# 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 ........... 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?

b. What is the direct labor content?

c. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)?

d. How long would it take to produce 100 units, starting with an empty system? The firm is hiring a fifth worker. Assume that tasks are allocated to the five workers to maximize capacity of the line, subject to the conditions that (i) a worker can only perform adjacent operations and (ii) all tasks need to be done in their numerical order.

e. What is the capacity of this line now? Again, assume the firm has hired a fifth worker. Assume further that tasks are allocated to maximize capacity of the line and that tasks can be performed in any order.

f. What is the maximum capacity that can be achieved?

g. What is the minimum number of workers that could produce at an hourly rate of 72 units? Assume the tasks can be allocated to workers as described in the beginning (i.e., tasks cannot be done in any order).

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?

b. What is the direct labor content?

c. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)?

d. How long would it take to produce 100 units, starting with an empty system? The firm is hiring a fifth worker. Assume that tasks are allocated to the five workers to maximize capacity of the line, subject to the conditions that (i) a worker can only perform adjacent operations and (ii) all tasks need to be done in their numerical order.

e. What is the capacity of this line now? Again, assume the firm has hired a fifth worker. Assume further that tasks are allocated to maximize capacity of the line and that tasks can be performed in any order.

f. What is the maximum capacity that can be achieved?

g. What is the minimum number of workers that could produce at an hourly rate of 72 units? Assume the tasks can be allocated to workers as described in the beginning (i.e., tasks cannot be done in any order).

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