Production Engineering

ENM/MSC 541

A Very Fine Practice Final ExamFall 2009

1. The assembly of a manufactured thing requires the following 12 tasks:

Task / A / B / C / D / E / F / G / H / I / J / K / L
Time
(minutes) / 20 / 6 / 5 / 21 / 8 / 35 / 15 / 10 / 15 / 5 / 46 / 16
Immediate
Predecessor(s) / A / B / C
D / G / E
H / C / F,I
J / K

Table 1 Data

For parts (a)and (b), complete the following tables 2 and 3.

Assigned Tasks
Workstation / (a) Positional Weight Method / (b) 4-station balance
I
II
III
IV
V
VI
VII
VIII

Table 2 Line Balance

Total Idle Time / Line Efficiency (LE) / Smoothness Index (SI)
Part (a)
Part (b)

Table 3 Performance Measures

(a)Using the ranked positional weight (RPW) method, determine the resulting balance using a cycle time of 70 minutes.

(b)Find the minimum cycle time that results in a four-station balance.

2. A maintenance project consists of 10 activities as defined in Table 1.

Activity / Duration (in days) / Precedes / Number workers / Activity / Duration (in days) / Precedes / Number workers
A / 7 / B,C / 5 / F / 6 / I / 3
B / 2 / D,F / 5 / G / 1 / J / 1
C / 4 / E,G / 4 / H / 5 / - / 4
D / 3 / H / 6 / I / 9 / - / 7
E / 5 / I / 2 / J / 8 / - / 4

(a) Develop the project network

(b) Find the critical path:

(c) If activity B takes 6 days instead of three, what change(s) in project completion occurs?

Change / Description
1
2
3
4

(d) If there are 10 workers available, attach a resource-feasible schedule and its profile.

3. A guidance and detection system is being built as part of a large defense project. The detection portion consists of radar and sonar subsystems. Separate equipment is required for each of the subsystems. In each case, the equipment must be calibrated prior to production. After production, each subsystem is tested independently. The radar and sonar are combined to form the detection system, which also must be tested prior to integration with the guidance system. The final test of the entire system requires complex equipment. Relevant data is given below:

Activity / Description / Time (days)
A / Calibrate machine 1 (for radar) / 2.0
B / Calibrate machine 2 (for sonar) / 3.5
C / Calibrate machine 1 (for guidance) / 1.5
D / Assemble and prepare final test gear / 7.0
E / Make radar subsystem / 4.5
F / Make sonar subsystem / 5.0
G / Make guidance subsystem / 4.5
H / Test radar subsystem / 2.0
I / Test sonar subsystem / 3.0
J / Test guidance subsystem / 2.0
K / Assemble detection subsystem (radar and sonar) / 1.5
L / Test detection subsystem / 2.5
M / Final assembly of three subsystems / 2.5
N / Testing of final assembly / 3.5

Develop the project network and answer the following:

(a) Determine the earliest and the latest starting and finishing times for all activities:

(a) Activity / Early start / Early finish / Late start / Late finish
A
B
C
D
E
F
G
H
I
J
K
L
M
N
(b) / Find the critical path
(c) / How much time (in days) is available for assembling and calibrating the final test gear without delaying the project?
(d) / What are the activities that must be completed by the end of 10 days to guarantee that the project is not delayed?
(e) / What are the activities that must be started by the end of 10 days to guarantee that the project is not delayed?

4. The Hi N. Mitey Company has recently purchased three new copying machines and has identified five possible locations for the machines. A survey was conducted to determine the usage each department would make of each machine. The following data applies:

Department
Site / 1 / 2 / 3 / 4 / 5
U / 8 / 4 / 5 / 3 / 1
V / 1 / 6 / 8 / 5 / 3
X / 9 / 8 / 4 / 1 / 4
Y / 5 / 3 / 8 / 6 / 1
Z / 4 / 4 / 1 / 7 / 8
Department
Machine / 1 / 2 / 3 / 4 / 5
A / 5 / 3 / 1 / 8 / 0
B / 1 / 4 / 0 / 3 / 6
C / 0 / 3 / 2 / 8 / 7

Trips per day

Distances in tenth of a mile

Determine which site at which each copy machine should be located.

5. Given the data below:

(a) Solve a two facility (m = 2) rectilinear distance problem where v12 = 3.

(b) Solve the same problem as a Euclidean distance problem.

i / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16
Wi,1 / 9 / 7 / 4 / 3 / 2 / 12 / 4 / 5 / 11 / 17 / 14 / 6 / 5 / 8 / 15 / 4
wi,2 / 5 / 16 / 0 / 3 / 4 / 1 / 1 / 22 / 24 / 18 / 17 / 8 / 6 / 0 / 4 / 3
ai / 0 / 10 / 8 / 12 / 4 / 18 / 4 / 5 / 14 / 19 / 20 / 14 / 3 / 6 / 9 / 10
bi / 0 / 3 / 8 / 20 / 9 / 16 / 1 / 3 / 6 / 0 / 4 / 25 / 14 / 6 / 21 / 10

6. A complex machine used in the manufacture of brake pads has an instantaneous repair cost rate given by C(u) = 10u2 where u is measured in years. The cost of replacing the machine is $25,000. It has a salvage value of $5,000 regardless of its age at replacement. Determine the replacement age that will minimize the average annual repair cost.

7. A fuel pump used in a jet engine if repaired will incur a fixed cost of $5000 for a special set of tools and a variable cost of $330 per failure. If discarded and replaced there is no fixed cost but a variable cost of $55. A condemnation rate of 5 percent is anticipated. (a) Determine the indifference curve between repairing and replacing the pump. (b) If repair results in a failure rate given by (t) = .05 t1.9 with t measured in years and the life of the engine is estimated to be 20 years, what is the largest unit cost for which repair is still optimal?

8. Assume the jet engine pump which costs $950 is repaired upon failure with the failure rate as given in problem 7. If the cost per repair is $330, when should the pump be replaced?

9. Kettering Labs has 420 florescent light fixtures each containing 2 light bulbs. When a bulb fails[1], a maintenance person must be dispatched and the University is charged for one hour of labor at the rate of $78 (fully burdened) per hour. The University pays 3 dollars for each light bulb (large quantity discount). An engineering case study has determined that all 840 lights could be replaced by a single maintenance person in 8 hours. Given the following fraction of failures each month, determine the optimum block replacement strategy and the savings that will be incurred.

number of months. / fraction failing
1 / 0.01
2 / 0.01
3 / 0.03
4 / 0.03
5 / 0.03
6 / 0.04
7 / 0.05
8 / 0.12
9 / 0.13
10 / 0.18
11 / 0.18
12 / 0.19

[1] Most failures begin with the light flickering and making an annoying noise that impacts negatively on the faculty and students. Therefore, they must be immediately replaced.