**Purpose***The following article is a primer on least-cost formulation. While explaining the fundamentals of least-cost formulation, the author also goes over more advanced features such as shadow prices, price maps and nutrient factoring. This is a must-read for those who want a concise introduction to least-cost formulation. *

In the not so distant past, feed manufacturers used to balance their feeds using hand calculations and often relied on tedious trial and error methods. The availability of commercial computers by the end of the 1960s meant that complex mathematical models could be solved much more easily and within a short duration of time. Twenty years later, the arrival of the personal computer provided affordable feed formulation solutions to the feed industry. Advancements in computer technology, mathematical modeling and animal nutrition have resulted in vast improvements in the last 20-25 years in the way feeds are formulated.

Least-cost feed formulation is combining many feed ingredients in a certain proportion to provide the target animal with a balanced nutritional feed at the least possible cost. Though least-cost formulation is a mathematical solution based on linear programming, it requires the professional knowledge of animal nutritionists who take into consideration the nutrient requirements of the target animal and its capability to digest and assimilate nutrients from various available ingredients. Feed formulators also need to be aware of the variations of nutritional requirements for different species at various stages of their lifespan. The linear programming performs what is designed to do and it is based on the information put in by the formulator. So, in essence, the formulation program is only as good as the nutrient and ingredient parameters entered into it.

There is a broad choice of feed formulation software packages in the market. The software range from simple, spreadsheet-based solutions to sophisticated and complex packages designed for large feed manufacturers that require multi-site, multi-server, and multi-blending capabilities. New and innovative add-on applications are being developed and introduced into the market every year. The software packages may also provide modules for inventory control, production, and interfaces to accounting systems among other features. Some feed formulation software is specifically designed for a certain species and they may provide tables of nutrient requirements or models of growth for those specific animals. Further, improvements in the look and feel of the software and seamless integration with other functionalities related to formulation also occur routinely. These applications and improvements enable feed formulators to perform their jobs much more efficiently.

For least-cost feed formulation software to be effective it should offer the following basic features that are applicable to all species. At this point it is important to keep in mind that feed formulation runs on data that have been entered into it by the user. The final feed formula will only be as accurate as the initial information that was input by the user.

All feed formulation software provides a way of entering and managing the ingredients which are available for inclusion in the formulas. Available feed ingredients are listed along with their unit price. Depending on the software being used, optional ingredient properties such as the ingredient types, alternate code names, and applicable species may also be entered.

Each feed ingredient available for inclusion in the formulas should have corresponding nutrient composition data. The nutrient values are preferably derived from chemical analysis of representative samples of the ingredient. When the nutrient composition is not available, tables of feed composition using average or typical values are used.

Specifications are set for each formula to be solved by the least-cost formulation software. Formula specifications generally define the nutrient levels desired in the formula and the ingredient inclusion levels. Either a lower limit and/or an upper limit for each nutrient and ingredient are set.

Once all the above necessary information is provided, the feed formulation software will produce formulas that meet the desired specifications at the lowest possible cost. A requirement for proper formulation, however, is that the formula result must be feasible both from a mathematical and a nutritional standpoint. If infeasible results are obtained the ingredient and nutritional composition should be carefully scrutinized to make sure the solution is nutritionally acceptable for the target species.

One of the most important uses of least-cost feed formulation is in choosing among the available ingredients to be used, based on their nutritional composition and cost. Many times one ingredient can be substituted by another with similar nutritional value. The software helps the user to achieve the highest profit margin when market conditions favor the use of one ingredient over the other. A number of tools are useful in the analysis of formulation results.

For those ingredients that were not included in the formula solution, the least-cost formulation software indicates how much the cost of these ingredients will have to fall before they can be included in the formula. This cost change is called the marginal price change of the ingredient.

Shadow price of an ingredient is calculated by subtracting the marginal cost change from the current ingredient cost. This amount represents the cost of the ingredient at which the ingredient can be included in the formula. Ingredients that are included in the formula results have a shadow price of zero.

Similarly, the change in formula cost with a change in a nutrient constraint is called the shadow price of the nutrient. The shadow price of a nutrient is zero if the level of nutrient use is not equal to the constraint level.

An important analytical use of least-cost feed formulation software is to observe the impact of changing ingredient prices in the formula solution. This allows the user to determine how much of an ingredient would be used if the ingredient were available at a different price. To accomplish this analysis, the user can change the ingredient price and re-solve as many times as necessary. Some feed formulation software allows the generation of summary graphs called price maps, which are the result of plotting the formula costs at different ingredient prices.

The ability to specify that several nutrients must exist in the resulting formula in relation to one another is called Nutrient Factoring. Advanced least-cost feed formulation software solutions provide this capability which allows setting a ratio between two nutrients, for example calcium and phosphorus. The ability to specify nutrients in proportion to one another is another application of this function. For example, the user can specify that amino acids be proportional to the total amount of protein in the formula.

This is a function of least-cost feed formulation that attempts to formulate with specific proportions among nutrients by relaxing the weight constraint of the formula, based on the theory that animals will consume feed to maintain a constant energy intake regardless of the energy level of the feed.

Sometimes feed formulators are faced with the problem of having limited amounts of some ingredients. An advanced feature of some least-cost feed formulation packages is multi-blending, which allows more than one formula to be solved at once, taking into consideration the ingredients that are available in limited qualities. The software then optimizes the allocation of the scarce ingredients to different formulas in order to achieve total least-cost solution.

Mr. Richard Rossi is President and founder of Feedsoft Corporation, a Dallas based company dedicated to providing affordable, powerful, and easy to use feed formulation software, services, and support to its clients world wide. Feedsoft® is a cost saving tool that enables animal practitioners to design feeds that maximize nutritional content while keeping costs down in order to increase profits.