Question

In: Operations Management

On a daily​ basis, the Vampire Van is dispatched from Maplewood Hospital to pickup blood and...

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. a. The Vampire Van travels from the Hospital​ (A) to​ (B) to​ (C) to​ (D) to​ (E) and then returns to the Hospital​ (A). What is the total number of miles that the van must travel using this​ route? ​(Enter your response rounded to one decimal​ place.) b. 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? ​(Enter your response rounded to one decimal​ place.) c. Using Westbrook ​(Upper C​) 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? ​(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)

3.1

5.3

3.2

4.4

City Center Donation Site​ (B)

3.1

6.7

2.2

4.3

Westbrook Donation Site​ (C)

5.3

6.7

6.2

2.5

Municipal Park Donation Site​ (D)

3.2

2.2

6.2

4.6

Valley Hills Donation Site​ (E)

4.4

4.3

2.5

4.6

Solutions

Expert Solution

1.

  1. ​A->B: 3.1
  2. B->C: 6.7
  3. C->D: 6.2
  4. D->E: 4.6
  5. E->A: 4.4

The total distance can be obtained by adding up the above figures, which is:

3.1+ 6.7+6.2+4.6+4.4 = 25 miles

Hence, the van has to travel 25 miles to cover this route

2. Now, let us see what the nearest neighbor route tells us. The heuristic is simple - it tells us that if we start from a particular location, the next location that we select should have the shortest distance from the starting point.

Given we start from A.

  1. The place which is closest to A is B, A->B, 3.1 miles
  2. Next, B -> D, 2.2 miles
  3. Next, D->E, 4.6 miles
  4. Next, E-> C, 2.5 miles
  5. Next C-> A, 5.3 miles

The route as per Nearest Neighbor algorithm is A->B->D->E->C->A, with a distance of 3.1+2.2+4.6+2.5+5.3 =17.7 miles

3) We now have to do the same thing using C as the starting location.

  1. C -> E : 2.5
  2. E -> B : 4.3
  3. B -> D : 2.2
  4. D -> A : 3.2
  5. A -> C : 5.3

The new route is C->E->B->D->A->C = 2.5 + 4.3 + 2.2+3.2+5.3 = 17.5 miles

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