Question

the elements together with the predecessor and processing time of two models A and B are shown in table below. hourly production rate of model a and b are 25 units/hr and 18 units/hr. assume E=1.0, Er=1.0 and M=1.
a) draw the precedence diagram for each model and both models
b) find the theoretical number of workstation needed to achieve the required production rate.
c) use K-W method to solve the line balancing problem
d) determine the balance efficiency for your solution in (c)
e) determine the fixed rate launching interval and fixed rate sequence

Work Element k Tek (min) Preceded byTek (min) Preceded by 0.5 0.3 0.7 0.4 1.2 0.5 0.3 0.8 2 1 4 No operation 2,3 No operation 1.3 6 0.4 0.6 No operation 0.7 0.5 4.5 5,6 9 0.5 4.2

Answer 1

(a) The precedence diagram of both the models is as shown below:

Model 1

Model 2

b) find the theoretical number of workstation needed to achieve the required production rate.

Cycle time = Time available / number of units to be produced

Number of theoretical workstations required = Total time required to produce one unit of a product / Cycle time

For Model 1

Cycle time = 60/25 = 2.4min

Number of theoretical workstations required = 4.2/2.4 = 1.75 ~ 2(Rounded Up)

Hence the number of theoretical workstations required = 2 workstations.

For Model 2

Cycle time = 60/18 = 3.3min

Number of theoretical workstations required = 4.5/3.3 = 1.35 ~ 2(Rounded Up)

Hence the number of theoretical workstations required = 2 workstations.

c) use K-W method to solve the line balancing problem

The procedure to solve the line balancing problem by Kilbridge and Wester method is as follows:
Step 1. Construct the precedence diagram, so those nodes representing work elements of identical precedence
are arranged vertically in columns.
Step 2. List the elements in order of their columns, column I at the top of the list. If an element can be located
in more than one column, list all columns by the element to show the transferability of the element.
Step 3. To assign elements to workstations, start with the column I elements. Continue the assignment
procedure in order of column number until the cycle time is reached (T).

For Model 1

Step 1. Construct the precedence diagram, so those nodes representing work elements of identical precedence
are arranged vertically in columns.

Step 2. List the elements in order of their columns, column I at the top of the list. If an element can be located in more than one column, list all columns by the element to show the transferability of the element.

Work Element	Column	T(mins)	Preceded by
1	1	0.5	-
2	2	0.3	1
3	2	0.7	1
4	3	0.4	2
5	3	1.2	2,3
7	4	0.6	4,5
9	5	0.5	7

Step 3. To assign elements to workstations, start with the column I elements. Continue the assignment
procedure in order of column number until the cycle time is reached (T).

Work station	Work Element	Column	T(mins)	Preceded by	Station time
1	1	1	0.5	-	1.9
	2	2	0.3	1
	3	2	0.7	1
	4	3	0.4	2
2	5	3	1.2	2,3	2.3
	7	4	0.6	4,5
	9	5	0.5	7

For Model 2

Step 1. Construct the precedence diagram so those nodes representing work elements of identical precedence
are arranged vertically in columns.

Step 2. List the elements in order of their columns, column I at the top of the list. If an element can be located
in more than one column, list all columns by the element to show the transferability of the element.

Work Element	Column	T(mins)	Preceded by
1	1	0.5	-
2	2	0.3	1
3	2	o.8	1
5	3	1.3	2,3
6	3	0.4	3
8	4	0.7	5,6
9	5	0.9	7

Step 3. To assign elements to workstations, start with the column I elements. Continue the assignment
procedure in order of column number until the cycle time is reached (T).

Work station	Work Element	Column	T(mins)	Preceded by	Station time
1	1	1	0.5	-	3.2
	2	2	0.3	1
	3	2	o.8	1
	5	3	1.3	2,3
	6	3	0.4	3
	8	4	0.7	5,6
2	9	5	0.9	7	0.9

(d) determine the balance efficiency for your solution in (c)

Balance delay is a measure of the line inefficiency which results from idle time due to an imperfect allocation of work among stations. The percentage representation of line efficiency is called as balance efficiency given by formula as below.

Balance line efficiency = $wOFb2E4kuf92AAAAABJRU5ErkJggg==$

For Model 1

For Model 2

$hJa0ye23OOEAAAAASUVORK5CYII=$