Goal Programming Weights Normalization

Let’s have a goal programming model objective function:


(uk)p                      vector of goals underachievement

(vk)p                      vector of goals underachievement weights

(ek)p                       vector of goals overachievement

(wk)p                    vector of goals overachievement weights

p                              number of goals (criteria functions in original model)


The weights vk (wk respectively) are called normalized weights when


If not,  weights vk (wk respectively) can be normalized by the following way


            vk, wk                       original weights

            v’k, w’k                     normalized weights