Gelöste und ungelöste Probleme der Unternehmensforschung / Produktionsplanung auf der Grundlage technischer Verbrauchsfunktionen

First an idea is given of the basic ideas underlying the new branch of science, Operations Research, and of the causes underlying its recent very rapid development. Then the main problems involved are introduced and classified according to the method of solution, and not, as would also be possible, according to the field of application. The most important of the methods is that of programming, by which one understands in this connection the maximization (or minimization) of a preference function of usually numerous variables, under usually numerous restraints, mostly in the form of inequalities. If the preference function and restraints are linear, then one speaks of linear programming, for which there exists a convenient solution process, G. B. Dantzig's Simplex Method. Should the preference function be quadratic and convex, while the restraints remain linear, then the solution process becomes more complicated. Recently, however, numerous methods have also been worked out for these conditions (Barankin and Dorfman, Wolfe, Frank and Wolfe, Beale, Hildreth, Rosen, Frisch and others). As yet unsolved remains the problem of non-linear restraints and non-convex preference functions. Inspite of considerable achievements (in particular those of Bellman), dynamic programming is still in a primary stage of development. Dynamic programming is concerned with problems in which the decision in one period alters the basis of the problem in the next period. Similarly in parametric programming the dependence of the solution on a parameter of the problem is examined.