Bastille College is going to purchase new computers for both faculty and staff. There are a total of 50 people who need new machines – 30 faculty and 20 staff
The cost of the basic personal computer with monitor and disk drive is $2,000, while the deluxe version with VGA and advanced processor is $3,500. Due to internal politics, the number of deluxe computers assigned to staff must be less than half the number of deluxe computers assigned to faculty. The College feels that it must purchase at least 5 deluxe computers for the faculty; if possible, it would like to purchase as many as 20 deluxe computers for the faculty. Staff members do feel somewhat "put upon" by having a limit placed upon the number of deluxe machines purchased for their use, so the College would like to purchase as many deluxe machines for the staff as possible (up to 10). The budget is $100,000. Develop a goal programming formulation of this problem that treats each of the requirements stated above as an equally weighted goal.
Let FR = number of regular computers purchased for faculty use
FD = number of deluxe computers purchased for faculty use
SR = number of regular computers purchased for staff use
SD = number of deluxe computers purchased for staff use
d1- = underachievement of minimum faculty deluxe computers
d1+ = overachievement of minimum faculty deluxe computers
d2- = underachievement of maximum faculty deluxe computers
d2+ = overachievement of maximum faculty deluxe computers
d3- = underachievement of deluxe ratio
d3+ = overachievement of deluxe ratio
d4- = underachievement of total faculty computers
d4+ = overachievement of total faculty computers
d5- = underachievement of maximum staff deluxe computers
d5+ = overachievement of maximum staff deluxe computers
d6- = underachievement of total staff computers
d6+ = overachievement of total staff computers
d7- = underachievement of budget
d7+ = overachievement of budget
Minimize d1- + d2+ + d3+ + d4- + d5- + d6- + d7+
Subject to: FD + d1- - d1+ = 5 Deluxe faculty
FD + d2- - d2+ = 20 Deluxe faculty
-0.5FD + SD + d3- - d3+ = 0 Deluxe ratio
FD + FR + d4- - d4+ = 30 Total faculty
SD + d5- - d5+ = 10 Deluxe Staff
SR + SD + d6- - d6+ = 20 Total staff
3500FD + 2000FR + 2000SR + 3500SD + d7- - d7+ = 100000 Budget
all variables ? 0
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