Q4.4 (Algo) 12 tasks to 4 workers [4.1, 4.2, 4.3, 4.4]

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	30
Task 2	25
Task 3	15
Task 4	20
Task 5	15
Task 6	20
Task 7	50
Task 8	15
Task 9	20
Task 10	25
Task 11	15
Task 12	20

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

a. What is the capacity of the current line? (Round your final answer to two decimal places.)

b. What is the direct labor content? (Round your final answer to one decimal place.)

c. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)? (Round your final answer to two decimal places.)

d. How long would it take to produce 130 units, starting with an empty system? (Round your final answer to two decimal places.)

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