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604 CHAPTER 14 MULTICRITERIA DECISIONS

Goal 3
þ

250E þ 125N d þ d ¼ 70 000
3 3
where
þ
d ¼ the amount by which the sales revenue is greater than
3
the target value of e70 000

d ¼ the amount by which the sales revenue is less than
3
the target value of e70 000

Goal 4 þ
E d þ d ¼ 200
4
4
where
þ
d ¼ the amount by which the number of established customer
4
contacts is greater than the target value of 200 established
customer contacts

d ¼ the amount by which the number of established customer
4
contacts is less than the target value of 200 established
customer contacts

Goal 5 þ
N d þ d ¼ 120
5
5
where
þ
d ¼ the amount by which the number of new customer
5
contacts is greater than the target value of 120 new
customer contacts

d ¼ the amount by which the number of new customer
5
contacts is less than the target value of 120 new
customer contacts

Formulating the Objective Function
To develop the objective function for the Suncoast Office Supplies problem, we
begin by considering the priority level 1 goals. When considering goal 1, if
þ
d ¼ 0; we will have found a solution that uses no more than 680 hours of
1
salesforce time. Because solutions for which d þ is greater than zero represent
1
overtime beyond the desired level, the objective function should minimize the

þ
value of d . When considering goal 2, if d ¼ 0; we will have found a solution
1 2
that uses at least 600 hours of salesforce time. If d is greater than zero,
2
however, labour utilization will not have reached the acceptable level. Thus,
the objective function for the priority level 1 goals should minimize the value

of d . Because both priority level 1 goals are equally important, the objective
2
function for the priority level 1 problem is:
þ
Min d þ d
2
1
In considering the priority level 2 goal, we note that management wants to achieve

sales revenues of at least E70 000. If d ¼ 0; Suncoast will achieve revenues of
3
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