Goal Programming Mathematical
Model

**Matrix
– vector formulation**

where

**x**
= *(x*_{j})_{n}…vector
of model variables

*X*…set
of feasible solutions

**A
= **(a_{ij})_{m.n }_{…}matrix
of coefficients of constraints

*b *=
*(b*_{i})_{m}…RHS
vector

**C***
= **(c*_{kj})_{p.n}_{…}matrix
of cost coefficients of criteria functions

*g *=
*(g*_{k})_{p}…vector
of goals

*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