Operations and Supply Chain Management The Core

​
PROJECTS chapter 5 145
Activity Expected Times and Variances
exhibit 5.8
ACTIVITY
ACTIVITY
DESIGNATION
TIME ESTIMATES
a m b
EXPECTED TIMES (ET)
__________ a + 4m + b
6
Design A 10 22 28 21 9
Build prototype B 4 4 10 5 1
ACTIVITY VARIANCES (σ 2 )
2
_____ b − a
( 6 )
​
Evaluate equipment C 4 6 14 7 2.7778
Test prototype D 1 2 3 2 0.1111
Write report E 1 5 9 5 1.7778
Write methods report F 7 8 9 8 0.1111
Write final report G 2 2 2 2 0
Excel: Project
Management
Computer Design Project with Three Time Estimates
exhibit 5.9
0 21
A
0 21
ET = 21
σ 2 = 9
ET = 7
σ 2 = 2.7778
21
C
28
21 28
ET = 8
σ 2 = 0.1111
28 36
F
36
28
21 26 26
28 33
28
B D E
21 26 26 28
31 36
ET = 5
σ 2 = 1
ET = 2
σ 2 = 0.1111
ET = 5
σ 2 = 1.7778
Legend
ES EF
LS
36 38
G
ET = 2
σ 2 = 0
LF
36 38
Looking at Appendix E, we see that a Z value of −0.87 yields a probability of 0.1922, which
means that the project manager has only about a 19 percent chance of completing the project in
35 weeks. Note that this probability is really the probability of completing the critical path
A–C–F–G. Because there is another critical path and other paths that might become critical, the
probability of completing the project in 35 weeks is actually less than 0.19.
•
Time–Cost Models and Project Crashing
In practice, project managers are as much concerned with the cost to complete a project
as with the time to complete the project. For this reason, time–cost models have been
devised. These models—extensions of the basic critical path method—attempt to
develop a minimum-cost schedule for an entire project and to control expenditures during
the project.
Time–cost models
Extension of the
critical path models
that considers the
trade-off between
the time required to
complete an activity
and the cost. This
is often referred to
as “crashing” the
project.