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Related Experiment Videos

Two mathematical programming models of cheese manufacture.

J A Burke1

  • 1Department of Agricultural and Applied Economics, University of Wisconsin, Madison 53706, USA. josephburke@wisc.edu

Journal of Dairy Science
|January 24, 2006
PubMed
Summary

This study presents a nonlinear programming model to optimize cheese production costs and yield, offering a linear approximation for practical application. The findings aid in efficient cheese standardization and input pricing.

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Area of Science:

  • Dairy Science
  • Operations Research
  • Food Engineering

Background:

  • Cheese production involves complex standardization challenges impacting cost and yield.
  • Existing methods may not fully optimize resource allocation and cost-effectiveness.
  • The Van Slyke cheese yield formula provides a basis for modeling.

Purpose of the Study:

  • To formulate the cheese standardization problem as a nonlinear programming model.
  • To develop a linear programming approximation for practical implementation.
  • To demonstrate the application of these models in Cheddar cheese production, including the use of ultrafiltered milk protein products.

Main Methods:

  • Formulation of a nonlinear programming model to minimize net production cost.
  • Development of a linear programming approximation of the standardization problem.

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  • Implementation and solution using Microsoft Excel's solver add-in.
  • Sensitivity analysis for input pricing.

    • Main Results:

    • The nonlinear model minimizes net cost for a target cheese quantity under production constraints.
    • A linear approximation provides a practical alternative for solving the standardization problem.
    • Examples illustrate the differences between nonlinear and linear approaches and the impact of ultrafiltered milk protein products on yield.
    • Sensitivity analysis demonstrates a method for pricing production inputs.

    Conclusions:

    • Nonlinear and linear programming models offer effective frameworks for cheese standardization.
    • These models can optimize production costs and provide insights into yield implications of new ingredients.
    • Sensitivity analysis is a valuable tool for determining optimal input pricing in dairy manufacturing.