Linear Programming in the Allocation of Milk Resources for Cheese Making

Abstract To use linear programming, the cheese making process can be modeled as a resource conversion process. The relationship between input milk resources and output products can be analyzed using mass balance assumptions. The variables used in the linear programming model will represent the pounds of each milk resource chosen to formulate a vat of cheese milk. Additional variables will be used to represent the pounds of cream to be removed from a milk resource that has the potential to have cream removed. Three objectives that could be considered are 1) maximize net returns, 2) maximize cheese yield, or 3) minimize cost. A hypothetical example is used to illustrate how the cheese making process can be modeled. This linear programming model depends on formulas that relate ratio of casein to fat of milk to the fat on the dry basis of the cheese. Sensitivity analysis is performed to determine at what cost a milk resource not in the optimal formulation will replace a milk resource currently in the optimal formulation. The linear programming model can be an effective management tool in the allocation of milk resources for cheese making.