Question

6. A project has been defined to contain the following list of activities, along with their precedence relations and time and cost estimates for the activity durations. Time estimates (weeks L Cost estimates ($) Activity Predecessor(s) Normal time Crashed time Normal cost Crashed cost 10 9 $6000 $8000 - 85 $1100 $2000 A 7 5 $3000 $3800 B 12 4 $4000 $6000 B 4 2 $5000 $6500 AD 6 3 $2500 $4000 CE $2800 $$3000 a. Draw the Activity-on-node (AON) diagram. b. Use the normal durations to compute the (total) slack on each of the activities. Identify the critical path(s). Activities can be crashed by any amount down to the minimum times given in the column "Crashed time". The crashing cost is proportional to the amount of time crashed; the column "Crashed cost" gives the cost at the minimum allowed time. In addition to the activity costs there are also indirect costs of $1500 per week as well as a penalty cost of $2500 for every week the project is delayed past week 20. If the manager wants to minimize the total project costs, when should the project be delivered, and how much will be the final project cost?

Answer 1

The AON diagram is:

Start Finish

The calculations are:

Data				Normal time	26						Minimum crash cost to meet project goal	$      1,700
Project goal	20			Minimum time	17						Project time	20
					Immediate Predecessors (1 per column)						Intermediate Computations
Activity	Normal Time (weeks)	Crash Time (weeks)	Normal Cost	Total Cost with Crashing	Pred 1	Pred 2	Pred 3	Pred 4		Crash days	Crash cost/day	Crash limit
A	10	9	$6,000	$8,000						0	2000	1
B	8	5	$1,100	$2,000						0	300	3
C	7	5	$3,000	$3,800	A					0	400	2
D	12	4	$4,000	$6,000	B					6	250	8
E	4	2	$5,000	$6,500	B					0	750	2
F	6	3	$2,500	$4,000	A	D				0	500	3
G	5	3	$2,800	$3,000	C	E				2	100	2