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Assembly Line 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 Task 2 Task 3 30 25 15 Task 4 20 Task 5 Task 6 15 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: P Public Worker 1: Tasks 1, 2, 3 Worker 2: Tasks 4, 5, 6 Worker 3: Tasks 7, 8, 9 Worker 4: Tasks 10, 11, 12 Answer the following questions: 1. What is the capacity of the current line? 2. What is the direct labor content? 3. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)? 4. How long would it take to produce 100 units, starting with an empty system? 5. The firm is hiring a fifth worker. Assume that tasks are allocated to the five workers to maximize capacity of the line under the condition that the tasks need to be done in their numerical order. What is the capacity of this line now? 6. 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. What is the maximum capacity that can be achieved?

Assembly Line 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 Task 2 Task 3 30 25 15 Task 4 20 Task 5 Task 6 15 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: P Public Worker 1: Tasks 1, 2, 3 Worker 2: Tasks 4, 5, 6 Worker 3: Tasks 7, 8, 9 Worker 4: Tasks 10, 11, 12 Answer the following questions: 1. What is the capacity of the current line? 2. What is the direct labor content? 3. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)? 4. How long would it take to produce 100 units, starting with an empty system? 5. The firm is hiring a fifth worker. Assume that tasks are allocated to the five workers to maximize capacity of the line under the condition that the tasks need to be done in their numerical order. What is the capacity of this line now? 6. 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. What is the maximum capacity that can be achieved?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 111P
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Assembly Line 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 Task 2 30 25 Task 3 Task 4 Task 5 15 20 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: P Public Worker 1: Tasks 1, 2, 3 Worker 2: Tasks 4, 5, 6 Worker 3: Tasks 7, 8, 9 Worker 4: Tasks 10, 11, 12 Answer the following questions: 1. What is the capacity of the current line? 2. What is the direct labor content? 3. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)? 4. How long would it take to produce 100 units, starting with an empty system? 5. The firm is hiring a fifth worker. Assume that tasks are allocated to the five workers to maximize capacity of the line under the condition that the tasks need to be done in their numerical order. What is the capacity of this line now? 6. 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. What is the maximum capacity that can be achieved?
Transcribed Image Text:Assembly Line 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 Task 2 30 25 Task 3 Task 4 Task 5 15 20 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: P Public Worker 1: Tasks 1, 2, 3 Worker 2: Tasks 4, 5, 6 Worker 3: Tasks 7, 8, 9 Worker 4: Tasks 10, 11, 12 Answer the following questions: 1. What is the capacity of the current line? 2. What is the direct labor content? 3. What is the average labor utilization (do not consider any transient effects such as the line being emptied before breaks or shift changes)? 4. How long would it take to produce 100 units, starting with an empty system? 5. The firm is hiring a fifth worker. Assume that tasks are allocated to the five workers to maximize capacity of the line under the condition that the tasks need to be done in their numerical order. What is the capacity of this line now? 6. 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. What is the maximum capacity that can be achieved?
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