Chapter 4.16, Problem 7P

Explanation of Solution

Formulation of pre-emptive goal programming model:

Take the following variables to solve the problem,

${\text{x}}_{\text{ij}}$= Number of students taking course j from teacher I where j is one of marketing $(M)$, finance $(F)$, production $(P)$ and statistics $(S)$ and I is one of 1,2,3,4.

${\text{d}}_{\text{1}}{}^{\text{-}}$= Underachievement in the effectiveness of marketing.

${\text{d}}_{\text{1}}{}^{\text{+}}$= Overachievement in the effectiveness of marketing.

${\text{d}}_{\text{2}}{}^{\text{-}}$= Underachievement in the effectiveness of finance.

${\text{d}}_{\text{2}}{}^{\text{+}}$= Overachievement in the effectiveness of finance.

${\text{d}}_{\text{3}}{}^{\text{-}}$= Underachievement in the effectiveness of production.

${\text{d}}_{\text{3}}{}^{\text{+}}$= Overachievement in the effectiveness of production.

${\text{d}}_4{}^{\text{-}}$= Underachievement in the effectiveness of statistics.

${\text{d}}_4{}^{\text{+}}$= Overachievement in the effectiveness of statistics.

The pre-emptive goal programming can be formulated as given below,

Minimize, ${\text{z=d}}_1{}^{\text{-}}+{\text{d}}_2{}^{\text{-}}+{\text{d}}_3{}^{\text{-}}+{\text{d}}_4{}^{\text{-}}+{\text{d}}_5{}^{\text{-}}$

Subject to,

$\begin{array}{c}{\text{7x}}_{\text{1M}}{\text{+7x}}_{\text{2M}}\end{array}$