Mathematical Model of Multi Criteria Linear Programming Problem


a)  Scalar formulation

Criteria functions :

subject to :
xijmodel variable
zk k-th criteria function

ckjcost coefficient of j-th variable in k-th criteria function

aijcoefficient of j-th variable in i-th constraint

biRHS of i-th constraint

p … number of criteria functions

m …number of constraints

n …number of variables

b)  Matrix – vector formulation
x = (xj)n        …    vector of model variables

C =(ckj)p.n      matrix of cost coefficients of criteria functions

X                    …   set of feasible solutions

A =(aij)m.n      matrix of coefficients of constraints

b= (bi)m        …   RHS vector