Model Formulation

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A linear programming model consists of certain common components and characteristics. The model components include decision variables, an objective function, and model constraints, which consist of decision variables and parameters. Decision variables are mathematical symbols that represent levels of activity by the firm. For example, an electrical manufacturing firm desires to produce x ₁ radios, x ₂ toasters, and x ₃ clocks, where x ₁ , x ₂ , and x ₃ are symbols representing unknown variable quantities of each item. The final values of x ₁ , x ₂ , and x ₃ , as determined by the firm, constitute a decision (e.g., the equation x ₁ = 100 radios is a decision by the firm to produce 100 radios).

Decision variables are mathematical symbols that represent levels of activity .

The objective function is a linear mathematical relationship that describes the objective of the firm in terms of the decision variables. The objective function always consists of either maximizing or minimizing some value (e.g., maximize the profit or minimize the cost of producing radios).

The objective function is a linear relationship that reflects the objective of an operation .

The model constraints are also linear relationships of the decision variables; they represent the restrictions placed on the firm by the operating environment. The restrictions can be in the form of limited resources or restrictive guidelines. For example, only 40 hours of labor may be available to produce radios during production. The actual numeric values in the objective function and the constraints, such as the 40 hours of available labor, are parameters .

A constraint is a linear relationship that represents a restriction on decision making .

Parameters are numerical values that are included in the objective functions and constraints .

The next section presents an example of how a linear programming model is formulated. Although this example is simplified, it is realistic and represents the type of problem to which linear programming can be applied. In the example, the model components are distinctly identified and described. By carefully studying this example, you can become familiar with the process of formulating linear programming models.