Theoretical and practical aspects of linear optimization

Linear Programming is developed more than fifty years ago and is since then an important tool for solving problems in a variety of fields. An excellent survey of the history of Linear Programming and its applications is given in G.B. Dantzig and M.N. Thapa[9]. In this thesis we will use the expression “Linear Optimization(LO)” instead of Linear Programming, since the meaning of the term is changed over the last fifty years; fifty years ago a program was a schedule or a plan, whereas nowadays a program is mostly associated with a list of instructions for a computer. Linear Optimization is concerned with the maximization or minimization of a linear objective function in a number of variables subject to equality and inequality constraints. In this definition the word inequality means ‘at most’ or ‘at least’, but not ‘not equal’