Homework SourseThe Shuman Company wishes to determine where to locate its d
The Shuman Company wishes to determine where to locate its distribution center. It has suppliers located in Monterrey, Mexico (200, 600) and Montreal, Canada (1400, 1600). The Shuman Company currently has major markets centering in the Mexico City (200, 400), Toronto
Ontario (1200, 1400), Detroit (1000, 1000), Albany (1200, 1000). (1) Using this information calculate the location of the distribution center using the information in Table-1. (2) Instead of
shipping goods from the distribution center to the markets in Mexico City and Toronto, suppose you drop-shipped these goods from the nearest supplier. Using the information given and the information in Table-2, calculate the location of the distribution center and how does this change the location of the distribution center.
Table-1: Central Distribution Center
Location TONS RATE
Monterrey, Mexico 300 $0.50
Montreal, Canada 200 $0.60
Mexico City, Mexico 100 $2.50
Detroit, USA 200 $2.00
Toronto, Canada 100 $2.50
Albany, USA 50 $2.00
Table-2: Drop Shipping & Distribution Center
Location TONS RATE
Monterrey, Mexico 300 $0.50
Montreal, Canada 200 $0.60
Mexico City, Mexico 100 $1.50
Detroit, USA 200 $2.00
Toronto, Canada 100 $1.50
Albany, USA 50 $2.00
Note: numbers in the parenthesis refer to miles (horizontal, vertical)
Solution
Part 1
The location of the DC should be (840.94, 970.08)
Part-2
The location of the DC should be (867.3, 983.1)
| Location (i) | Coordinate | Xi | Yi | TONS (Vi) | RATE (Ci) | Vi.Ci | Xi.Vi.Ci | Yi.Vi.Ci |
| Monterrey, Mexico | (200, 600) | 200 | 600 | 300 | $0.50 | $150.00 | $30,000.00 | $90,000.00 |
| Montreal, Canada | (1400, 1600) | 1400 | 1600 | 200 | $0.60 | $120.00 | $168,000.00 | $192,000.00 |
| Mexico City, Mexico | (200, 400) | 200 | 400 | 100 | $2.50 | $250.00 | $50,000.00 | $100,000.00 |
| Detroit, USA | (1000, 1000) | 1000 | 1000 | 200 | $2.00 | $400.00 | $400,000.00 | $400,000.00 |
| Toronto, Canada | (1200, 1400) | 1200 | 1400 | 100 | $2.50 | $250.00 | $300,000.00 | $350,000.00 |
| Albany, USA | (1200, 1000) | 1200 | 1000 | 50 | $2.00 | $100.00 | $120,000.00 | $100,000.00 |
| Cx = Sum of (Xi.Vi.Ci) / Sum of (Vi.Ci) | 840.94 | |||||||
| Cy = Sum of (Yi.Vi.Ci) / Sum of (Vi.Ci) | 970.08 |
