A Computer Code for Integer Solutions to Linear Programs

Abstract

This paper reports on a new computer code (called “LIP1”) for solving integer programming problems, which will be distributed for general use through SHARE. LIP1 was written as an experimental program for the purpose of reexamining and further testing the efficiency of Gomory's original cutting-plane technique. Many trial problems have now been solved with this code. Of particular interest, however, are 25 test problems that have been solved with other integer programming codes (all these other codes incorporate the method of Gomory's more recent all-integer algorithm). The basis for comparing the performance of the various codes is the number of iterations required to solve each problem. For these 25 test problems LIP1 appears generally as efficient as the other codes tested. Moreover, on the more difficult problems LIP1 generally performed better than the other codes. We conclude that Gomory's original cutting-plane method merits further investigation and development as an efficient computational technique.