Linear-Fractional Programming Theory, Methods, Applications and Software

1. Front Matter

   Pages i-xxvii

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2. Introduction

   • Erik B. Bajalinov

   Pages 1-6

3. Basic Linear Algebra

   • Erik B. Bajalinov

   Pages 7-39

4. Introduction to LFP

   • Erik B. Bajalinov

   Pages 41-74

5. The Simplex Method

   • Erik B. Bajalinov

   Pages 75-127

6. Duality Theory

   • Erik B. Bajalinov

   Pages 129-175

7. Sensitivity Analysis

   • Erik B. Bajalinov

   Pages 177-203

8. Interconnection Between LFP and LP

   • Erik B. Bajalinov

   Pages 205-218

9. Integer LFP

   • Erik B. Bajalinov

   Pages 219-244

10. Special LFP Problems

    • Erik B. Bajalinov

    Pages 245-286

11. Advanced Methods and Algorithms in LFP

    • Erik B. Bajalinov

    Pages 287-301

12. Advanced Topics in LFP

    • Erik B. Bajalinov

    Pages 303-310

13. Computational Aspects

    • Erik B. Bajalinov

    Pages 311-380

14. The Wingulf Package

    • Erik B. Bajalinov

    Pages 381-408

15. Back Matter

    Pages 409-423

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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.

• design
• duality
• linear optimization
• programming

From the reviews:

"Although several books on general (nonlinear) fractional programming are available, this is the first monograph entirely devoted to linear-fractional problems. As the title indicates, it deals with both the theoretical and the algorithmic aspects of the subject, including the description of a program package for Windows." (Juan-Enrique Martínez-Legaz, Zentralblatt MATH, Vol. 1067 (18), 2005)

• Department of Computer Science Institute of Informatics, Debrecen University, Hungary

  Erik B. Bajalinov

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