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SYSTEM AT W. R. GRACE A LOGISTICSPLANNING
DARWIN KLINGMAN,JOHN MOTE and NANCY V.PHILLIPS
The University of Texas at Alustin,Austin, Texas (Received October 1986; revisions received May 1987, January 1988; accepted February 1988) This paper describes an optimization-based logistics planning system developed for W. R. Grace Company, one of the nation's largest suppliers of phosphate-based chemical products. The mathematical model underlying this system includes production,distribution, multiple time periods, and multiple commodities. W. R. Grace initially formulated the model as a linear programming problem with 3,696 constraints and 21,564 variables. We developed an innovative modeling/ solution approach to enhance top management's understanding of the model and to make the problem more tractable for the company's DEC 20/60 computer. The key features of thismodeling/solution approach are: decomposition of the problem into a generalized network component and a small linear nonnetwork component, transformation of the generalized network component into a pure network, incorporation of most of the nonnetwork component into the pure network via an innovative relaxation approach, and incorporation of the remainder into the objective function via Lagrangianprocedures. We solve the resulting model relaxation using highly efficient pure network solution techniques to obtain an advanced starting basis for a basis partitioning algorithm. This approach reduces solution time approximately 10-fold. In addition, W. R. Grace used insights gleaned from the solutions to make multimillion dollar decisions.
Jogistics planning continues to receive increased attentionin many companies today for several reasons. Foremost among these is the need to remain competitive. For economic survival, the companies must control production, distribution, and inventory costs. The important role of operations research in logistics planning has been recognized since its inception. Mathematical optimization has been instrumental in recent applications at numerous companiesincluding International Paper Company (Bender, Northrup and Shapiro 1981), Hunt Wesson Foods (Geoffrion and Graves 1974), Agrico Chemical Company (Glover et al. 1979), General Motors (Glover and Klingman 1977), Cahil May Roberts Pharmaceutical Company (Harrison 1979), Kelly-Springfield Tire Company (King and Love 1980), Citgo Petroleum Corporation (Klingman et al. 1986), and Shell Oil Company...