Pricing Feed Ingredients on the Basis of Market Values of Nutrients

In many instances, nutritionists, feed
manufacturers, dairy producers, and their advisors
need an estimate of what a feed is worth on a
nutritional basis to facilitate the formulation of
balanced diets and the purchase of appropriate and
price competitive feedstuffs. Up until now, all
methods used shared common flaws. We derived a
maximum likelihood method that uses composition
and prices of all feedstuffs traded in a given market
to estimate unit costs of nutrients and break-even
prices of feedstuffs. The method was programmed as
a WindowsÒ application named SESAME. The
software can be used (1) to rapidly and accurately
identify commodity purchasing opportunities, and (2)
to benchmark feed costs from nutrient requirements
and nutrient unit prices.

Introduction
A variety of methods have been proposed to
estimate unit costs of nutrients and, implicitly, the
break-even price of feedstuffs. All methods fall into
one of two general categories: equation-based (EBM)
and inequation-based methods (IBM). For EBM, a
set of equations developed from the nutritional
composition of referee feeds is solved using their
market prices. The best-known method among this
group is the Petersen Method (PM), in which the
energy and protein compositions of corn grain and
soybean meal are equated to their respective prices,
setting a set of two equations with two unknowns.
The method dates back to 1932 (Petersen, 1932) and
is presented and discussed at length by Morrison
(1956). Although widely used, the method is
fundamentally flawed in that it assumes perfect
markets in corn and soybean trading and implies
economically incoherent behavioral patterns by
buyers and sellers of commodities.
The second series of methods, IBM, are basically
constrained optimization models solved using
mathematical programming techniques (Beneke and
Winterboer, 1973; St-Pierre and Glamocic, 2000).
Linear programming (LP) is the best-known member
of this group and became widely used in animal
nutrition with the discovery of an efficient algorithm
(Dantzig, 1960) and the advent of high-speed
computers. Within an LP model, a cost function is
minimized subject to a series of inequations forcing
the solution to meet the nutritional requirements of
the animal for which the diet is being optimized.
Many have assumed that linear (and nonlinear)
optimization models yield accurate and precise
estimates of break-even prices of feedstuffs. This
thinking is erroneous. Optimization programs suffer
from being very case specific, and they deliver little
information on the unit costs of nutrients. They
assume perfect knowledge of unit prices of
feedstuffs, nutrient requirements, and nutrient
composition of feedstuffs. In practice, none of these
assumptions are met and complex stochastic
optimization models must be used to solve correctly
in the presence of uncertainty in nutrient composition
(St-Pierre and Harvey, 1986). Even when the
solution is deemed optimal, nutrients with nonbinding
constraints have an implicit unit cost of zero.
Shadow costs of binding nutrients provide
information on unit costs that can only be valid at the
margin. Additionally, the information delivered has a
very narrow inference range because it provides
estimates that are applicable only to one group of
animals in a given herd. Consequently, IBM is
limited in providing estimates of aggregate unit costs
of nutrients within a given market. To circumvent
these problems, we developed a new procedure that
provides estimates of aggregate unit costs of nutrients
and break-even prices of feedstuffs based on the
trading of all feed commodities in a given market (St-
Pierre and Glamocic, 2000).

The method is based on maximum likelihood
estimation of nutrient costs. The objective of this
paper is to describe briefly the method that we
developed, the computer software that we wrote to
make our procedure available to the industry, and to
show examples of how this information can be used
by professional nutritionists and dairy producers to
identify buying opportunities and to benchmark total
feed (nutrient) costs.