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606 CHAPTER 14 MULTICRITERIA DECISIONS

To solve the Suncoast Office Supplies problem, we begin by solving the P 1 problem:
þ
Min d þ d
2
1
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

þ

þ

þ

þ
E; N; d ; d ; d ; d ; d ; d ; d ; d ; d ; d 0
2
2
1
1
3
5
5
4
3
4
In Figure 14.4 we show the computer solution for this linear programme. Note that

þ

D1PLUS refers to d , D2MINUS refers to d , D1MINUS refers to d and so on.
1 2 1
The solution shows E ¼ 250 established customer contacts and N ¼ 60 new cus-
tomer contacts. Because D1PLUS ¼ 0 and D2MINUS ¼ 0, we see that the solution
achieves both goals 1 and 2. Alternatively, the value of the objective function is 0,
confirming that both priority level 1 goals have been achieved. Next, we consider
goal 3, the priority level 2 goal, which is to minimize D3MINUS. The solution in
Figure 14.4 shows that D3MINUS ¼ 0. Thus, the solution of E ¼ 250 established
customer contacts and N ¼ 60 new customer contacts also achieves goal 3, the
priority level 2 goal, which is to generate a sales revenue of at least E70 000. The
fact that D3PLUS ¼ 0 indicates that the current solution satisfies goal 3 exactly at
E70000. Finally, the solution in Figure 14.4 shows D4PLUS ¼ 50 and D5MINUS ¼ 60.
These values tell us that goal 4 of the priority level 3 goals is overachieved by 50
established customers, but that goal 5 is underachieved by 60 new customers. At this
point, both the priority level 1 and 2 goals have been achieved, but we need to solve
another linear programme to determine whether a solution can be identified that
will satisfy both of the priority level 3 goals. Therefore, we go directly to the P 3
problem.
The linear programming model for the P 3 problem is a modification of the linear
programming model for the P 1 problem. The objective function must now be

expressed in terms of the priority level 3 goal and we seek to minimize d 4 +2d 5 .
The original five constraints of the P 1 problem remain but we must add two
Figure 14.4 The Computer Solution of the P 1 Problem
Objective Function Value = 0.000
Variable Value Reduced Costs
-------------- --------------- -----------------
D1PLUS 0.000 1.000
D2MINUS 0.000 1.000
E 250.000 0.000
N 60.000 0.000
D1MINUS 0.000 0.000
D2PLUS 80.000 0.000
D3PLUS 0.000 0.000
D3MINUS 0.000 0.000
D4PLUS 50.000 0.000
D4MINUS 0.000 0.000
D5PLUS 0.000 0.000
D5MINUS 60.000 0.000
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