Allocation of Milk Resources in Cheese Making

In a step in the manufacture of cheddar cheese, a variety of milk resources are blended in a cheese vat with other ingredients (5). Making the blend is called standardizing, and the resulting blend is called cheese milk. The blend is allowed to coagulate before other processing steps are taken. The milk resources used are valuable; the cheese-maker pays to acquire them. Furthermore, the cheese yield and cheese quality are affected by which combination and proportions of resources are used in the blend. In the United States, the composition of the resulting product (which is determined by the composition of the cheese milk) is also constrained by government regulations and definitions. A recurring decision that the cheesemaker faces is determining the constituent amounts for each of the inputs to the cheese milk. The decision is constrained in many ways, but it is made regularly with the ordinary business objective of making a profit.

Technological investigation has determined a cheese yield formula (6) that allows the cheesemaker to predict the cheese yield if enough detail is known about the casein, fat, salt retention, and water retention of this step in the process. This technological model requires that the casein-to-fat ratio of the cheese milk be restricted to a small range. If this is done, the formula can be used to predict pounds of output for a given set of inputs. The potential inputs to the cheese milk include milk, condensed skim milk, nonfat dry milk, whey protein concentrate, cream, frozen cream, water, and other ingredients. Almost all the inputs affect the casein-to-fat ratio and the cheese yield. Because each of these resources will have different prices at different times, the cheesemaker can optimize the cheese milk by making the optimal choice of resources for the current set of price and availability circumstances.

This optimization opportunity may be modeled as a linear program (7). The variables are the inputs to the cheese milk; the constraints may be constructed out of these variables to restrict the casein-to-fat ratio and to reflect government regulations, company policies, resource availability, and other restrictions on the cheese product. An objective measure may be constructed from the variables and corresponding costs coupled with the sales value of the resulting product. The advantage of casting this as a linear program is that the resulting model cam then be solved by computer to quickly determine the optimal constituents of the cheese milk. The result will simultaneously reflect the technological, legal, and economic realities facing the cheesemaker. Solutions generated this way have been shown to have a profound impact on the profitability of the cheesemaker. Without such a model and the computer support, cheesemakers can make good guesses, but they cannot be assured of regularly choosing optimal inputs to the cheese vat.

In this example we have a high-volume product (the vats may hold 20,000 lb of cheese milk) and variable inputs (the fat and solids content of incoming milk varies from farm to farm and animal to animal) and the recurring decision of how to standardize the cheese milk to achieve uniform outputs. Because of its recurring nature, this decision has important economic consequences for the cheesemaker. Investigation of cheese technology provided the model (the cheese yield formula) that enables the application of optimization methods to assist with the decision of how to standardize the cheese milk.

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