OR Practice—A Logistics Planning System at W. R. Grace

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 this modeling/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 Lagrangian procedures. 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.