Generally , it is not feasible to attempt to "see" the whole formulation of the constraints and objective function at once, following the definition of the decision variables . A more prudent approach is to construct the objective function first (without direct concern for the constraints) and then to direct attention to each problem restriction and its corresponding model constraint. This is a systematic approach to model formulation, in which steps are taken one at a time. In other words, it is important not to attempt to swallow the whole problem during the first reading.
A systematic approach to model formulation is first to define decision variables, construct the objective function, and finally develop each constraint separately; don't try to "see" it all at once .
Formulating a linear programming model from a written problem statement is often difficult, but formulating a model of a "real" problem that has no written statement is even more difficult. The steps for model formulation described in this section are generally followed; however, the problem must first be defined (i.e., a problem statement or some similar descriptive apparatus must be developed). Developing such a statement can be a formidable task, requiring the assistance of many individuals and units within an organization.
Developing the parameter values that are presented as givens in the written problem statements of this chapter frequently requires extensive data collection efforts. The objective function and model constraints can be very complex, requiring much time and effort to develop. Simply making sure that all the model constraints have been identified and no important problem restrictions have been omitted is difficult. Finally, the problems that one confronts in actual practice are typically much larger than those presented in this chapter. It is not uncommon for linear programming models of real problems to encompass hundreds of functional relationships and decision variables. Unfortunately, it is not possible in a textbook to re-create a realistic problem environment with no written problem statement and a model of large dimensions. What is possible is to provide the fundamentals of linear programming model formulation and solutionprerequisite to solving linear programming problems in actual practice.