Characteristics of Linear Programming Problems
Characteristics of Linear Programming ProblemsNow that we have had the opportunity to construct several linear programming models, let's review the characteristics that identify a linear programming problem.
The
A linear programming problem requires a choice between alternative courses of action (i.e., a decision). The decision is represented in the model by decision variables. A typical choice task for a business firm is deciding how much of several different products to produce, as in the Beaver Creek Pottery Company example presented earlier in this chapter. Identifying the choice task and defining the decision variables is usually the first step in the formulation process because it is quite difficult to construct the objective function and constraints without first identifying the decision variables.
The problem encompasses an objective that the decision maker wants to achieve. The two most frequently
A third characteristic of a linear programming problem is that restrictions exist, making unlimited achievement of the objective function
Properties of Linear Programming Models
In addition to encompassing only linear relationships, a linear programming model also has several other implicit properties, which have been exhibited consistently throughout the examples in this chapter. The
Proportionality means the slope of a constraint or objective function line is constant. Linear programming also requires that the objective function terms and the constraint terms be additive. For example, in the Beaver Creek Pottery Company model, the total profit ( Z ) must equal the sum of profits earned from making bowls ($40 x _{ 1 } ) and mugs ($50 x _{ 2 } ). Also, the total resources used must equal the sum of the resources used for each activity in a constraint (e.g., labor).
The terms in the objective function or constraints are additive .
Another property of linear programming models is that the solution values (of the decision variables) cannot be restricted to integer values; the decision variables can take on any
The values of decision variables are continuous or divisible .
The final property of linear programming models is that the values of all the model parameters are assumed to be constant and known with
All model parameters are assumed to be known with certainty .
To summarize, a linear programming model has the following general properties:
