## Background

The concepts and general techniques used in developing mathematical models of production systems are not new. Rather, they stem from systems analysis approaches applied to military and industrial problems almost a half century ago.[1] Forrester[2] is a classic treatise on the principles of systems analysis that remains relevant today and Spedding[3] provides an entry point to the use of systems analysis in addressing agricultural problems. Optimization and simulation are two fundamental approaches that have been applied in modeling livestock production systems. Linear programming has been a widely used optimization technique in addressing problems from ration formulation to enterprise analysis. The fundamental concept of optimization is to derive a maximum (or minimum) yield from a production system subject to existing constraints on the system. From a managerial perspective, optimization approaches may be philosophically consistent with maximizing profit or minimizing cost. However, optimization approaches have been largely superceded by simulation to describe the essential elements of a system and their relationships to each other without respect to a specific outcome. In developing and using simulation models, the concern is that each of several variables characterizing the state of the system has values within a tolerable degree of error relative to those observed in nature. Once a model has been built, it is analogous to a scientific hypothesis of the way in which the system works. The truth of this hypothesis is tested by: 1) verifying the model's ability to reproduce the data used in its construction and 2) demonstrating its ability to predict outcomes of independent trials.

Models may be organized on any of several levels depending upon their intended use.[4] Ordinarily, models of production systems are formulated at the level of process within individual animals (e.g., digestion and tissue deposition) or with a greater degree of aggregation (e.g., whole animals, herds, or flocks). The level of organization is most often related to the intended scope of the inferences to be made from the model. For instance, models to be used in planning livestock production systems as components of national economies are generally more highly aggregated than models for evaluating responses of individual animals to varying levels of ingested energy. Depending on whether or not the simulation reflects random fluctuations in component processes, models may be either stochastic or deterministic, respectively.