R70-4 Analysis of Algorithms for the Zero–One Programming Problem

By "zero–one programming" the authors mean linear mathematical programming with variables that can take on only the values 0 or 1. Such problems are of great practical importance—arising, for example, when optimality is sought in such contexts as airline crew scheduling, capital budgeting, disk balancing, menu planning, plant location, political apportionment, and project selection. A great deal of effort has been expended in recent years in quest of efficient algorithms, as is evident from the size of the literature that has grown up. The authors give a rather superficial review of the "implicit enumeration" portion of this literature. An attempt is made to indicate the nature of the algorithms proposed by the following authors and, in most cases, to show how their proposals relate to the framework for implicit enumeration exposited by the reviewer.1 These authors are Glass, Balas, Glover, Lawler and Bell, Geoffrion, Lemke and Spielberg, Balintfy, and Healy. A brief discussion of comparative computational experience is given, and the tentative conclusion offered that the reviewer\´s algorithm2 "seems to be the most promising of existing converging algorithms."