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In order to determine optimal present decisions in such industries, it is necessary to develop and use dynamic models that describe how the biological resources grow and how the growth is affected by present harvesting and other management decisions. Braun, M., Differential Equations and Their Applications, Springer-Verlag, Applied Mathematical Sciences 15, 3 ed., 1983ДЎ7 In agriculture, fishing, forestry, wildlife management and hunting, resources are used for many different purposes, including food, building materials, paper, energy and much more. Hence, multi period analysis is often relevant.ДЎ6 Many types of resources are continuously used, thanks to biological growth.Д«raun gives a very good presentation of ordinary differential equations, which is key to the understanding and modeling of dynamical systems, including biological resources of all kinds. In most problems, present decisions have consequences for the future development of the system under analysis.

For instance, if we want to determine the optimal decision in a particular problem, we may define it as a one dimensional optimization problem, or as a multidimensional problem where we simultaneously optimize several decisions that may be linked in different ways.ДЎ5 We may also consider constraints of different sorts. In many cases, the optimal decisions that are the results of the analyses, differ considerably. Winston, W.L., Operations Research, Applications and Algorithms, Thomson, Brooks/Cole, Belmont, USA, 2004 Winston, W.L., Introduction to Probability Models, Operations Research: Volume two, Thomson, Brooks/Cole, Belmont, USA, 2004ДЎ4 The operations research literature contains large numbers of alternative methods and models, applied to very similar types of applied problems. The two books by Winston, references and, give a good and rather complete presentation of most operations research methods, algorithms and typical applications.

This may seem obvious to the reader, but it is far from trivial to determine the problem relevant method and models. Anon, LINGO, the Modeling Language and Optimizer, Lindo Systems Inc., Chicago, 2013ДЎ3 A particular applied problem should, if possible, be analyzed with a problem relevant operations research method, using a problem relevant set of mathematical models.

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The reference book of the software package LINGO contains large numbers of alternative operations research models and applications with numerical solutions. Usually, in applied problems, there are many different ways to define the mathematical models representing the components of the system under analysis. Chiang, A.C., Fundamental Methods of Mathematical Economics, McGraw-Hill, Inc., 2 ed., 1974ДЎ2 Mathematical modeling is central to operations research. The classical analytical methods of optimization and comparative statics analysis, basic economic theory and fundamental linear programming are well presented in Chiang. In this paper, we will focus on operations research in connection to optimization of decisions, with one or more decision maker(s). Keywords: Operations Research, Mathematical Modeling, Optimization.ДЈ Introductory examples of important real world decision problems that can be developed to applications of operations researchДЎ0 Introduction to mathematical modeling and operations researchДЎ1 Operations research is a very large area. The discussed methods and examples are motivated from the points of view of empirical relevance and computability. This paper presents fundamental and general decision and information structures, theories and examples that can be expanded and modified in several directions. The numbers of alternative models, methods and applications of operations research are very large. Theoretical understanding of the relevant problem structure and consistent mathematical modeling are necessary keys to formulating operations research models to be used for optimization of decisions in real applications.

Presentation on theme: 'Keynote presentation at:'- Presentation transcript:ДЄPPLICATIONS AND MATHEMATICAL MODELING IN OPERATIONS RESEARCH Version Peter Lohmander Professor Dr., Optimal Solutions & Linnaeus University, Sweden & Keynote presentation at:Дў APPLICATIONS AND MATHEMATICAL MODELING IN OPERATIONS RESEARCH Peter Lohmander Abstract

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