Linear Programming Books

The other classics besides Winston are Hillier and Lieberman's Introduction to Operations Research and Chvátal's Linear Programmming. I learned linear programming out of Bob Vanderbei's Linear Programming: Foundations and Extensions, which is also a fine book. The last time I taught linear programming I used Dave Rader's new book, Deterministic Operations Research, and was happy with it.

As for a comparison, Winston focuses on how the different methods work and gives lots of examples but doesn't spend much time on theory. Hillier and Lieberman is at a slightly higher level than Winston, with a more leisurely pace and a little more theory but with fewer examples. Chvátal and Vanderbei have a more noticeable focus on the theory. Rader takes a different approach in that the simplex method does not appear until about halfway through the book. Instead, he spends a lot of time early on algorithm design and on what an algorithm for solving linear programs might look like so that when you finally do see the simplex method the reaction is closer to "Of course" than to "Where in the world did that come from?" He doesn't do the tableau form of the simplex method, which, while a plus in my opinion, may make it hard to understand his version of the simplex method if you're used to the tableau.

Many LP books spend little time on how to construct linear programming models (i.e, how to come up with variables, an objective function, and constraints that describe the problem you're trying to solve). Of these five, Winston and Rader discuss construction of LP models the most.

I recommend Introduction to Linear Optimization by Dimitris Bertsimas and John N. Tsitsiklis. The authors are professors at MIT.

I feel like I have to mention Schrijver's "Theory of Linear and Integer Programming" as it is a classic, but I don't feel like it is the best text for an introduction or for application.

There are many books. A cheap one that is also very good is Combinatorial Optimization: Algorithms and Complexity by Papadimitriou and Steiglitz.