Question

Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There is unlimited demand.

	Time to Complete Task (seconds)
Task 1	20
Task 2	20
Task 3	10
Task 4	15
Task 5	10
Task 6	15
Task 7	40
Task 8	10
Task 9	15
Task 10	20
Task 11	10
Task 12	15

The current conveyor-paced assembly-line configuration assigns the workers in the following way:

• Worker 1: Tasks 1, 2, 3
• Worker 2: Tasks 4, 5, 6
• Worker 3: Tasks 7, 8, 9
• Worker 4: Tasks 10, 11, 12

e. Assume the firm has hired a fifth worker. The task assignments for the five workers are shown below. What is the capacity of this line now? (Round your final answer to two decimal places.)

Worker	Task(s)
1	1,2
2	3,4,5
3	6,7
4	8,9
5	10,11,12

f. Again, assume the firm has hired a fifth worker. The task assignments for the five workers are shown below. What is the capacity of this line now? (Round your final answer to two decimal places.)

Worker	Task(s)
1	1,2
2	3,4,6
3	5,8,10
4	7
5	9,11,12

g. Now assume the firm is using eight workers. The task assignments for the eight workers are shown below. What is the capacity of this line now? (Round your final answer to two decimal places.)

Worker	Task(s)
1	1
2	2,3
3	4,5
4	6
5	7
6	8,9
7	10,11
8	12

Answer 1

The capacities are computed in 'units per hour' as nothing was mentioned. The numbers will be different if they want you to enter it in 'units per minute' or 'per second'. Please make a note of this.

(e)

Worker	Task(s)	Processing time per unit (P)	No. of workers (N)	Capacity in units per hr. = 3600*N/P
1	1,2	20+20=40	1	90.00
2	3,4,5	10+15+10=35	1	102.86
3	6,7	15+40=55	1	65.45
4	8,9	10+15=25	1	144.00
5	10,11,12	20+10+15=45	1	80.00

So,

the capacity is Min(90, 102.86, 65.45, 144,80) = 65.45 units per hour

(f)

Worker	Task(s)	Processing time per unit (P)	No. of workers (N)	Capacity in units per hr. = 3600*N/P
1	1,2	20+20=40	1	90
2	3,4,6	10+15+15=40	1	90
3	5,8,10	10+10+20=40	1	90
4	7	40	1	90
5	9,11,12	15+10+15=40	1	90

So,

the capacity is 90 units per hour

(g)

Worker	Task(s)	Processing time per unit (P)	No. of workers (N)	Capacity in units per hr. = 3600*N/P
1	1	20	1	180
2	2,3	20+10=30	1	120
3	4,5	15+10=25	1	144
4	6	15	1	240
5	7	40	1	90
6	8,9	10+15=25	1	144
7	10,11	20+10=30	1	120
8	12	15	1	240

So,

the capacity is Min(180, 120, ..., 240) = 90 units per hour