In the following a simple example shows that Matrix of Savings can be better tha nearest neighbor heuristics:
Consider the following point to be sequenced in a classical TSP:
The case was developed for the student of the course of Facility Management and Industrial Logistics
O is the Distribution Center, so the Root must start and end there. The Coordinated are the following:
Points  X  Y 
O  0  0 
A  1  1 
B  1  2 
C  1  2 
D  5  0 
By using the rule of nearest neighbor the, starting from O and ending in O and not visiting more than once each point., we obtain:
Bound 
OA 
AB 
BC 
CD 
D0 
Tot 
Distance 
1.41 
1.00 
2.00 
6.32 
5.00 
15.73 
In the following figure the route is shown:
Figure 1 Nearest Neighbor rule based Route
It is quite straightforward that the following route should be better:
Figure 2 Nearest NeighBor improved
Bound 
OA 
AC 
CB 
BD 
D0 
Total 
Distance 
1.41 
2.24 
2.00 
4.47 
5.00 
15.12 
But by using the Saving Matrix Method we have:
A 
B 
C 
D 

A 
0.00 


B 
2,65 
0.00 

C 
1.41 
2.47 
0.00 

D 
2.29 
2.76 
0.91 
0.00 
Savings Matrix
So the cost is less than for near neighbor rule. In figure the route is shown
Savings Matrix Method based Route