This paper is the result of a survey made during the summer of 1956. It is a progress report on applications of linear programming by a number of oil companies. Examples are presented of applications to a variety of problems arising in the areas of Drilling and Production, Manufacturing, and...

The well known chemical equilibrium problem is expressed in the form of minimizing the free energy of a mixture in order to compute the chemical composition at equilibrium. By piece-wise linear approximations to the free energy function, the problem becomes a linear program which can be solved...

From the Preface. The preparation of this book started in 2004, when George B. Dantzig and I, following a long-standing invitation by Fred Hillier to contribute a volume to his International Series in Operations Research and Management Science, decided finally to go ahead with editing a volume...

The Linear Programming Problem -- Solving Simple Linear Programs -- The Simplex Method -- Interior-Point Methods -- Duality -- Equivalent Formulations -- Price Mechanism and Sensitivity Analysis -- Transportation and Assignment Problem -- Network Flow Theory.