A firm is planning to set up an assembly line to assemble 40 units per hour, and 57 minutes per hour are productive. The time to perform each task and the tasks that precede each task are contained in the following table

Question

Task Preceding Task Time to perform (min.)
A -- .69
B A .55
C B .92
D B .59
E B .70
F B 1.10
G C, D, E .75
H G, F .43
I H .29

(a) Draw a network diagram of precedence relationships.
(b) Compute the required cycle time per unit in minutes.
(c) Compute the theoretical minimum number of workstations required to produce 40 units per hour.
(d) Balance this line using the longest processing time heuristic.
(e) What is the efficiency of the line obtained in part d?

Answer 1

(a) The appropriate diagram appears below.
(b) Cycle time is 57/40 = 1.425 minutes.
(c) The theoretical minimum number of stations required is 6.02/1.425 = 4.22 or 5.
(d) The balanced line appears in the software output panel below.
(e) The line's efficiency is 6.02/8.55 = 70.4%

Station Task Time (minutes) Time left (minutes) Ready tasks
A
1 A 0.69 0.735 B
B 0.55 0.185 C,D,E,F
2 F 1.1 0.325 C,D,E
3 C 0.92 0.505 D,E
4 E 0.7 0.725 D
D 0.59 0.135 G
5 G 0.75 0.675 H
H 0.43 0.245 I
6 I 0.29 1.135
Summary Statistics
Cycle time 1.425 minutes
Time allocated (cycle time ∗ #) 8.549999 minutes/cycle
Time needed (sum of task times) 6.02 minutes/unit
Idle time (allocated-needed) 2.529999 minutes/cycle
Efficiency (needed/allocated) 70.40936%
Balance Delay (1-efficiency) 29.59064%
Min (theoretical) # of stations 5