey on computational techniques for the different classes of singularly perturbed problems is given. This survey is a continuation of work performed earlier by the first author and contains the literature of the work done by the researchers during the years 2000-2009. However some older important relevant papers are also included in this survey. We also mentioned those papers which are not surveyed in the previous survey papers by the first author of this paper, see [Appl. Math. Comput. 30 (1989) 223-259, 130 (2002) 457-510, 134 (2003) 371-429] for details. Thus this survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems.     

中国运筹学发展研究报告

运筹学是自20世纪三四十年代发展起来的一门新兴交叉学科,主要研究如何应用数学和计算的理论与方法对社会系统和工程系统做出最优或满意的决策。为了更好地推动中国运筹学及相关领域的研究和应用,学会组织国内运筹学领域的部分专家,并参考了国内外运筹学多个分支代表性人物对运筹学的起源和发展的回忆与评述,共同完成了此报告。报告概述了运筹学的主要特征和方法,简述了运筹学的发展历程,剖析了运筹学研究中的成功经验,综述了运筹学几个主要分支的发展状况,介绍了运筹学中十几个有代表性的难题,展望了运筹学未来发展的方向。希望此报告能引起读者进一步思考运筹学的本质,运筹学是如何成长和将如何发展,并在一定程度上推动中国运筹学更好地发展。     

Chapter 1:general introduction

One of the most active and continuing subjects in matrix theory during the past century is the study of those linear operators on matrices that leave certain properties or relations of subsets invariant. Such questions are usually called "Linear Preserver Problems." The earliest papers in our reference list are [Frobenius, 1897] and [Kantor, 1897]. Since much effort has been devoted to this type of problem, there have been several excellent survey papers, e.g., [Marcus, 1962], [Marcus, 1971], and [Grone, 1976]. Since the time of Grone's thesis, there have been many developments, encouraged by the introduction of new techniques, many from outside matrix theory itself. We hope this monograph will provide a useful update and convenient reference for the reader. In this introduction, we describe some typical questions and results on linear preserver problems, give some motivation for the study of the subject and finally provide some guidance fur the use of the monograph.     

The need for education and research in administrative data processing

This paper contains some points of view concerning the need felt by many computer-people for more intensive education and research activities in administrative data processing. After a short out-line of the main problems in administrative data processing we will try to indicate some topics where research is most needed. Then follows a survey of the need of knowledge specified for different categories of persons working in this field. Finally, we will draw some conclusions regarding the responsibility of different institutions to certify these needs.     

From the 1-2-3 conjecture to the Riemann hypothesis

This survey presents some combinatorial problems with number-theoretic flavor. Our journey starts from a simple graph coloring question, but at some point gets close to dangerous territory of the Riemann Hypothesis. We will mostly focus on open problems, but we will also provide some simple proofs, just for adorning.     

A global optimization method for the design of space trajectories

The problem of optimally designing a trajectory for a space mission is considered in this paper. Actual mission design is a complex, multi-disciplinary and multi-objective activity with relevant economic implications. In this paper we will consider some simplified models proposed by the European Space Agency as test problems for global optimization (GTOP database). We show that many trajectory optimization problems can be quite efficiently solved by means of relatively simple global optimization techniques relying on standard methods for local optimization. We show in this paper that our approach has been able to find trajectories which in many cases outperform those already known. We also conjecture that this problem displays a “funnel structure” similar, in some sense, to that of molecular optimization problems.     

TOBIT模型在医疗费用研究中的应用

对一般人群进行医疗费用调查研究时,会存在有相当一部分人的医疗费用支出为零,以此作为因变量使用经典的线性回归进行统计建模时将会导致估计值的偏差。本文尝试使用Tobit模型及其半参数估计方法解决因变量存在大量零删失数据的问题,通过对太原市城镇居民医疗费用相关影响因素调查数据的实证分析,用以为医疗费用控制和医疗保险制度改革提供更有效的统计学方法支持和政策依据。     

A survey of dynamic network flows

Dynamic network flow models describe network-structured, decision-making problems over time. They are of interest because of their numerous applications and intriguing dynamic structure. The dynamic models are specially structured problems that can be solved with known general methods. However, specialized techniques have been developed to exploit the underlying dynamic structure. Here, we present a state-of-the-art survey of the results, applications, algorithms and implementations for dynamic network flows.Presented at the XII International Symposium on Mathematical Programming, Cambridge, Massachusetts, August 1985.Prepared under National Science Foundation Grant ECS-8307549. Reproduction in whole or in part is permitted for any purpose of the United States Government. This document has been approved for public release and sale; its distribution is unlimited.     

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research.     

Borsuk's problem and the chromatic numbers of metric spaces

In this paper, we will give a short survey of various old and new results concerning two closely connected problems of combinatorial geometry - that of K. Borsuk and that of E. Nelson - P. Erdös - H. Hadwiger. We will also present here our very recent achievements on Ramsey numbers.     

Optimization of Discrete-Continuous Dynamic Systems Based on Disjunctive Programming

In this contribution, a novel approach for the modeling and optimization of discrete-continuous dynamic systems based on a disjunctive problem formulation is proposed. It will be shown that a disjunctive model representation, which constitutes an alternative to mixed-integer model formulations, provides a very flexible and intuitive way to formulate discrete-continuous dynamic optimization problems. Moreover, the structure and properties of the disjunctive process models can be exploited for an efficient and robust numerical solution by applying generalized disjunctive programming techniques. The proposed modeling and optimization approach will be illustrated by means of an optimal control problem that embeds a linear discretecontinuous dynamic system. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Ramsey Type Problems in Combinatorial Geometry

In this paper, we will give a short survey of various old and new results on Ramsey type problems in combinatorial geometry.     

On the effectiveness of scenario generation techniques in single-period portfolio optimization

In single-period portfolio selection problems the expected value of both the risk measure and the portfolio return have to be estimated. Historical data realizations, used as equally probable scenarios, are frequently used to this aim. Several other parametric and non-parametric methods can be applied. When dealing with scenario generation techniques practitioners are mainly concerned on how reliable and effective such methods are when embedded into portfolio selection models. In this paper we survey different techniques to generate scenarios for the rates of return. We also compare the techniques by providing in-sample and out-of-sample analysis of the portfolios obtained by using these techniques to generate the rates of return. Evidence on the computational burden required by the different techniques is also provided. As reference model we use the Worst Conditional Expectation model with transaction costs. Extensive computational results based on different historical data sets from London Stock Exchange Market (FTSE) are presented and some interesting financial conclusions are drawn.     

Results and problems on congruence lattice representations

We survey some results and problems on congruence lattice representations. We will consider congruence representations and similarity type, and we will consider simultaneous congruence representations. A seemingly innocuous problem unites the sections. This paper is dedicated to Walter Taylor. Received October 9, 2005; accepted in final form January 3, 2006.     

An introduction to infinite particle systems

In 1970, Spitzer wrote a paper called “Interaction of Markov processes” in which he introduced several classes of interacting particle systems. These processes and other related models, collectively referred to as infinite particle systems, have been the object of much research in the last ten years. In this paper we will survey some of the results which have been obtained and some of the open problems, concentrating on six overlapping classes of processes: the voter model, additive processes, the exponential family, one dimensional systems, attractive systems, and the Ising model.     

Regularization of quasi-plurisubharmonic functions on complex manifolds

In this paper, we give a survey of various regularization theorems of quasi-plurisubharmonic functions on complex manifolds, and we also discuss the ideas used in their proofs. Moreover, we will present their applications in our studies on extension problems.