# Corporate Finance

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• Published : November 12, 2012

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Review Problems and Solutions for
Chapter 6: Process Selection and Facility Layout
For the following three problems (1, 2, 7), we assume that parallel workstations are not allowed.
1. An assembly line with 17 tasks is to be balanced. The longest task is 2.4 minutes, and the total time for all tasks is 18 minutes. The line will operate for 450 minutes per day. a. What are the minimum and maximum cycle times?

b. What range of output is theoretically possible for the line? c. What is the minimum number of workstations needed if the maximum output rate is to be sought?
d. What cycle time will provide an output rate of 125 units per day? e. What output potential will result if the cycle time is (1) 9 minutes? (2) 15 minutes?
Solution:

OT = 450 minutes
a. Minimum cycle time = length of longest task, which is 2.4 minutes. Maximum cycle time = Σ task times = 18 minutes.
b. Range of output:

450
= 187.5 units
2.4
450
@18 min . :
= 25 units
18
Dx ∑ t 187.5(18)
N=
=
= 7.5, which rounds to 8
OT
450

@ 2.4 min . :

c.

OT
450
Solving for CT, CT =
= 3.6 minutes per cycle
CT
125
e. Potential output:

d.

Output =

(1) CT = 9 min . :

OT 450
=
= 50 units
CT
9

(2) CT = 15 min . :

450
= 30 units
15

2. A manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 33⅓ units. Assume the shop works a 60-minute hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules:

a. In order of most following tasks. Tiebreaker: greatest positional weight. b. In order of greatest positional weight.
c. What is the efficiency?

Solution:

Desired output = 33.33 units per hour
Operating time = 60 minutes per hour

CT =

Operating time 60 minutes per hour
=
= 1.80 minutes per unit
Desired output 33.33 units per hour

a.

A
B
C
D
E
F
G
H

Number of following tasks
7
6
2
2
2
1
1
0

Positional Weight
6
4.6
1.6
2.2
2.3
1.0
1.5
0.5

Assembly Line Balancing Table (CT = 1.8)
Work Station

Time Remaining

Remaining

I

A

1.4

0.4

II

B

0.5

1.3

C, D, E

E

0.8

0.5

D

0.7

1.1

C

C

0.6

0.5

F

F

0.5

0

III

G

1.0

0.8

H

H

IV

0.5

0.3

b.
Assembly Line Balancing Table (CT = 1.8)
Work Station

Time Remaining

Remaining

I

A

1.4

0.4

II

B

0.5

1.3

C, D, E

E

0.8

0.5

D

0.7

1.1

C

C

0.6

0.5

F

F

0.5

0

G

1.0

0.8

H

H

0.5

0.3

III

IV

c. Efficiency =

Total time
6.0
=
= 83.3%
CT x no. of stations 7.2

7. For the set of tasks given below, do the following:
a.
b.
c.
d.
e.

Develop the precedence diagram.
Determine the minimum and maximum cycle times in seconds for a desired output of 500 units in a 7-hour day. Why might a manager use a cycle time of 50 seconds?
Determine the minimum number of workstations for output of 500 units per day.
Balance the line using the largest positional weight heuristic. Break ties with the most following tasks heuristic. Use a cycle time of 50 seconds. Calculate the percentage idle time for the line.

Solution:

g

a.
a

c

b

h

d

b.

CT =

i

j

f

e

OT 7(60)
=
= .84 minutes = 50.4 seconds (maximum cycle time)
D
500

Minimum cycle time = maximum task time = 45 seconds (results in 560 units of production)
c.

N=