A Linear–Programming Method for the Combinatorial Grouping of an Incomplete Power Set

Abstract The Combinatorial Grouping Problem is defined as the general problem of computing a set of boolean bounds (GLB, LUB) for an incomplete power set P(U)so that a system of lattice-theoretic filter-ideal intersections (GLB, LUB) results which optimizes a cost function defined on the parent set U. The problem arises as a mathematical formulation of the Group-Technology Problem of Industry. A system of independent Production Cells is required which provides the manufacturing capacity for the commercial life of an industrial product. A group of components is matched with a group of facilities so that there is a maximal degree of scheduling flexibility and a minimal cost of manufacture. A Set-Partitioning Algorithm has been developed which may be adapted to solve a wide class of related combinatorial problems.