goal programming

In classical LP model, the objective was represented in the objective function that was to be either maximised or minimised. For example objective function was maximise profit. Sometimes, the model can be used to explore secondary objectives. The secondary objective is providing better service.

One approach to multiple objectives is to include some objectives as model constraints.

Other way is to reformulate the model as a Goal Programming model:

  1.  Define new variables for the amount that the actual exposures exceed or fall short of the goals – deviation variables.
  2. Construct new objective function that includes only deviation variable. The goal is always minimisation of the total deviation from the goals.
  3. Assign weights to unsatisfied exposures (to deviation variables in goal function)
Now the goal-programming model becomes linear programming model. The goal programming assigned weights to the amounts that goal were unsatisfied, a common approach to multiple objective. This approach can be used for as many objectives as desired. For each objective, you introduce a goal constrain with theoretically two deviational variables – undersatisfying and oversatisfying (in fact only one of them is useful according to the feature of the goal – maximising or minimising).