Question

4. A large manufacturer of pencil sharpeners is planning to add a new sharpener, and you have been asked to bal- ance the assembly line, given the following task times and precedence relationships. Assume that cycle time is 1.3 minutes per unit.

Answer 1

(i)

(ii)

Station	Remaining time	Eligibles (# followers)	Was fit	Assigned time	Time remains	Idle time	Tie-breaker
I	1.3	a(4), c(3), e(3)	a	0.2	1.1
	1.1	c(3), e(3), b(3)	b	0.4	0.7		b
	0.7	c(3), e(3)	c	0.3	0.4		c
	0.4	e(3), d(2)	e	0.1	0.3
	0.3	d(2), f(2)	-	-	0.3	0.3
II	1.3	d(2), f(2)	d	1.3	0.0		d
	0.0	f(2)	-	-	0.0	0.0
III	1.3	f(2)	f	0.8	0.5
	0.5	g(1)	g	0.3	0.2
	0.2	h(0)	-	-	0.2	0.2
IV	1.3	h(0)	h	1.2	0.1	0.1

So, the assignment is as follows:

Station-I: a, b, c, e
Station-II: d
Station-III: f, g
Station-IV: h

(iii)

Percentage idle time = Total idle time per cycle / (No. of stations * cycle time) = (0.3+0+0.2+0.1) / (4*1.3) = 11.54%

(iv)

The actual cycle time is also 1.3 minutes (Station-II being the bottleneck).

So, actual output in 420 minutes = 420/1.3 = 323 units per day