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GOAL PROGRAMMING: SOLVING MORE COMPLEX PROBLEMS 607

additional constraints. One is to ensure that the solution to the P 3 problem contin-
ues to satisfy the priority level 1 goal and the second that the solution continues to
satisfy the priority level 2 goal. The new formulation is then:

þ
Min d þ 2d
4 5
s:t:
þ
2E þ 3N d þ d ¼ 680 Goal 1
1 1
þ
2E þ 3N d þ d ¼ 600 Goal 2
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
d þ d 2 ¼ 0 Priority level 1
1
d ¼ 0 Priority level 1
3
þ

þ
þ

þ

þ

E; N; d ; d ; d ; d ; d ; d ; d ; d ; d ; d 0
1 1 2 2 3 3 4 4 5 5
Making these modifications to the P 1 problem, we obtain the solution to the P 3
problem shown in Figure 14.5.
Referring to Figure 14.5, we see the objective function value of 120 indicates
that the priority level 3 goals cannot be achieved. Since D5MINUS ¼ 60, the
optimal solution of E ¼ 250 and N ¼ 60 results in 60 fewer new customer contacts
than desired. However, the fact that we solved the P 3 problem tells us the goal
programming solution comes as close as possible to satisfying priority level 3 goals
given the achievement of both the priority level 1 and 2 goals. Because all priority
levels have been considered, the solution procedure is finished. The optimal
solution for Suncoast is to contact 250 established customers and 60 new custom-
ers. Although this solution will not achieve management’s goal of contacting at
least 120 new customers, it does achieve each of the other goals specified. If
management isn’t happy with this solution, a different set of priorities could be
considered. Management must keep in mind, however, that in any situation involv-
ing multiple goals at different priority levels, rarely will all the goals be achieved
with existing resources.
Figure 14.5 The Computer Solution of the P 3 Problem
Objective Function Value = 120.000
Variable Value Reduced Costs
-------------- --------------- -----------------
D1PLUS 0.000 0.000
D2MINUS 0.000 1.000
E 250.000 0.000
N 60.000 0.000
D1MINUS 0.000 1.000
D2PLUS 80.000 0.000
D3PLUS 0.000 0.008
D3MINUS 0.000 0.000
D4PLUS 50.000 0.000
D4MINUS 0.000 1.000
D5PLUS 0.000 2.000
D5MINUS 60.000 0.000

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