Question

In a warehouse, it is required to locate a temporary storage area for 5 shelves operations that are located in the following coordinates (1,4),(1,8),(1,12),(4,4) and (4,10) with flows to the temporary area of 50,45,62,35, and 48 respectively. There are only two options for locating this temporary area: - Location 1(2.5,2) - Location 2 (2.5, 13) Determine the Total Distance Traveled for each option. Which of the two options is better? Assume Manhattan distances.

Answer 1

• distance 1: 1804
• distance 2: 1556
• Location 2 is better (shorter distance)

Explanation:

You want the total Manhattan distance for flows of {50,45,62,35, 48} from {(1, 4), (1, 8), (1, 12), (4, 4), (4, 10)} to one of A(2.5, 2) or B(2.5, 13), and which is better.

Distance

The Manhattan distance from a point will be the sum of absolute values of the difference between the coordinates of the point and those of the ending point (A or B).

Total distance

Each distance sum will be weighted by the flow from that point. The total distance is the sum of these weighted distances.

Computation

There are a number of ways the computation of total distance can be carried out. One of them is shown in the attached calculator display.

The total in each case shows the x- and y-distances separately. The total distance traveled for each option is ...

A: 360 +1444 = 1804 (location 1)

B: 360 +1196 = 1556 (location 2)

The option for putting the temporary area at Location 2 is better, because it has a shorter total distance.

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