It is important to consider model formulation before launching into the details of goal programming solutions.
Model formulation is the process of transforming a real word decision problem into an operations research model. A key to successful application of goal programming is the ability to recognize when a problem can be solved by goal programming and to formulate the corresponding model.
"Great ability develops and reveals itself increasingly with every new assignment." -Baltasar Gracian
The approach to formulate the goal programming model is similar to that of linear programming model. The mathematical model is given as follows:
Minimize wi (di− + di+)
aijxj + di− - di+ = bi; i = 1, 2, ....., m
and xj, di−, di+ ≥ 0 for all i, j
The objective function contains primarily the deviational variables (di− & di+) that represent each goal or subgoal.
The deviational variables are represented as both positive and negative deviations from each goal or subgoal. Thus, the objective function becomes the minimization of these deviations based on the relative importance or priority assigned to them.
The steps in model formulation can be summarized as follows:
"The reason why most major goals are not achieved is that we spend a lot of time doing second things first." -Vinay Chhabra & Manish Dewan