| Twelve products are made with
various routings through a flow shop consisting of 10 machines.
The table shows operation times in the machines expressed in
hours. Blank cells indicate that no processing is required.
Machines are passed in numerical sequence.
| |
|
Product |
|
Machine |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
1 |
Mould |
|
0.1 |
0.2 |
0.2 |
0.3 |
0.1 |
0.4 |
0.6 |
0.7 |
0.4 |
0.1 |
0.1 |
2 |
De-fraze |
0.3 |
0.5 |
|
|
|
|
0.2 |
|
0.1 |
|
|
0.2 |
3 |
Barrel Polish |
|
|
|
0.3 |
0.6 |
0.2 |
|
|
|
0.2 |
|
|
4 |
Test |
|
|
|
0.4 |
|
0.1 |
|
|
|
0.3 |
|
|
5 |
Machine |
|
|
0.4 |
|
0.2 |
0.2 |
|
|
0.3 |
|
0.4 |
|
6 |
Paint |
|
0.2 |
|
0.2 |
|
|
0.2 |
|
0.2 |
0.2 |
0.2 |
0.6 |
7 |
Sub-assemble |
|
|
0.1 |
|
|
0.3 |
|
0.2 |
0.3 |
0.1 |
0.1 |
|
8 |
Chemical Test |
|
0.2 |
|
|
|
|
|
|
|
|
|
|
9 |
Dimensional insp. |
0.1 |
0.3 |
|
0.1 |
0.2 |
0.5 |
0.4 |
|
|
0.2 |
|
0.2 |
10 |
Final insp. |
0.4 |
0.4 |
0.2 |
0.3 |
0.3 |
0.2 |
0.2 |
0.4 |
0.1 |
0.2 |
0.3 |
0.3 |
Machine characteristics are shown in the table below. The cost
added is the cost of the raw materials accumulated at each machine
through which a product passes. The machine cost is the cost
of operating a machine per week. The cost does not depend on
the time used on the machines. Machines operate 40 hours per
week.
Machine |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
Machine Size (sq. m.) |
2 |
3 |
4 |
5 |
4 |
3 |
2 |
3 |
4 |
1 |
Machine cost ($/week) |
50 |
30 |
40 |
30 |
100 |
80 |
60 |
20 |
70 |
40 |
Cost Added ($) |
10 |
1 |
2 |
1 |
3 |
1 |
2 |
2 |
1 |
1 |
Weekly sales and unit revenues for the products are in the
table below with unit revenue
| |
Product |
|
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
Sales |
|
200 |
50 |
300 |
80 |
40 |
120 |
200 |
250 |
100 |
120 |
180 |
Unit Revenue
($) |
$20 |
28 |
28 |
24 |
28 |
24 |
24 |
22 |
21 |
22 |
26 |
25 |
a. |
Use the process flow add-in to determine
the number of machines necessary to manufacture the amounts
required to meet the projected sales. Provide enough capacity
so that machines have an 80% utilization. Specify the number
of machines required. |
b. |
Based on the economic data given above, what is the weekly
profit for the system? |
c. |
Assume the order arrivals for the products are Poisson
processes with expected values as in the sales table above.
Assume processing times are exponentially distributions.
Use a queuing analysis to estimate the queue delays at each
machine. |
d. |
In addition to the machine space requirements allow at
least 1.5 times the expected queue lengths (rounded up to
the nearest integer) for waiting products. Assume that WIP
in queues requires 0.4 sq. meters of space. Use the space
requirements and the flow between machines for a facility
layout analysis. Use a plant size that is 30 meters long
by 10 meters wide. What is the total material flow per week
for the best plant layout you can find? |
|
