Question

An assembly line is to be designed to operate 10 hours per day and supply a steady demand of 450 units per day. Here are the tasks and their performance times:

TASK	PRECEDING TASKS	PERFORMANCE TIME (SECONDS)	TASK	PRECEDING TASKS	PERFORMANCE TIME (SECONDS)
a	—	35	g	d	18
b	—	60	h	e	22
c	—	40	i	f	20
d	a	15	j	g	40
e	b	25	k	h, i	15
f	c	30	l	j, k	45

b. What is the workstation cycle time required to meet the desired output rate?

Workstation cycle time             seconds per unit

c. What is the theoretical minimum number of workstations required to meet the desired output rate? (Round up your answer to the next whole number.)

Minimum number of workstations            

d. Assign tasks to workstations using the longest operating time. (Leave no cells blank - be certain to enter "0" wherever required.)

Work Station	Task	Idle Time
I	(Click to select)b-dbc-fca-d-gc-b
II	(Click to select)ac-aa-bbb-ec-e-d
III	(Click to select)f-e-hec-j-hjd-g-fc-b
IV	(Click to select)gi-e-h-ji-g-jeh-f-if-i
V	(Click to select)lk-j-li-k-lk-lf-i-k-lj-l

e. What is the efficiency of your line balance, assuming it is running at the cycle time determined in part b? (Round your answer to 1 decimal place.)

Efficiency             %

f. Suppose demand increases by 10 percent. How would you react to this? Assume that you can operate only 10 hours per day using regular time. (Round your answer for cycle time down to the nearest whole number. Round your answer for overtime up to the nearest whole number.)

(Click to select)IncreaseReduce cycle time to  seconds per unit. Another option is to work  minutes overtime using the cycle time found in part b.

Answer 1

We will first draw the network precedence diagram based on the details given, as below

b.

Workstation cycle time = Production time per day/ Output per day = (10 hrs per day)/ (450 hours per day) = 1.33 minutes or 80 seconds

c.

Theoretical minimum number of workstations required to meet the desired output rate = Sum of total task times/ cycle time

= (35+60+40+15+25+30+18+22+20+40+15+45) seconds/ 80 seconds

= 365/ 80

= 4.56 ~ 5 (rounded)

d. Assign tasks to workstations using the longest operating time

Beginning with the first workstation, assign each task, one at a time, based on longest operating time until the sum of the task times is equal to the workstation cycle time or until no other tasks can be assigned due to sequence or time restrictions. Repeat for the remaining workstations until all the tasks have been assigned to a workstation.

Work Station	Task	Idle Time
I	b	80-60=20
II	c, a	80-(40+35) =5
III	f, e, d	80- (30+25+15)=10
IV	h, i, g	80 - (22+20+18)=20
V	j, k	80 - (40+15) = 25
VI	l	80 - 45 = 35

Hence, the actual number of workstations needed is 6.

e.

Efficiency of line balance = (Sum of all task times)/ (Actual number of workstations)*(cycle time) = (365 seconds)/ (6*80 seconds)

= 76.04%

f.

If Demand is increased by 10% then output is 450*1.1 = 495 per day. Cycle time is further reduced to 10/ 495 = 72.72 seconds.

Hence, reducing cycle time to 72.72 seconds per unit is correct.

This may also lead to adding another workstation to meet the required output.

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