Question

PERT/CPM Model 5. During the Corona-Quarantine, Emily decides to teach her kids how to bake cookies. She wants to take the opportunity to practice her own PERT/CPM project management skills as well. So, she lists out the activities that are required to bake two batches of cookies including the predecessors (if any) for each activity and the optimistic, most probable, and pessimistic time (in minutes) it takes to complete each activity; especially since she knows that everything can take longer when working with children. Some of the timings are fixed (e.g. baking or cooling times) so you will see that she has the same values for the optimistic, most probable, and pessimistic times.

a. Create the network diagram and create the activity schedule.

b. Identify which activities have slack time.

c. What is the probability that Emily is able to successfully finish and put away both batches of cookies within 54 minutes?

Activity	Description	Immediate	Optimistic	Most	Pessimistic
		Predecessor	Time	Probable	Time
				Time (m)
A	Preheat oven		10	10	10
B	Assemble/measure ingredients		6	8	10
C	Mix dough	B	2	3	4
D	Shape first batch	C	3	4	5
E	Bake first batch	A,D	12	12	12
F	Cool first batch	E	10	10	10
G	Shape second batch	C	3	5	5
H	Bake second batch	E,G	12	12	12
I	Cool second batch	H	10	10	10
J	Store cookies in a jar	F,I	2	3	4

Answer 1

Answer A:

Answer b:

Activity	Duration, D	Early start, ES=Max of early finish of preceding activities	Early finish, EF = ES + D	Late finish, LF= Min of LS of successor activities	Late start, LS= LF - D	Total slack= LF-EF	Critical activity, activities with 0 slack time
A	10.00	0.00	10.00	15.00	5.00	5.00	No
B	8.00	0.00	8.00	8.00	0.00	0.00	Yes
C	3.00	8.00	11.00	11.00	8.00	0.00	Yes
D	4.00	11.00	15.00	15.00	11.00	0.00	Yes
E	12.00	15.00	27.00	27.00	15.00	0.00	Yes
F	10.00	27.00	37.00	49.00	39.00	12.00	No
G	4.67	11.00	15.67	27.00	22.33	11.33	No
H	12.00	27.00	39.00	39.00	27.00	0.00	Yes
I	10.00	39.00	49.00	49.00	39.00	0.00	Yes
J	3.00	49.00	52.00	52.00	49.00	0.00	Yes

Activities with slack time are, A, F and G

Answer c: Critical path length is = sum of the critical path activities= B-C-D-E-H-I-J =

Paths	Duration	Variance
B-C-D-E-H-I-J	52.00	0.78

step 1	we will find the variance of the tasks which lie on critical path	0.78
step 2	mean project time (u) of critical path is=	52.00
step 3	Required completion time		54
step 4	standard deviation= sqrt(variance)=		0.882
step 5	because Z= (given completion time- u/)/standard deviation	2.268
step 6	P(z)= using NORM.S.DIST(z,true)		0.9883

PROBABILITY TO COMPLETE BEFORE 54 mind= 98.83%