Question

Agent Smith, operations manager at the Matrix franchise, faces assembly line balancing problems. He has been told that the firm needs to assemble 1400 agents per day. There are 420 minutes of productive time in each working day. The assembly line activities are given below:

Task	Time (seconds)	Predecessor
A	13	-
B	4	A
C	10	B
D	10	-
E	6	D
F	12	E
G	5	E
H	6	F, G
I	7	H
J	5	H
K	4	I, J
L	15	C, K

a) Determine the maximum and minimum cycle times. b) Determine the required cycle time to produce 1400 agents per day. c) What is the minimum number of stations needed? d) Draw a precedence diagram. Use the cells in Excel to enter the durations and add arrows to indicate the precedence relationships. e) Assign tasks to stations in order of most following tasks first, if there is a tie, use the task with the longest processing time first. f) Determine the average utilization and the percentage idle time of the assembly line.

Answer 1

a) Determine the maximum and minimum cycle times.

Maximum Cycle time = total time of completing al the task by single worker = total task time = 97 seconds

Minimum Cycle time = highest task time = 15 seconds of activity J

b) Determine the required cycle time to produce 1400 agents per day.

Demand = 1400 agents per day

Available time = 420 minutes per day = 420 x 60 = 25200 seconds per day

Cycle time = Available time/Demand = 25200/1400= 18 seconds per unit

Cycle time = 18 seconds per agent

c) What is the minimum number of stations needed?

Total work content =97 seconds

Theoretical number of workstation required = Total work content/Cycle time = 97/18 = 5.38

Minimum theoretical number of WS = 6

d) Draw a precedence diagram.

e) Assign tasks to stations in order of most following tasks first, if there is a tie, use the task with the longest processing time first.

By applying most following tasks method, the task is assigned the workstation first which is having highest no. of following task.

The assignment for workstation is as follows:

Task	Time (seconds)	Predecessor	No, of following tasks
A	13	-	3
B	4	A	2
C	10	B	1
D	10	-	8
E	6	D	7
F	12	E	6
G	5	E	6
H	6	F, G	4
I	7	H	2
J	5	H	2
K	4	I, J	1
L	15	C, K	0

Station	Task	Cycle time available	Time (Seconds)	Time left (Seconds)	Ready tasks (# followers)
					A(3),D(8)
1	D	18	10		A(3),E(7)
	E	8	6	2	A(3),F(5),G(5)
2	F	18	12		A(3),G(5)
	G	6	5	1	A(3),H(4)
3	H	18	6		A(3),I(2),J(2)
	I	12	7		A(3),J(2)
	J	5	5	0	A(3),K(1)
4	A	18	13		K(1),B(2)
	B	5	4	1	K(1),C(1)
5	K	18	4		C(1)
	C	14	10	4	L(0)
6	L	18	15	3
			Total idle time	11

f) Determine the average utilization and the percentage idle time of the assembly line.

Utilization = Total work content/(# of workstation x cycle time) x 100

Utilization = 97/(6 x 18) x 100

Utilization = 89.81 %

%idle time = 100 – Utilization = 100 – 89.91% = 10.19%

%idle time = 10.19%