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602 CHAPTER 14 MULTICRITERIA DECISIONS

2 You might think of the general goal programming illustrate this point with a problem that has a
model as having ‘hard’ and ‘soft’ constraints. The coefficient of 2 for one of the deviation variables.
hard constraints are the ordinary linear 3 Note that the constraint added in moving from the
programming constraints that cannot be violated. linear programming problem at one priority level
The soft constraints are the ones resulting from the to the linear programming problem at the next
goal equations. Soft constraints can be violated lower priority level becomes a hard constraint. No
but with a penalty for doing so. The penalty is amount of achievement of a higher priority goal
reflected by the coefficient of the deviation variable may be sacrificed to achieve a lower priority goal.
in the objective function. In Section 14.2 we

14.2 Goal Programming: Solving More Complex Problems

In Section 14.1 we formulated and solved a goal programming model that involved
one priority level 1 goal and one priority level 2 goal. In this section we show how to
formulate and solve goal programming models that involve multiple goals within the
same priority level. Although specially developed computer programs can solve goal
programming models, these programs are not as readily available as general purpose
linear programming software packages. Thus, the computer solution procedure
outlined in this section develops a solution to a goal programming model by solving
a sequence of linear programming models with a general purpose linear program-
ming software package.

Suncoast Office Supplies Problem
Suncoast Office Supplies is based in Seville, Spain, and provides office supplies to
local companies in Southern Spain. The management of Suncoast Office Supplies
establishes monthly goals, or quotas, for the types of customers contacted. For the
next four weeks, Suncoast’s customer contact strategy calls for the salesforce, which
consists of four salespeople, to make 200 contacts with established customers who
have previously purchased supplies from the firm. In addition, the strategy calls for
120 contacts of new customers. The purpose of this latter goal is to ensure that the
salesforce is continuing to investigate new sources of sales.
After making allowances for travel and waiting time, as well as for demonstration
and direct sales time, Suncoast allocated two hours of salesforce effort to each
contact of an established customer. New customer contacts tend to take longer
and require three hours per contact. Normally, each salesperson works 40 hours
per week, or 160 hours over the four-week planning horizon; under a normal work
schedule, the four salespeople will have 4(160) ¼ 640 hours of salesforce time
available for customer contacts.
Management is willing to use some overtime, if needed, but is also willing to accept
a solution that uses less than the scheduled 640 hours available. However, manage-
ment wants both overtime and underutilization of the workforce limited to no more
than 40 hours over the four-week period. Thus, in terms of overtime, management’s
goal is to use no more than 640 + 40 ¼ 680 hours of salesforce time; and in terms of
labour utilization, management’s goal is to use at least 640 40 ¼ 600 hours of
salesforce time.

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