A manufacturing company that utilizes five specialized machines for various production tasks The table below outlines the estimated processing time each machine would require to complete different tasks. Machine 1 2 3 4 5 Task 1 9 22 58 11 19 Task 2 43 78 72 50 63 Task 3 41 28 91 37 45 74 42 27 49 39 Task 4 Task 5 36 11 57 22 25 Each cell signifies the estimated processing time required for a specific task to be completed by a particular machine. Your objective is to optimize the assignment of tasks to machines, aiming to minimize the total processing time while ensuring that each machine is assigned only one task, and each task is handled by only one machine. a. Solve the assignment problem using the Hungarian method. b. Provide the optimal task assignments. c. Calculate the minimum total processing time. Solution a. The Hungarian method C. b. Task Machine 1 2 3 4 5 Processing time = carch CEAS
A manufacturing company that utilizes five specialized machines for various production tasks The table below outlines the estimated processing time each machine would require to complete different tasks. Machine 1 2 3 4 5 Task 1 9 22 58 11 19 Task 2 43 78 72 50 63 Task 3 41 28 91 37 45 74 42 27 49 39 Task 4 Task 5 36 11 57 22 25 Each cell signifies the estimated processing time required for a specific task to be completed by a particular machine. Your objective is to optimize the assignment of tasks to machines, aiming to minimize the total processing time while ensuring that each machine is assigned only one task, and each task is handled by only one machine. a. Solve the assignment problem using the Hungarian method. b. Provide the optimal task assignments. c. Calculate the minimum total processing time. Solution a. The Hungarian method C. b. Task Machine 1 2 3 4 5 Processing time = carch CEAS
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:A manufacturing company that utilizes five specialized machines for various production tasks
The table below outlines the estimated processing time each machine would require to complete
different tasks.
Machine
1
2
3
4
5
Task 1
9
22
58
11
19
Task 2
43
78
72 50
63
Task 3
41
28
91
37
45
74 42 27 49
39
Task 4
Task 5
36 11 57 22 25
Each cell signifies the estimated processing time required for a specific task to be completed
by a particular machine. Your objective is to optimize the assignment of tasks to machines,
aiming to minimize the total processing time while ensuring that each machine is assigned only
one task, and each task is handled by only one machine.
a. Solve the assignment problem using the Hungarian method.
b. Provide the optimal task assignments.
c. Calculate the minimum total processing time.
Solution
a.
The Hungarian method
Transcribed Image Text:C.
b.
Task
Machine
1
2
3
4
5
Processing time =
carch
CEAS
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