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Discrete and Fractional Programming Techniques for Location Models

2013-11-21 Mathematics
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Release : 2013-11-21
Genre : Mathematics
Kind : eBook
Book Rating : 720/5 ( reviews)

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Book Synopsis Discrete and Fractional Programming Techniques for Location Models by : A.I. Barros

Download or read book Discrete and Fractional Programming Techniques for Location Models written by A.I. Barros. This book was released on 2013-11-21. Available in PDF, EPUB and Kindle. Book excerpt: At first sight discrete and fractional programming techniques appear to be two com pletely unrelated fields in operations research. We will show how techniques in both fields can be applied separately and in a combined form to particular models in location analysis. Location analysis deals with the problem of deciding where to locate facilities, con sidering the clients to be served, in such a way that a certain criterion is optimized. The term "facilities" immediately suggests factories, warehouses, schools, etc. , while the term "clients" refers to depots, retail units, students, etc. Three basic classes can be identified in location analysis: continuous location, network location and dis crete location. The differences between these fields arise from the structure of the set of possible locations for the facilities. Hence, locating facilities in the plane or in another continuous space corresponds to a continuous location model while finding optimal facility locations on the edges or vertices of a network corresponds to a net work location model. Finally, if the possible set of locations is a finite set of points we have a discrete location model. Each of these fields has been actively studied, arousing intense discussion on the advantages and disadvantages of each of them. The usual requirement that every point in the plane or on the network must be a candidate location point, is one of the mostly used arguments "against" continuous and network location models.

Discrete and Fractional Programming Techniques for Location Models

1995-01-01 Combinatorial optimization
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Release : 1995-01-01
Genre : Combinatorial optimization
Kind : eBook
Book Rating : 207/5 ( reviews)

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Book Synopsis Discrete and Fractional Programming Techniques for Location Models by : Ana Isabel Barros

Download or read book Discrete and Fractional Programming Techniques for Location Models written by Ana Isabel Barros. This book was released on 1995-01-01. Available in PDF, EPUB and Kindle. Book excerpt:

Network and Discrete Location

2011-02-14 Mathematics
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Release : 2011-02-14
Genre : Mathematics
Kind : eBook
Book Rating : 737/5 ( reviews)

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Book Synopsis Network and Discrete Location by : Mark S. Daskin

Download or read book Network and Discrete Location written by Mark S. Daskin. This book was released on 2011-02-14. Available in PDF, EPUB and Kindle. Book excerpt: The comprehensive introduction to the art and science of locating facilities to make your organization more efficient, effective, and profitable. For the professional siting facilities, the task of translating organizational goals and objectives into concrete facilities requires a working familiarity with the theoretical and practical fundamentals of facility location planning and modeling. The first hands-on guide to using and developing facility location models, Network and Discrete Location offers a practiceoriented introduction to model-building methods and solution algorithms, complete with software to solve classical problems of realistic size and end-of-chapter exercises to enhance the reader's understanding. The text introduces the reader to the key classical location problems (covering, center, median, and fixed charge) which form the nucleus of facility location modeling. It also discusses real-life extensions of the basic models used in locating: production and distribution facilities, interacting services and facilities, and undesirable facilities. The book outlines a host of methodological tools for solving location models and provides insights into when each approach is useful and what information it provides. Designed to give readers a working familiarity with the basic facility location model types as well as an intuitive knowledge of the uses and limits of modeling techniques, Network and Discrete Location brings students and professionals alike swiftly from basic theory to technical fluency.

Linear-Fractional Programming Theory, Methods, Applications and Software

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 743/5 ( reviews)

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Book Synopsis Linear-Fractional Programming Theory, Methods, Applications and Software by : E.B. Bajalinov

Download or read book Linear-Fractional Programming Theory, Methods, Applications and Software written by E.B. Bajalinov. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: This is a book on Linear-Fractional Programming (here and in what follows we will refer to it as "LFP"). The field of LFP, largely developed by Hungarian mathematician B. Martos and his associates in the 1960's, is concerned with problems of op timization. LFP problems deal with determining the best possible allo cation of available resources to meet certain specifications. In particular, they may deal with situations where a number of resources, such as people, materials, machines, and land, are available and are to be combined to yield several products. In linear-fractional programming, the goal is to determine a per missible allocation of resources that will maximize or minimize some specific showing, such as profit gained per unit of cost, or cost of unit of product produced, etc. Strictly speaking, linear-fractional programming is a special case of the broader field of Mathematical Programming. LFP deals with that class of mathematical programming problems in which the relations among the variables are linear: the con straint relations (i.e. the restrictions) must be in linear form and the function to be optimized (i.e. the objective function) must be a ratio of two linear functions.

Quasiconvex Optimization and Location Theory

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 261/5 ( reviews)

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Book Synopsis Quasiconvex Optimization and Location Theory by : J.A. dos Santos Gromicho

Download or read book Quasiconvex Optimization and Location Theory written by J.A. dos Santos Gromicho. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: grams of which the objective is given by the ratio of a convex by a positive (over a convex domain) concave function. As observed by Sniedovich (Ref. [102, 103]) most of the properties of fractional pro grams could be found in other programs, given that the objective function could be written as a particular composition of functions. He called this new field C programming, standing for composite concave programming. In his seminal book on dynamic programming (Ref. [104]), Sniedovich shows how the study of such com positions can help tackling non-separable dynamic programs that otherwise would defeat solution. Barros and Frenk (Ref. [9]) developed a cutting plane algorithm capable of optimizing C-programs. More recently, this algorithm has been used by Carrizosa and Plastria to solve a global optimization problem in facility location (Ref. [16]). The distinction between global optimization problems (Ref. [54]) and generalized convex problems can sometimes be hard to establish. That is exactly the reason why so much effort has been placed into finding an exhaustive classification of the different weak forms of convexity, establishing a new definition just to satisfy some desirable property in the most general way possible. This book does not aim at all the subtleties of the different generalizations of convexity, but concentrates on the most general of them all, quasiconvex programming. Chapter 5 shows clearly where the real difficulties appear.

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