An Adjustable Nutrient Margin of Safety Comparison Using Linear and Stochastic Programming in an Excel Spreadsheet

Abstract

A stochastic-linear program Excel workbook was developed that consisted of 2 worksheets illustrating linear and stochastic program approaches. Both approaches used the Excel Solver add-in. A published linear program problem served as an example for the ingredients, nutrients, and costs and as a benchmark in the development of the linear and stochastic programs. Standard deviations for ME and nutrients were taken or calculated from CV, and from a commercial publication of sources for amino acids. The Excel spreadsheet was set up so that the calculated margin of safety (MOS) value, according to the requested probability, was the same for both the linear and stochastic programs. As an example, the probability for meeting the nutrient value for protein was compared at 50% (MOS = 0) and 69% (MOS = 0.5) by using both linear and stochastic programming. Spreadsheet results illustrated the flexibility, accuracy, and precision of the stochastic program over the linear program in meeting the requested nutrient probability.