Use of nonlinear programming to optimize performance response to energy density in broiler feed formulation

Area of Science:

• Animal Science
• Agricultural Economics
• Operations Research

Background:

• Broiler feed formulation traditionally uses linear programming, which may not fully capture complex biological responses to nutrient variations.
• Optimizing feed costs while maximizing broiler performance is crucial for profitability in the poultry industry.

Purpose of the Study:

• To develop and present a nonlinear programming (NLP) optimization model for broiler feed formulation.
• To maximize margin over feed cost and identify the optimal feed mix.
• To compare the effectiveness of NLP with conventional linear programming (LP) in broiler feed optimization.

Main Methods:

• Developed an NLP model using Excel Solver to maximize profit margin over feed cost.
• Fitted broiler performance data (weight gain, feed consumption) to quadratic equations based on energy density.
• Transformed nutrient:energy ratio constraints into equivalent linear constraints for the NLP model.

Main Results:

• The NLP model successfully identified optimal feed mixes maximizing profit margin.
• Compared to LP, NLP demonstrated differences in energy density, margin, and diet cost when simulating price variations.
• The model showed that NLP is more adaptable as it does not require a predetermined energy level.

Conclusions:

• Nonlinear programming offers a more effective approach than linear programming for optimizing broiler feed formulation.
• The NLP model provides greater flexibility in optimizing performance response to energy density.
• This method allows for better adaptation to market price fluctuations and biological variability in broiler production.