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“Dr. Taha is an excellent author and presents materials in his book very well in terms of readability and clarity. The topics within every chapter are presented in a cohesive and logical manner.”
-M. Jeya Chandra, PENN STATE UNIVERSITY
“The book is very clear and readable. Figures do a good job of illustrating Dr. Taha’s points. It is very useful to have the Solver & TORA output shown in the chapter with discussion of how to interpret results.”
-Marc E. Posner, THE OHIO STATE UNIVERSITY
|About the Author|
|Ch. 1||What Is Operations Research?||1|
|Ch. 2||Introduction to Linear Programming||11|
|Ch. 3||The Simplex Method||71|
|Ch. 4||Duality and Sensitivity Analysis||115|
|Ch. 5||Transportation Model and Its Variants||165|
|Ch. 6||Network Models||213|
|Ch. 7||Advanced Linear Programming||289|
|Ch. 8||Goal Programming||347|
|Ch. 9||Integer Linear Programming||361|
|Ch. 10||Deterministic Dynamic Programming||401|
|Ch. 11||Deterministic Inventory Models||429|
|Ch. 12||Review of Basic Probability||463|
|Ch. 13||Forecasting Models||491|
|Ch. 14||Decision Analysis and Games||503|
|Ch. 15||Probabilistic Dynamic Programming||547|
|Ch. 16||Probabilistic Inventory Models||559|
|Ch. 17||Queuing Systems||579|
|Ch. 18||Simulation Modeling||639|
|Ch. 19||Markovian Decision Process||675|
|Ch. 20||Classical Optimization Theory||701|
|Ch. 21||Nonlinear Programming Algorithms||731|
|App. A||Review of Vectors and Matrices||765|
|App. B||TORA Primer||779|
|App. C: Statistical Tables||785|
|App. D: Partial Answers to Selected Problems||789|
The main thrust of the seventh edition is the extensive software support used throughout the book:
The TORA software offers modules for matrix inversion, solution of simultaneous linear equations, linear programming, transportation models, network models, integer programming, queuing models, project planning with CPM and PERT, and game theory. TORA can be executed in automated or tutorial mode. The automated mode reports the final solution of the problem, usually in the standard format followed in commercial packages. The tutorial mode is a unique feature that provides immediate feedback to test the reader's understanding of the computational details of each algorithm. As with its DOS predecessor, the different screens in TORA are accessed in a logical and unambiguous manner, essentially eliminating the need for a user's manual.
Excel spreadsheet templates complement TORA's modules. These templates include linear programming, dynamic programming, analytical hierarchy process (AHP), inventory models, histogramming of raw data, decision theory, Poisson queues, P-K formula, simulation, and nonlinear models. Some of the templates are direct spreadsheets. Others use Excel Solveror VBA macros. Regardless of the design, all templates offer the unique feature of being equipped with an input data section that allows solving different problems without the need to modify the formulas or the layout of the spreadsheet. In this manner, the user can experiment with, test, and compare different sets of input data in a convenient manner. Where possible, the formulas and the layout of the spreadsheets have been protected to minimize the chance of inadvertently corrupting them.
The book includes examples of the commercial packages LINGO and AMPL for solving linear programming problems. The objective is to familiarize the reader with how very large mathematical programming models are solved in practice.
TORA software and the Excel spreadsheets are integrated into the text in a manner that facilitates introducing and testing concepts that otherwise could not be presented effectively. From my personal experience, I have found TORA's tutorial module and Excel spreadsheets to be highly effective in classroom presentations. Many concepts can be demonstrated instantly, simply by changing the data of the problem. To cite a few examples, TORA can be used to demonstrate the bizarre behavior of the branch-and-bound algorithm by applying it to a (small) integer programming problem, where the solution is found in nine iterations but its optimality verified in more than 25,000 iterations. Without the software and the special design of TORA, it would be impossible to demonstrate this situation in an effective manner. Another example is the unique design of the dynamic programming and the AHP spreadsheets, where the user interactive input is designed to enhance effective understanding of the details of these two topics. A third example deals with explaining the congruential method for generating 0-1 pseudo-random numbers. With the spreadsheet, one can instantly demonstrate the effect of selecting the seed (and the parameters) on the "quality" of the generator, particularly with regard to the cycle length of the random number sequence and, hence, warn the student about the danger of a "causal" implementation of the congruential method within a simulation model.
In addition to the software support in the book, all chapters have been streamlined (many rewritten) to present the material in a concise manner. New material includes a new introduction to operations research (Chapter 1); the generalized simplex method (Chapter 4); representation of all network models, including CPM, as linear programs (Chapter 6); PERT networks (Chapter 6); solution of the traveling sales Person problem (Chapter 9); and the golden section method (Chapter 21).
As in the sixth edition, the book is organized into three parts: deterministic models, probabilistic models, and nonlinear models. Appendices A through D include a review of matrix algebra, a TORA primer (though TORA's design makes a user's manual unnecessary), basic statistical tables, and partial answers to selected problems.