On a daily basis, the Vampire Van is dispatched from Maplewood Hospital to picku

Question

On a daily basis, the Vampire Van is dispatched from Maplewood Hospital to pickup blood and platelet donations made at its local donation centers. The distances in miles between all locations may be found in the table below.

Maplewood Hospital (A)

City Center Donation Site (B)

Westbrook Donation Site (C)

Municipal Park Donation Site (D)

Valley Hills Donation Site (E)

Maplewood Hospital (A)

7.3

3.3

6.3

3.8

City Center Donation Site (B)

7.3

4.6

4.5

3.6

Westbrook Donation Site (C)

3.3

4.6

7.9

5.8

Municipal Park Donation Site (D)

6.3

4.5

7.9

6.9

Valley Hills Donation Site (E)

3.8

3.6

5.8

6.9

Using Maplewood Hospital as the beginning location, create a route using the Nearest Neighbor heuristic. What is the total number of miles that the van must travel using this route?

The new route is A _, _, _, _, A and requires a total distance of ____miles. (Enter your response rounded to one decimal place.)

Maplewood Hospital (A)

City Center Donation Site (B)

Westbrook Donation Site (C)

Municipal Park Donation Site (D)

Valley Hills Donation Site (E)

Maplewood Hospital (A)

7.3

3.3

6.3

3.8

City Center Donation Site (B)

7.3

4.6

4.5

3.6

Westbrook Donation Site (C)

3.3

4.6

7.9

5.8

Municipal Park Donation Site (D)

6.3

4.5

7.9

6.9

Valley Hills Donation Site (E)

3.8

3.6

5.8

6.9

Explanation / Answer

Nearest Neighbor heuristic

Here we see that our starting destination is A -Maplewood Hospital

Now we check the table for our nearest destination.

Since the least value in the corresponding row is 3.3, our next destination is C

Now, we move on to C and check the next nearest destination :

Since the least value in the corresponding row is 4.6, our next destination is B

Now, we move on to B and check the next nearest destination :

Since the least value in the corresponding row is 3.6, our next destination is E

Now, we move on to E and only destination left is D. Let's check the distance for that step as well :

Distance to D is 6.9 miles.

And finally we need to get back to A from D, so the corresponding distance is :

Finally, distance to A is 6.3 miles.

Hence, our new route will look like :

A , C , B , E , D , A

Total distance = 3.3 + 4.6 + 3.6 + 6.9 + 6.3 = 24.7 miles

A B C D E A 7.3 3.3 6.3 3.8 B 7.3 4.6 4.5 3.6 C 3.3 4.6 7.9 5.8 D 6.3 4.5 7.9 6.9 E 3.8 3.6 5.8 6.9

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