Chemical Company makes hundreds of chemical products. One of them, anhydride, is used in many products, ranging from boat hulls to agricultural chemicals. Annual anhydride production capacity represents annual capacity of amount 359 million pounds. A savings of a fraction of a cent per pound in producing anhydride translates into large annual savings.

Anhydride is produced in two plants. The newer and larger plant is located in Pensacola, the other plant is located in St. Louis. Anhydride is produced by catalytic oxidation of butane or benzene in a reactor. Both the Pensacola plant and the St. Louis plant have many reactors. Before the construction of the Pensacola plant, the Company could sell all of the malefic anhydride it produced. After the construction of the Pensacola plant, it had extra anhydride capacity.

The Company recognized that the trade-off between the production and yield of anhydride provided an opportunity for substantial cost savings. Yield is the pounds of anhydride per pound of raw material. Both the production rate and the yield are functions of reactor velocity, raw material feed rate, and reactor pressure. Maximizing production decreases the yield. Maximizing the yield decreases the production rate. Because of the Company's extra anhydride capacity, a Management Science study was conducted to assign production to each plant and to adjust reactor operating conditions to minimize cost for the target quantities.

Three models were developed. A global model considered both of the plants and all of the reactors. The global model assigned production to the two plants to meet an overall production goal at minimum costs. A separate model for each plant enabled plant management to make adjustments based on minor production disruptions, such as an unexpected reactor shutdown. For major problems, the global model was used to adjust the plant plans.

The relationship of yield to raw material feed rate, reactor velocity, and reactor pressure is not linear. An integer linear programming model was used to approximate the yield of each reactor under different operating conditions. A binary variable was introduced for several sets of operating conditions for each reactor. An overall constraint ensured that the desired amount was produced at each plant.

The older plant has several methods of providing the oxygen required for the manufacturing process. A separate optimization model determines the most economical method of providing the oxygen needed by the St. Louis plant.

The Company developed a computer system that processes the output from the optimization models and creates reports in a form that is meaningful to its users. Production engineers use the separate plant models to finetune the manufacturing process. Because of the interactive computer system, the models can be run several times in a half-hour period.

The system generates direct cost savings estimated at $1-3 million per year. The system is also used to evaluate changes in the configuration of facilities at the plants. Indirect benefits of the Management Science study included a greater understanding of the cost and operation of compressors used in the manufacturing process. Consequently, the operating efficiency of some of this equipment was improved by adjustments.

Adapted from: R. F. Boykin, "Optimizing Chemical Production at Monsanto," Interfaces 15, no. 1 (January-February 1985), pp. 88-95.