Goal Programming Weights Normalization

Let’s have a goal programming model objective function:

where

u = (u_k)_p … vector of goals underachievement

v = (v_k)_p … vector of goals underachievement weights

e = (e_k)_p … vector of goals overachievement

w = (w_k)_p … vector of goals overachievement weights

p … number of goals (criteria functions in original model)

The weights v_k (w_k respectively) are called normalized weights when

.

If not, weights v_k (w_k respectively) can be normalized by the following way

where

v_k, w_k … original weights

v’_k, w’_k … normalized weights