PROBLEMS
1. Mabel’s Ceramics spent $3000 on a new kiln last year, in the belief that it would cut energy usage 25% over the old kiln. This kiln is an oven that turns “greenware” into finished pottery. Mabel is concerned that the new kiln requires extra labor hours for its operation. Mabel wants to check the energy savings of the new oven, and also to look over other measures of their productivity to see if the change really was beneficial. Mabel has the following data to work with:
The year before
Year just ended
Production (finished units)
4000
4100
Labor (hrs)
350
375
Capital ($)
15000
18000
Energy (kWh)
3000
2600
Also, suppose that the average labor cost is $12 per hour and cost of energy is $0.40 per kwh.
a. Were the modifications beneficial? (Compute labor, energy, and capital productivity for the two years and compare.)
b. Compute percentage change in multi-factor productivity of the year just ended from that of year before.
c. If the multifactor productivity must be restored next year to what is was the year before, assuming the same output next year as the year just ended, by how the input must be reduced from what it is this year?
2. An Appliance Service company made house calls and repaired 10 lawn-mowers, 2 refrigerators, and 3 washers in an 8-hour day with his standard crew of 3 workers. The retail price for each respective service is $50, $200, and $120. The average wage for the workers is $12 per hour. The materials cost for a day was $200 while the overhead cost was $50.
a. What is the companys labor productivity?
b. What is the multifactor productivity?
c. How much of a reduction in input is necessary for a 5% increase in multifactor productivity?
3. Consider the tasks, durations, and predecessor relationships in the following network. Draw the AON network and answer the questions that follow.
Activity Description
Immediate
Predecessor(s)
Optimistic
(Weeks)
Most Likely
(Weeks)
Pessimistic
(Weeks)
A
—
4
7
10
B
A
2
8
20
C
A
8
12
16
D
B
1
2
3
E
D, C
6
8
22
F
C
2
3
4
G
F
2
2
2
H
F
6
8
10
I
E, G
4
8
12
J
I
1
2
3
a. Schedule the activities of this project and determine (i) the expected project completion time, (ii) the earliest and latest start and finish times, and the slack for all the activities, and (iii) all the critical paths.
b. What is the probability of completion of the project before week 42?
c. What is the probability of completion of the project before week 35?
d. With 99% confidence what is your estimate for the project completion time.
4. Consider the following project. All activity times are in weeks.
Activity
Immediate
Predecessor(s)
Normal Time
Crash time
Normal cost
Crash cost
A
–
7
4
20000
38000
B
–
8
5
50000
74000
C
A
9
7
80000
110000
D
A, B
8
8
30000
30000
E
B
9
8
10000
12000
F
C
10
8
90000
124000
G
D, E
5
5
25000
25000
H
E
10
8
32000
40000
I
F, G
5
4
28000
35000
a. Draw an AON network.
b. Identify all the unique paths from start to finish and determine the critical path, normal project completion time, and normal project cost.
c. Compute MTR, Cost of crashing/week.
d. Which activity would you crash first and by how many weeks?
e. Determine the project time and cost after crashing the activity selected in (d).
5. Consider the following CPM Solver model.
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a) Determine the successor activities in cells I2 to I10.
b) Determine the Excel formulas for the following cells: F2, G2, C15, C18, D18, D21, C25, G19, G16, G15, H15, B27, B28, and B29.
c) What is the Solver Target cell for minimizing the project completion time?
d) What is the Solver changing cell range?
e) What are the Solver constraints?
