Blending Aviation Gasolines–A Study in Programming Interdependent Activities in an Integrated Oil Company - Charnes, A.; Cooper, W. W.; Mellon, B. (Econometrica, 1952)
SUMMARY THE TECHNIQUES of linear programming are here explained in a commercial application-blending aviation gasolines. Blending is critically important to almost all other areas of programming in an integrated oil company. Intelligent programming of production, transportation, manufacturing, or marketing generally requires solution of blending problems as an initial or integral part of the whole process for it is in blending that the final outputs are determined. In the first part of the paper, questions of optimum programming in a given technological and institutional structure are explored. Computations are executed primarily by means of the simplex technique of Dantzig [4]. Because of the presence of multiple degeneracy and the absence of a general method (at the time these computations were made)2 of handling such problems, it was not possible to rest securely on the simplex method. Alternative methods of computation were, therefore, explored and bounding techniques were employed to discover possible divergences from optimality. Finally, to test the validity of the results, calculations undertaken by a company programming official were obtained for purposes of check and comparison. A relatively simple program is first calculated and more than one optimal program obtained. These results are then extended to more complex problems. Finally, the sensitivity of the matrix to possible changes in the coefficients is studied. The problem of linear programming may be sta-ted as follows: A