Project Scheduling
Professor Al E. Gator, who has been teaching Management Science at the Swamproot University School of Business, has decided to publish his own textbook based on the materials that he has developed over the past 25 years. He expects his textbook to be a big hit, as does his publisher, John Smiley, & Sons, Inc.
Professor Gator asked his graduate assistant, Amanda, to help him organize the schedule of core macro-level activities that constitute this project. She has estimated that it will take about 21 months (i.e., 452 business days) to complete the entire publishing process. After discussions with Smiley and Sons, Amanda determined that Al will lose about $10,000 per business day in book royalties from textbook sales if the project is not completed by the deadline.
Table 1 shows the precedence relationships among the macro-level activities that constitute the upcoming project, as well as the optimistic(a), most likely(m), and pessimistic(b) activity times estimated in business days.
Table 1
|
MACRO-
|
ACTIVITY DESCRIPTION
|
IMMEDIATE
|
ESTIMATED ACTIVITY TIMES
|
|
LEVEL
|
|
PREDECESSOR
|
(IN BUSINESS DAYS)
|
|
ACTIVITY
|
|
|
Optimistic
|
Most Likely
|
Pessimistic
|
|
A
|
Al arranges for a meeting with
|
-
|
8
|
10
|
12
|
|
|
Smiley editor to discuss the project
|
|
|
|
|
|
B
|
Al prepares an outline for the text
|
A
|
20
|
22
|
25
|
|
C
|
Al prepares and sends editor two
|
A
|
51
|
55
|
59
|
|
|
sample chapters
|
|
|
|
|
|
D
|
Al prepares and sends a formal
|
B,C
|
4
|
5
|
5
|
|
|
proposal to Smiley
|
|
|
|
|
|
E
|
Editor engages faculty for review
|
C
|
10
|
10
|
12
|
|
|
and compiles their suggested
|
|
|
|
|
|
|
changes
|
|
|
|
|
|
F
|
Al implements editor's changes on
|
D, E
|
8
|
10
|
13
|
|
|
the two sample chapters
|
|
|
|
|
|
G
|
Al negotiates final contract details
|
E
|
18
|
19
|
24
|
|
|
with Smiley
|
|
|
|
|
|
H
|
Al prepares and sends the
|
E
|
172
|
185
|
197
|
|
|
remaining seven chapters to editor
|
|
|
|
|
|
I
|
Al drafts all figures and graphs
|
F, H
|
51
|
56
|
65
|
|
J
|
Editor reviews the preliminary
|
I
|
9
|
10
|
13
|
|
|
figures and graphs
|
|
|
|
|
|
K
|
Editor reviews the entire text and
|
J
|
53
|
55
|
61
|
|
|
makes final changes
|
|
|
|
|
|
L
|
Al reviews editor's final changes
|
K
|
8
|
9
|
11
|
|
M
|
Smiley marketing department
|
G
|
43
|
50
|
58
|
|
|
executes promotional program for
|
|
|
|
|
|
|
text
|
|
|
|
|
|
N
|
Smiley prints copies of the text
|
L
|
32
|
37
|
41
|
|
O
|
Smiley distributes copies to
|
M, N
|
11
|
12
|
14
|
|
|
warehouses
|
|
|
|
|
|
P
|
Smiley distributes copies from
|
O
|
7
|
7
|
7
|
|
|
warehouses to campus bookstores
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Part A.
Please use your understanding of project scheduling to help Amanda address the following:
1. Please identify the critical path using the activity letters provided, and explain the significance of the critical path.
2. With respect to the total project, what is your best estimate of:
a. the expected project-completion time?
b. the most-likely project-completion time?
c. the variance of the project completion time?
Also, one-by-one, please discuss briefly the specific statistical assumptions, if any, that you made in answering questions 2a., 2b., and 2c.
3. Please create the fully-labeled network diagram for the project using the activity letters provided as labels, and explain its usefulness in managing this project. What information and insights does the labeled network diagram provide?
4. Please create the Gantt chart and explain its potential incremental usefulness in managing this project. What additional information and insights does it provide above and beyond those provided by the network diagram in question 3?
5. Please calculate the free slack for activities F and M. What do they tell you about the risk of the critical path identified in question 1 being overtaken by another path when the project is actually conducted?
6. On which activity would you focus on most heavily to reduce the total-project-completion time? Please explain how you arrived at your answer.
7. How likely it is that the project will not meet the current deadline of 452 business days? Please explain how you arrived at your answer.
Part B.
Suppose that Professor Gator, who is extremely risk-adverse, feels that the probability of missing the 452-business-day deadline (from Q.A.7) is too high. As a consequence, he wants to have Amanda evaluate various activity-crashing scenarios that would reduce the likelihood of incurring a penalty cost for missing this completion time. Since the most-likely activity-time estimates (m's) provided in Part A are frequently closer to their respective optimistic time estimates (a's) than they are to their pessimistic estimates (b's), Al wants to use a more conservative approach to estimating each activity's normal time. He has decided to use the mid-point between a and b in estimating each activity's normal time [i.e., NT=(a+b)/2] instead of using m or m. He feels that optimistic time estimates from Part A are good estimates for the crash times. The corresponding normal and crash direct costs for all 16 activities are presented in Table 2.
Table 2
|
Activity
|
Normal Cost
|
Crash Cost
|
|
A
|
$0
|
$0
|
|
B
|
$16,500
|
$24,300
|
|
C
|
$20,500
|
$48,700
|
|
D
|
$5,000
|
$8,500
|
|
E
|
$42,300
|
$73,700
|
|
F
|
$23,300
|
$40,500
|
|
G
|
$20,500
|
$30,500
|
|
H
|
$57,500
|
$81,500
|
|
I
|
$17,300
|
$25,500
|
|
J
|
$4,500
|
$5,700
|
|
K
|
$11,900
|
$14,500
|
|
L
|
$3,000
|
$6,500
|
|
M
|
$227,100
|
$285,500
|
|
N
|
$118,300
|
$149,300
|
|
O
|
$47,500
|
$93,300
|
|
P
|
$42,900
|
$42,900
|
Please use your understanding of project scheduling to help Amanda address the following:
1. What is the normal project duration (i.e., without any crashing)? What is the associated total direct cost? What is the associated likelihood that the target completion time of 452 business days will be met? Please explain the rationale that you used in arriving at your probability estimate.
2. What is the minimum project duration? What is the associated all-crash total direct cost? What is the critical path associated with the all-crash scenario?
3. Which activities have been crashed without reducing the total project completion time? After accounting for activities that do not need to be crashed, what is the minimum total direct cost associated with the minimum project duration? What are the savings in total direct cost due to optimization of the crashing process? Does the critical path differ from your answer to B.2? Explain why or why not.
4. Provide the Crash Cost per Day for each activity. From a cost perspective, which activity should be crashed first? Which activity, or activities, should Amanda recommend crashing in order to reduce the project completion time by 10 business days for the minimum cost? What is the crash cost for those 10 days?
5. Professor Gator agrees with Amanda's recommendation to crash by 10 business days, but wants to go even further and crash by a total of 20 business days. What is the difference in cost between crashing 20 days and 10 days? How can you explain this difference?