Linear and mixed integer programming

Abstract

Linear Programming (LP) is one of the most famous optimization techniques introduced independently by Kantarowitsch in 1939 and by Dantzig in 1949 (Krekó 1973). LP is applicable in decision situations where quantities (variables) can take any real values only restricted by linear (in-) equalities, e. g. for representing capacity constraints. Still, LP has turned out to be very useful for many companies so far. LP is used in APS e. g. in Master Planning as well as in Distribution and Transport Planning. Very powerful solution algorithms have been developed (named solvers), solving LP models with thousands of variables and constraints within a few minutes on a personal computer. © 2008 Springer-Verlag Berlin Heidelberg.