Linear Programming and Generalizations: A Problem-Based Introduction with Spreadsheets

ISBN-13: 9781441964908 / Angielski / Twarda / 2011 / 673 str.

Eric V. DeNardo

Opis

The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics. It surveys models that optimize something, subject to constraints. The simplest such models are linear, and the ideas used to analyze linear models generalize easily. The book fuses five components: -It uses examples to introduce general ideas. -It engages the student in spreadsheet computation. -It surveys the uses of constrained optimization. -It presents the mathematics that relates to constrained optimization. -It links the subject to economic reasoning. Fusing these components makes constrained optimization more accessible and more valuable. It stimulates the student's interest, it quickens the learning process, it helps students to achieve mastery, and it prepares them to make effective use of the material. A well-designed example provides context. It can illustrate the applicability of the model, reveal a concept that holds in general, and introduce the notation that will be needed for a more general discussion. Examples mesh naturally with spreadsheet computation, and this book is keyed to two software packages, Solver and Premium Solver for Education. To compute on a spreadsheet is to learn interactively - the spreadsheet gives instant feedback. Spreadsheets help the student to become facile with the subject, and they help them use it to shape their professional identities. Constrained optimization draws upon several branches of mathematics. Linear programming builds upon linear algebra. Its generalizations draw upon analysis, differential calculus, and convexity. Including the relevant math in a course on constrained optimization helps the student to master the math and to use it effectively. Nearly every facet of constrained optimization has a close link to economic reasoning. I cite two examples, among many: A central theme of economics is the efficient allocation of scarce resources, and the canonical model for allocating scarce resources is the linear program. Marginal analysis is a key concept in economics, and it is exactly what the simplex method accomplishes. Emphasizing the links between constrained optimization and economics makes both subjects more comprehensible, and more germane. The scope of this book reflects its components. Spreadsheet computation is used throughout as a teaching-and-learning aide. Uses of constrained optimization are surveyed. The theory is dovetailed with the relevant mathematics. The links to economics are emphasized.

Recenzje

From the reviews:

"This text includes a more in-depth review of LP, lending the student thorough knowledge of the art and science of problem solving using LP. ... Undergraduate students in applied commerce or business programs are clearly part of the audience. It is also suitable for a course that introduces LP, its application, and its integration with widely used software ... . Practitioners with an interest in refreshing their knowledge in LP or expanding their knowledge to include LP will be equally satisfied by this book." (Geoffrey T. Pond, Interfaces, Vol. 42 (3), May-June, 2012)

Spis treści

Chapter 1. Introduction to Linear Programs.- Chapter 2. Spreadsheet Computation.- Chapter 3. Mathematical Preliminaries.- Chapter 4. The Simplex Method, Part 1.- Chapter 5. Analyzing Linear Programs.- Chapter 6. The Simplex Method, Part 2.- Chapter 7. A Survey of Optimization Problems.- Chapter 8. Path-Length Problems and Dynamic Programming.- Chapter 9. Flows in Networks.- Chapter 10. Vector Spaces and Linear Programs.- Chapter 11. Multipliers and the Simplex Method.- Chapter 12. Duality.- Chapter 13. The Dual Simplex Pivot and Its Uses.- Chapter 14. Introduction to Game Theory.- Chapter 15. The Bi-Matrix Game.- Chapter 16. Fixed Points and Equilibria.- Chapter 17. Convex Sets.- Chapter 18. Differentiation.- Chapter 19. Convex Functions.- Chapter 20.- Nonlinear Programs.

Blurb

This book on constrained optimization is novel in that it fuses these themes: • use examples to introduce general ideas; • engage the student in spreadsheet computation; • survey the uses of constrained optimization;. • investigate game theory and nonlinear optimization, • link the subject to economic reasoning, and • present the requisite mathematics. Blending these themes makes constrained optimization more accessible and more valuable. It stimulates the student’s interest, quickens the learning process, reveals connections to several academic and professional fields, and deepens the student’s grasp of the relevant mathematics. The book is designed for use in courses that focus on the applications of constrained optimization, in courses that emphasize the theory, and in courses that link the subject to economics.