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2. Develop the Net Savings Matrix

1 2 3 4

0 .. ..

..

..

1 32

3

Net Savings of going 0 to 1 to 2 to 0 (rather than 0 to 1 and 0 to 2 and back to 0) is:

= D0i + D0j Dij

= 3 + 3 3

= 3

Distance between 0 and 1 = D0i = D01 = 3

Distance between 0 and 2 = D0j = D02 = 3

Distance between 1 and 2 = Dij = D12 = 3

1 2 3 40 .. .

.

.

.

..

1 3 3 0

2 2 0

3 5

Net Savings per Route

1 to 3 3 + 4 4 = 31 to 4 3 + 3 6 = 0

2 to 3 3 + 4 5 = 2

2 to 4 3 + 3 8 = -2 or 0

3 to 4 4 + 3 -2 = 5

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This table above is called the _________________________________

3. Run the Optimization

A) Start with the most inefficient route 3 + 3 + 3 + 3 + 4 + 4 + 3 + 3 = 26 miles

a. Original Net Savings Matrix with the bold values being the original Tvalues.

1 2 3 4

0 2 2 2 2

1 3 3 0

2 2 0

3 5

b. Find the highest number on the Net Savings Matrix and see if the route

satisfies our assumptions.

Route 3 to 4 has a savings of 5 miles if we dont go back to the warehouse.

1 2

0

3

4

3

3

4

3

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Does it meet the assumptions?

1st Assumption is that the D0i and D0j do not have a T value of

0Answer: This is true. In this model, D03 currently has T = 2 and

D04 has T = 2

2nd Assumption is that D0i and D0j are not on the same path

Answer: This is true.

Reroute the original trip from: 0 3 0 4 - 0 to: 0 3 4 0

c. Update the Net Savings table with the new T value

1 2 3 4

0 2 2 2 2

1 3 3 0

2 2 0

3 1

12

0

3

4

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B) Go to the next highest value on the Net Savings Matrix. It is 3 (doesnt matter

which 3 you choose)

1 2 3 4

0 2 2 2 2

1 3 3 0

2 2 0

3 1

Does it meet the assumptions?

1st Assumption is that the D0i and D0j do not have a T value of0

Answer: This is true. In this model, D01 currently has T = 2 and

D02 has T = 2

2nd Assumption is that D01 and D02 are not on the same path

Answer: This is true.

Reroute the original trip from: 0 1 0 2 - 0 to: 0 1 2 0

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a. Update the Net Savings table with the new T value

1 2 3 4

0 2 2 2 2

1 1 3 0

2 2 0

3 1

C) Go to the next highest value on the Net Savings Matrix. It is 3 (trips between1 and 3).

1 2 3 4

0 2 2 2 21 1 3 0

2 2 0

3 1

12

0

3

4

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Does it meet the assumptions?

1st Assumption is that the D0i and D0j do not have a T value of0

Answer: This is true. In this model, D01 currently has T = 1 and

D03 has T = 1

2nd Assumption is that D01 and D02 are not on the same path

Answer: This is true.

Reroute the original trip from: 0 1 0 3 - 0 to: 0 1 3 0

a. Update the Net Savings table with the new T value

1 2 3 4

0 2 2 2 2

1 1 1 0

2 2 0

3 1

12

0

3

4

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Now, take a look at the model. We can eliminate the trip between 0 and 3 because it

serves no purpose. The most efficient route becomes 0 2 1 3 4 0 or

3 + 3 + 4 + 2 + 3 = 15 miles

12

0

3

4