Mathematical Model of Multi Criteria Linear Programming Problem

 

a)  Scalar formulation
 

Criteria functions :

subject to :
where 
xij …model variable
zk …k-th criteria function

ckj…cost coefficient of j-th variable in k-th criteria function

aij…coefficient of j-th variable in i-th constraint

bi …RHS of i-th constraint

p … number of criteria functions

m …number of constraints

n …number of variables
 

b)  Matrix – vector formulation
where 
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