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.
Task 1Task 2Task 3Task 4Task 5Task 6Task 7Task 8Task 9Task 10Task 11Task 12Time to Complete Task (seconds)302515201520501520251520
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
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 the 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 the 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).