Production and Sales Planning with Limited Shared Tooling at the Key Operation

The focus of this paper is multiperiod production and sales planning when there is a single dominant production operation for which tooling (dies, molds, etc.) can be shared among parts and is limited in availability. Our interest in such problems grew out of management issues confronting an injection molding manufacturer of plastic pipes and fittings for the building and chemical industries, but similar problems abound in the manufacture of many other cast, extruded, molded, pressed, or stamped products. We describe the development and successful application of a planning model and an associated computational approach for this class of problems. The problem is modeled as a mixed integer linear program. Lagrangean relaxation is applied so as to exploit the availability of highly efficient techniques for minimum cost network flow problems and for single-item dynamic lot-sizing type problems. For the practical application at hand, provably good solutions are routinely being obtained in modest computing time to problems far beyond the capabilities of available mathematical programming systems.