Question

Question #1: Some of the tasks in this project can be done in parallel. Prepare a diagram showing the required network of tasks and define the critical path. What is the length of the project without crashing? Do not just answer, but show the whole process.

Question #2: If the critical path is longer than 29 days, what is the least additional amounting that Dr. Watage can spend and still achieve this schedule objective (29 days)? Do not just answer, but show the whole process.

Here is the Scenario:

Dr. John Watage, deputy director of the family planning Research Center in Nigeria’s Over-The-River Providence, was assigned the task of organizing and training five teams of field workers to perform educational and outreach activities as part of a large project to demonstrate acceptance of a new method of birth control. These workers already had training in family planning education but must receive specific training regarding the new method of contraception. Two types of materials must also be prepared: (1) those for use in training the workers and (2) those for distribution in the field. Training faculty must be brought in and arrangements made for transportation and accommodations for the participants. Dr. Watage first called a meeting of his office staff. Together they identified the activities that must be carried out, their necessary sequences, and the time that they would require. Their results are displayed in Table 1. Louis Odaga, the chief clerk, noted that their project had to be completed in 29 days. Whipping out his solar-powered calculator, he added up the time needed. “no,” Dr. Watage replied, “some of these tasks can go forward in parallel.” “Be careful, though,” warned Mr. Oglagadu, the chief nurse, “there aren’t that many of us to go around. There are only 12 of us in this office.” “I can check whether we have enough heads and hands once I have tentatively scheduled the activities,” Dr. Watage responded. “If the schedule is too tight, I have permission from the Pathminder Fund to spend some funds to speed it up, just so long as I can prove that it can be done at the least cost necessary. Can you help me prove that? Here are the costs for the activities with the elapsed time that we planned and the costs and times if we shorten them to an absolute minimum.” Those data are given Table 2.

Here are the Tables

Table 1 Family Planning Research Center Activities Activity Immediate Predecessor A. Identify faculty and their schedules B. Arrange transport to base C. Identify and collect training materials D. Arrange accommodations E. Identify team F. Bring in team G. Transport faculty to base H. Print program material I. Have program materials delivered J. Conduct training program K. Perform fieldwork training A A B, E A, B C H D, F, G, I Time (Days) 6 8 4 3 7 5 3 6 7 10 10 J

Answer 1

Activity	Predecessor	Time	Crash time	Cost per day
A	-	6	3	3000
B	-	8	4	4000
C	-	4	2	3000
D	A	3	1	2000
E	A	7	3	6000
F	B,E	5	1	2000
G	A,B	3	1	3500
H	C	6	4	10000
I	H	7	1	7000
J	D,F,G,I	10	9	5500
K	J	10	5	4500

The activity diagram is given below:

E 7 D A 6 3 B חד | תU J 10 K 10 8 C G 3 4 - Н. 6 7

The different paths with total times are given below:

Path	Time
A-E-F-J-K	38
A-D-J-K	29
B-F-J-K	33
B-G-J-K	31
C-H-I-J-K	37

hence path A-E-F-J-K is the critical path taking 38 days

To complete the project in 29 days, we have to reduce 9 days

Critical path is A-E-F-J-K out of which F has least cost

we can reduce cost of activity F by 1 day with cost of 2000

Now both A-E-F-J-K and C-H-I-J-K take 37 days
Common activities are J and K out of which K is the least
We can reduce activity K by 5 days
Cost incurred will be 4500X5 =	22500

Next we can crash activity J by 1 day
Cost incurred will be 5500

Now for both A-E-F-J-K and C-H-I-J-K taking 31 days we need to check which uncommon
activity will have least cost
For A-E-F-J-K we can reduce activity F by 2 days incurring cost of 2000X2 = 4000
For C-H-I-J-K we can reduce activity C by 2 days incurring cost of 3000X2 = 6000

The summary of the movement of total time for all paths is given below when we do the activities listed above:

		Activity F	Activitiy K	Activity J	Activity F	Activity C
	Crash by	1 day	5 days	1 day	2 days	2 days
Path	Time
A-E-F-J-K	38	37	32	31	29	29
A-D-J-K	29	29	24	23	23	23
B-F-J-K	33	32	27	26	24	24
B-G-J-K	31	30	25	24	24	24
C-H-I-J-K	37	37	32	31	31	29

Hence total extra cost taken =  2000 + 22500 + 5500 + 4000 + 6000 = 40000