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(1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). A B C 10 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 11 9 14 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route A B с D 8 14 10 13 D

(1) Find an optimal assignment of trucks to routes to minimize the total cost (using the Hungarian Method). A B C 10 6 12 15 10 11 7 16 9 Truck / Route 1 2 3 4 11 9 14 Step la: Row subtraction (show your steps, e.g., see cell 1A) Truck / Route A B с D 8 14 10 13 D

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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**Assignment of Trucks to Routes Using the Hungarian Method** This exercise involves finding the optimal assignment of trucks to routes to minimize total costs. Follow the Hungarian Method step by step: **Initial Cost Matrix:** | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | 10 | 6 | 12 | 8 | | 2 | 11 | 15 | 10 | 14 | | 3 | 9 | 12 | 7 | 10 | | 4 | 14 | 16 | 9 | 13 | ### Step 1a: Row Subtraction - Subtract the smallest entry in each row from all entries in that row. - Example: For Truck 1, \(10 - 6 = 4\). | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | 4 | | | | | 2 | | | | | | 3 | | | | | | 4 | | | | | ### Step 1b: Column Subtraction - Subtract the smallest entry in each column from all entries in that column. | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | | | | | | 2 | | | | | | 3 | | | | | | 4 | | | | | ### Step 2: Testing for Optimal Solution - Draw the minimum number of lines needed to cover all zeros. Minimum lines required: _____ ### Step 3: Revise the Opportunity Cost Table - Adjust the matrix based on the uncovered numbers. | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | | | | | | 2 | | | | | | 3 | | | | | | 4 | |
Transcribed Image Text:**Assignment of Trucks to Routes Using the Hungarian Method** This exercise involves finding the optimal assignment of trucks to routes to minimize total costs. Follow the Hungarian Method step by step: **Initial Cost Matrix:** | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | 10 | 6 | 12 | 8 | | 2 | 11 | 15 | 10 | 14 | | 3 | 9 | 12 | 7 | 10 | | 4 | 14 | 16 | 9 | 13 | ### Step 1a: Row Subtraction - Subtract the smallest entry in each row from all entries in that row. - Example: For Truck 1, \(10 - 6 = 4\). | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | 4 | | | | | 2 | | | | | | 3 | | | | | | 4 | | | | | ### Step 1b: Column Subtraction - Subtract the smallest entry in each column from all entries in that column. | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | | | | | | 2 | | | | | | 3 | | | | | | 4 | | | | | ### Step 2: Testing for Optimal Solution - Draw the minimum number of lines needed to cover all zeros. Minimum lines required: _____ ### Step 3: Revise the Opportunity Cost Table - Adjust the matrix based on the uncovered numbers. | Truck/Route | A | B | C | D | |-------------|----|----|----|----| | 1 | | | | | | 2 | | | | | | 3 | | | | | | 4 | |
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