Question

The White Tooth Device Company is a manufacturer of high-end electric toothbrushes. For each toothbrush, there are a sequence of assembly steps performed by five workers. Each worker does two tasks. Workers are paid $15 per hour.

Worker Task Time (seconds) A T1 40 A T2 25 B T3 20 B T4 15 C T5 10 C T6 15 D T7 10 D T8 20 E T9 25 E T10 35 Instruction: Round "cost of direct labor" and "average labor utilization" to 2 decimal places. Round "target manpower" and "capacity of the process" to 1 decimal place. a. What is the labor content of a toothbrush (seconds)? b. What is the cost of direct labor for a toothbrush ($)? c. What is the utilization (as a percent) of worker A? d. What is the average labor utilization of this process? e. Suppose demand is 40 toothbrushes per hour. What is the takt time (seconds)? f. Suppose the takt time is 50 seconds. What is the target manpower? g. Suppose one additional employee could be hired. The new employee can be assigned to the same set of tasks as one of the current workers. For example, the new worker could do tasks 1 and 2 (like worker A) or tasks 7 and 8 (liker worker D). What would be the capacity of the process (toothbrushes per hour) after hiring the new worker? toothbrushes per hour h. Suppose the company changes the assignment of tasks to workers to maximize its capacity. Each task is still assigned to one worker and each worker is still assigned consecutive tasks. What would be the capacity of the process (toothbrushes per hour)? toothbrushes per hour i. Suppose the company changes the assignment of tasks to workers to maximize its capacity. tasks can be assigned to multiple workers and workers can be assigned nonconsecutive tasks. What would be the capacity of the process (toothbrushes per hour)? toothbrushes per hour

Answer 1

labor content = sum of the time taken by all tasks = 215 sec

Hourly Output of different steps

worker A = 3600/ 65 =55.38

worker B = 3600 /35 =103

worker C =3600/ 25 =144

worker D = 3600 /30 =120

worker E =3600/60 =60

Process is constrained by the worker A which has the lowest output of 55.38 per hour

b. Direct labor cost = cost incurred / toothbrushes produced = 15x5 /55.38 = 1.354

c.Utilisation of person A = 1= 100%

d Utilisation of B = 55.38/103 =0.5376

Utilisation of C = 55.38/144 = 0.3845

Utilisation of D = 55.38 / 120 =0.4615

Utilisation of E = 55.38 /60 =0.923

average of these numbers ( A to E) = 0.6613

e.takt time = time available / units to be produced = 60/40 =1.5 min

f For takt time of 50, the hourly output should be 3600/50 =72

resources needed at different steps would be

T1+T2 =2

T3+T4 =1

T5+T6 =1

T7+T8 =1

T9+T10 =2

total = 7

g. Bottleneck A would be the right place for the new worker, which will double the capacity of this step. However, the new bottleneck will now be E which will have capacity of 60 per hr.

h. The step with 40 sec is the longest one. It can be combined with either step having time 25 sec ( as before) or 35 sec. The earlier arrangement is better. The capacity would remain the same.

i the highest time 40 needs to be combined with lowest number which is 10. It gives a task time of 50. It is not possible to find a highest combination which is less than 50. Hence the capacity

= 3600/50 = 72 per hour