A Model to Schedule Sales Optimally Blended from Scarce Resources

In early 1973, it became apparent to the management of the Swift Chemical Company that the overcapacity and consequent general recession in the fertilizer industry was rapidly coming to an end. This paper describes the design, implementation and impact of the model developed to help them both plan for and operate under the new market conditions.The model is a linear program of the Swift Chemical Company Phosphate Rock Mining and Sales Operation. The model starts with mining forecasts and optimally blends the rock to fill contracted sales in a multiple period environment. The results of a run include suggested scheduling of shipments by month for the current year, anticipated revenues intermediate inventory positions, and any outside purchase requirements.A full 12 month run contains approximately 1,400 rows and 4,000 columns. Mine plans and sales requirements are entered on forms familiar to the nontechnical personnel in charge of running the model. Separate FORTRAN programs convert the data to usable form, automatically generate the Linear Program Matrix, solve the problem (Using IBM's MPSX), analyze the solution, revise the matrix and resolve the problem since the objective function is nonlinear, and produce output reports which summarize all the information in a form that nontechnical people can readily understand.The model has been in operation about 15 months and has helped the management to plan both short range and long range sales strategies, along with the initial objective of optimizing on the mining and blending of rock. Validation runs indicate the model is increasing profits by several million dollars per year over a parallel manually prepared plan.