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
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).
Define new variables for the amount that the actual
exposures exceed or fall short of the goals – deviation variables.
Construct new objective function that includes only
deviation variable. The goal is always minimisation of the total deviation
from the goals.
Assign weights to unsatisfied exposures (to deviation
variables in goal function)