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GOAL PROGRAMMING: SOLVING MORE COMPLEX PROBLEMS 605

at least E70 000, and if d > 0; revenues of less than E70 000 will be obtained. Thus,
3
the objective function for the priority level 2 problem is:
Min d 3
Next, we consider what the objective function must be for the priority level 3

problem. When considering goal 4, if d ¼ 0; we will have found a solution with at
4

least 200 established customer contacts; however, if d > 0; we will have underach-
4
ieved the goal of contacting at least 200 established customers. Thus, for goal 4 the

objective is to minimize d . When considering goal 5, if d ¼ 0; we will have found a
4 5

solution with at least 120 new customer contacts; however, if d > 0; we will have
5
underachieved the goal of contacting at least 120 new customers. Thus, for goal 5 the

objective is to minimize d : If both goals 4 and 5 are equal in importance, the
5
objective function for the priority level 3 problem would be:

Min d þ d
4
5
However, suppose that management believes that generating new customers is vital
to the long-run success of the firm and that goal 5 should be weighted more than
goal 4. If management believes that goal 5 is twice as important as goal 4, the
objective function for the priority level 3 problem would be:

Min d þ 2d
4 5
Combining the objective functions for all three priority levels, we obtain the
overall objective function for the Suncoast Office Supplies problem:

þ

Min P 1 ðd Þþ P 1 ðd Þþ P 2 ðd Þþ P 3 ðd Þþ P 3 ð2d Þ
5
1
4
2
3
As we indicated previously, P 1 , P 2 and P 3 are simply labels that remind us that goals
1 and 2 are the priority level 1 goals, goal 3 is the priority level 2 goal and goals 4 and
5 are the priority level 3 goals. We can now write the complete goal programming
model for the Suncoast Office Supplies problem as follows:
þ

Min P 1 ðd Þþ P 1 ðd Þþ P 2 ðd Þþ P 3 ðd Þþ P 3 ð2d Þ
1 2 3 4 5
s:t:
þ
2E þ 3N d þ d ¼ 680 Goal 1
1
1
þ
2E þ 3N d þ d 2 ¼ 600 Goal 2
2
þ
250E þ 125N d þ d ¼ 70 000 Goal 3
3 3
þ
E d þ d ¼ 200 Goal 4
4 4
þ
N d þ d ¼ 120 Goal 5
5
5

þ

þ

þ

þ
þ

E; N; d ; d ; d ; d ; d ; d ; d ; d ; d ; d 0
5
1
5
4
4
3
3
1
2
2
Computer Solution
The following computer procedure develops a solution to a goal programming
model by solving a sequence of linear programming problems. The first problem
comprises all the constraints and all the goal equations for the complete goal
programming model; however, the objective function for this problem involves only
the P 1 priority level goals. Again, we refer to this problem as the P 1 problem.
Whatever the solution to the P 1 problem, a P 2 problem is formed by adding a
constraint to the P 1 model that ensures that subsequent problems will not degrade
the solution obtained for the P 1 problem. The objective function for the priority level
2 problem takes into consideration only the P 2 goals. We continue the process until
we have considered all priority levels.
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