Introduction to Linear Programming
The goal of this chapter is to introduce those optimization problems which, just after World War II, G. B. Dantzig named “linear programs.” The great success of linear programming (i.e., the study of linear programs) led authors who became interested in various optimization problems to link the term “programming” with that of a more or less fitted adjective, thus calling these problems convex programming, dynamic programming, integer programming, and so on. The result is that in operations research the term “program” has acquired the very precise meaning “optimization problem.” It is not possible, however, to use the word “programming” for the study of general problems of optimization (hence, we say “mathematical programming”), because more or less simultaneously the term “program” was taking on another meaning-much more in harmony with the original one - that of a sequence of instructions in the context of computer science. This nice example of the development of scientific language does not make things clear for the beginner. To avoid confusion in this book we therefore use the term “program” as equivalent to an optimization problem and “code” or “computer code” for what is called a program in computer science.
KeywordsTransportation Problem Parametric Linear Programming Special Linear Program
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