Chapter 9, Problem 21P

Suppose production requirements in Solved Problem 9.2 (see page 383) increase and require a reduction in cycle time from 3 minutes to 7 minutes. Balance the line once again, using the new cycle time. Note that it is not possible to combine task times so as to group tasks into the minimum number of workstations. This condition occurs in actual balancing problems fairly often.

The assembly line whose activities are shown in Figure 9.18 has an 8-minute cycle time. Draw the precedence graph and find the minimum possible number of one-person workstations. Then arrange the work activities into workstations so as to balance the line. What is the efficiency of your line balance?

TASK	PERFORMANCE TIME (MINUTES)	TASK MUST FOLLOW THIS TASK
A	5	—
B	3	A
C	4	B
D	3	B
E	6	C
F	1	C
G	4	D,E,F
H	2	G
	28

Figure 9.18 Four-Station Solution to the Line-Balancing Problem

Solution

The theoretical minimum number of workstations is:

$\frac{{\displaystyle \sum t_i}}{\text{Cycle}\text{time}}=\frac{\text{28}\text{minutes}}{\text{8}\text{minutes}}=3.5\text{,}\text{or}\text{4}\text{stations}$

The precedence graph and one good layout are shown in Figure 9.18:

$\text{Efficiency}\text{=}\frac{\text{Total}\text{task}\text{time}}{\text{(Actual}\text{number}\text{of}\text{workstations)}\text{×}\left(\text{Largest}\text{assigned}\text{cycle}\text{time}\right)}\text{=}\frac{\text{28}}{\text{(4)(8)}}\text{=87}\text{.5\%}$