POM 3310-201: Production and Operations Management
Assignment 3
1. A network consists of the following list. Times are given in weeks.
|
Activity |
Preceding |
Optimistic |
Probable |
Pessimistic |
|
A |
— |
5 |
11 |
14 |
|
B |
— |
3 |
3 |
9 |
|
C |
— |
6 |
10 |
14 |
|
D |
A, B |
3 |
5 |
7 |
|
E |
B |
4 |
6 |
11 |
|
F |
C |
6 |
8 |
13 |
|
G |
D, E |
2 |
4 |
6 |
|
H |
F |
3 |
3 |
9 |
(a) Draw the network diagram. (5 Points)
(b) Calculate the expected duration and variance of each activity. (5 Points)
(c) Calculate the expected duration and variance of the critical path. (5 Points)
(d) Calculate the probability that the project will be completed in less than 28 weeks. (5 Points)
2. Pirmin’s Bike Shop is behind on a custom bike and needs to crash 8 hours of time from the 8-step project.
(a) Given the project table below calculate the crash cost for 8 hours of time-savings (10 points)
(b) Suppose Pirmin calls the customer and asks for a project extension, reducing the amount of time he needs to crash. Pirmin has a $20 crash budget. Is the budget sufficient to crash 4 hours of time? (5 points)
|
Activity |
Normal Duration (hours) |
Normal Cost ($) |
Crash Duration (hours) |
Crash Cost (S) |
Immediate Predecessors |
|
A |
2 |
10 |
2 |
0 |
None |
|
B |
3 |
15 |
2 |
23 |
A |
|
C |
5 |
25 |
4 |
30 |
B |
|
D |
3 |
20 |
1 |
24 |
C |
|
E |
6 |
30 |
4 |
45 |
C |
|
F |
1 |
5 |
1 |
0 |
C,E |
|
G |
7 |
35 |
6 |
50 |
F |
|
H |
10 |
50 |
7 |
62 |
D,G |
3. Jim’s department at a local department store has tracked the sales of a product over the last ten weeks. Forecast demand using exponential smoothing with an alpha of 0.3, and an initial forecast of 30.0 for period 1. Calculate the MAD covering periods 2-10. Calculate the tracking signal covering periods 2-10. What do you recommend? (15 points)
|
Period |
Demand |
|
1 |
24 |
|
2 |
23 |
|
3 |
26 |
|
4 |
36 |
|
5 |
26 |
|
6 |
30 |
|
7 |
32 |
|
8 |
26 |
|
9 |
25 |
|
10 |
28 |
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