Research Progress Report 93
February, 1964
Interpreting Least-Cost Feed Formula Data
Joseph H. Stafford, Economic Research Service, U.S. Department of Agriculture, and James C. Snyder, Department of Agricultural Economics
Linear programming is becoming a widely used mathematical technique in the feed manufacturing industry. The technique is used to find the feed formula which is least-cost for a given set of formula quality specifications and ingredient prices.
This report avoids duplication of the large quantity of literature on how to set up a least-cost formulation problem. The objective is to outline procedures for making full use of the information generated by the linear programming procedure. Particular attention is given to information other than the formula itself. The article focuses on:
1.	The sensitivity of least-cost formulas to ingredient price changes.
2.	The cost of individual quality specifications in feed formulation.
3.	The sensitivity of formula cost to quality specification changes.
4.	Computer report generation of least-cost information.
In all cases, emphasis is on routine commercial use of linear programming by firms purchasing their raw materials in dynamic feed ingredient markets.
Current Industry Applications
Current industry application of LP has brought impressive ingredient cost reductions without sacrifice of product quality. A recent case study of a major Indiana feed manufacturer illustrates this point. In general, the case study firm is representative of the level of management and technology of production found in most of the medium to large feed manufacturing firms. Least-cost formulas for prices prevailing in each of 20 consecutive weeks were linear programmed for three of the firms' high volume protein supplement feeds. Over the 20 weeks the per ton ingredient costs for the linear programmed formulas averaged $2.31, $2.77, and $0.73 less than the ingredient cost for the formulas derived by conventional methods. Assuming an average weekly production of only 150 tons per week for each feed, the potential gross return to the linear programming technique is $871 per week. Similar savings have been experienced by other feed manufacturers.
Improved Analysis Needed
Despite the widespread adoption of the technique, use of the full potential of LP is much more limited. All too frequently, management is content to compute only the basic least-cost formula. Additional LP
PURDUE UNIVERSITY • Agricultural Experiment Station • Lafayette, Indiana