Waiting Lines and Queuing Theory Models

Shortest Route Tutorial

In this tutorial, we will cover the concept of shortest route, or finding the shortest distance possible to get through a network. The shortest path will not necessarily connect all nodes. In this example, one of our best customers truck has broken down and he has asked us to transport supplies from his warehouse to his distribution center. Node 1 in our network represents his warehouse and node 6 represents his distribution center.

Node 1 Node 2 Distance 1 4 160 1 2 70 1 3 45 2 4 32 2 5 55 3 5 200 4 5 110 4 6 40 5 6 127

We have a total of 6 nodes, so open Excel QM, click on the Excel QM tab, alphabetical, network analysis, shortest distance. Here you must be very careful entering the distance between each nodes. Not every node pair is connected. There are several possible solutions. One solution is presented below. 1-2-4-6 for a total distance of 142 miles.

Data - Distance Table From\to City 1 City 2 City 3 City 4 City 5 City 6 City 1 0 70 45 160 0 0 City 2 0 0 0 32 55 0 City 3 0 0 0 0 200 0 City 4 0 0 0 0 110 40 City 5 0 0 0 0 0 127 City 6 0 0 0 0 0 0

1 0 0 0 0 -1

Start=1,Finish=-1

Shortest Route Tutorial

Flows From\to City 1 City 2 City 3 City 4 City 5 City 6

City 1 1 City 2 1 City 3 City 4 1 City 5 City 6 Inflow

1

1

1

Outflow 1 1

1 Net Outflow 1

-1

Minimum distance 142