Question

3. Office Automation, Inc., developed a proposal for introducing a new computerized office system that will standardize the electronic archiving of invoices for a particular company. Contained in the proposal is a list of activities that must be accomplished to complete the new office system project. Use the following relevant information about the activities:

Activity	Description	Immediate Predecessor	Normal Time (weeks)	Crash Time (weeks)	Normal Cost ($1000s)	Crash Cost ($1000s)
A	Plan needs	------	10	8	30	70
B	Order equipment	A	8	6	120	150
C	Install equipment	B	10	7	100	160
D	Set up training lab	A	7	6	40	50
E	Conduct training course	D	10	8	50	75
F	Test system	C,E	3	3	60	-------

1. Formulate the crash problem as a Linear Programming problem. Do not solve the LP problem.

Answer 1

SOLUTION

Minimize Z = total cost = 400,000 + 20,000 CA + 15,000 CB + 20,000 CC + 10,000 CD + 12,500 CE

Subject to,

Precedence constraints:

TB - TA + CA >= 10
TD - TA + CA >= 10
TC - TB + CB >= 8
TE - TD + CD >= 7
TF - TC + CC >= 10
TF - TE + CE >= 10

Crash limit constraints:

CA <= 2
CB <= 2
CC <= 3
CD <= 1
CE <= 2
CF <= 0

Project completion constraint:

TF + 3 - CF <= 26 i.e. TF - CF <= 23

Tj, Cj >= 0 for j=A, B, ..., F