Customer Reviews

Model Building in Mathematical Programming, 4th Edition

5 star:		(5)
4 star:		(1)
3 star:		(0)
2 star:		(0)
1 star:		(0)

 

 

If there is anything that I would hold against my favorite Operations Research books - it would be the lack of emphasis on model and structure. Williams' book fills in that gap and is an essential companion to every Math Prog book. It is not a cookbook where one can look up a particular problem and the possible ways to model it. Instead, it takes a systematic and very sensible approach to modeling.
The three chapters on Integer Programming Models are amazingly easy to understand and were a real help during a graduate course in the subject. The huge number of practical examples in Parts 2, 3 and 4 of the book is the real value of the book. I would be hard-pressed for space to describe the range of problems that are modeled in Part 2... Part 3 covers a good deal of discussion on these formulations and Part 4 follows it up with solutions. Though solutions are not discussed in detail, they are a great help for someone who has worked hard through the problems and needs a verification of the solutions.
Another useful section in the book is a chapter on the interpretation of Linear Programming solutions. For a person without a Math Prog background (say, a manager), this kind of material is very useful. In fact, it once served as a good refresher for me in a hurry... and an excellent one at that.
The only sore point is a very limited discussion on nonlinear models.

Some books are good for mathematicians, some books are good for managers. This book is different. Williams did a good job to combine both mathematic and application perfective in a single book. Even you have only high school background, this book is readable. For senior researchers or grad students or strong math background person, this book is still enjoyable to recall your fundamental of math modeling. The references are not quite updated, however. Also, this book should added some current optimization tools. Even though the title is model building, not solving, it won't be harmful to have the metaheuristics (only introduction) or KKT.

This is one of the only books I have ever encountered that focuses on the practical aspects of model formulation. This is a frequently overlooked aspect of optimization, but models that are well formulated will often result in superior performance. It is particularly strong in the formulation of mixed-integer problems, with a variety of tips for linearizing variable products and for incorporation of logical constructs. It also shows how to model SOS1 and SOS2 variable types. One other area that I found to be particularly useful was a section covering convexity analysis. This was the only book that I've read that did a good job of explaining the concepts and ramifications of problem convexity. Finally, the examples in the book cover a wide range of practical problems. Most are fairly simple, but do a good job of illustrating important techniques.

I highly recommend this book for linear and mixed-integer modelers. However, if you don't use these types of solvers in your work, the book is less likely to be valuable.

That's it. It's the best book for learning modeling in a practical fashion. The learning from this book is practical and you'll learn to build practical and useful models.

This is an excellent book if you want to go deep understanding the true meaning of basic math programs.

The book is wonderful. If I have the money, I think I will buy it. Sigh!