Two Mathematical Programming Models of Cheese Manufacture

The standardization problem faced by cheese makers is formulated as a nonlinear programming problem using the assumptions of the Van Slyke cheese yield formula. The objective function of the model is to minimize the net cost of producing a given quantity of cheese subject to a set of production constraints. An approximation of the standardization problem formulated as a linear programming problem is also presented. Two different approaches to finding a solution are provided. The model is implemented in Microsoft Excel and solved with the standard add-in solver available in that program. An example is provided to contrast the difference between the nonlinear programming and its linear approximation, and a second example is used to illustrate the yield implications of ultrafiltered milk protein products in Cheddar cheese production. Additionally, a method for pricing inputs using the sensitivity analysis generated by the solver is demonstrated.