Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem

Later in 1957, as the end of my three-year tour of duty in the Navy was approaching, Princeton invited me to return as Higgins Lecturer in Mathematics. I had been a Williams undergraduate and a then a graduate student at Cambridge and Princeton while getting my Ph.D. I had published 4 papers in non-linear differential equations, a subject to which I had been introduced by two wonderful people whose support and encouragement made an unforgettable and wonderful difference in my life: Professor Donald Richmond of Williams College and Professor Solomon Lefschetz of Princeton. Because of my interest in applied work I had planned to look for an industrial position rather than an academic one on leaving the Navy, but I decided instead to accept this attractive offer and spend a year or two at Princeton before going on. When I returned to Princeton late in the fall of 1957, I got to know Professor A. W. Tucker, then the department head, who was the organizer and prime mover of a group interested in game theory and related topics. This group included Harold Kuhn and Martin (E. M. L.) Beale. As the Navy had kept me on as a consultant I continued to work on Navy problems through monthly trips to Washington. On one of these trips a group presented a linear programming model of a Navy Task Force. One of the presenters remarked that it would be nice to have whole number answers as 1.3 aircraft carriers, for example, was not directly usable. I thought about his remark and determined to try inventing a method that would produce integer results. I saw the problem as clearly important, indivisibilities are everywhere, but I also thought it should be possible. My view of linear programming was that it was the study of systems of linear inequalities and that it was closely anal-