A tourist car rental firm has one car in each of the five depots D1, D2, D3, D4, D5 and a customer in each of the five cities C1, C2, C3, C4, C5. The distances in Kilometers between the depots and the cities are given in the following matrix. How should be cars be assigned to the customers so as to minimize the total distance covered? Deposits Cities C1 C2 C3 C4 C5 D1 140 115 120 30 35 D2 110 100 90 30 15 D3 155 90 135 60 50 D4 170 140 150 60 60 D5 180 155 165 90 85
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This is an assignment problem, where we need to minimize the total distance covered. I am attaching an excel sheet that explains how this is done.
Since the least distance from D2 to C5 is 15, we assign this route. Similarly, the next least distance is 30 from D1 to C4. If we keep assigning the least distances like this across all routes, we get the ones as given in the excel sheet.
Thus, the least distance covered would be 465km.
Since the least distance from D2 to C5 is 15, we assign this route. Similarly, the next least distance is 30 from D1 to C4. If we keep assigning the least distances like this across all routes, we get the ones as given in the excel sheet.
Thus, the least distance covered would be 465km.
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