14. Shortest Path Problem | Optimization using Excel

This is the 14th video of the lecture series 'Optimization using Excel'. In this video, we have described how to solve a specific type of network flow model - The Shortest Path Problem using Excel. Viewers are required to watch the previous video (i.e., 13. Network Flow Models) in order to appreciate the use of the =SUMIF() function used in this model. In the shortest path problem, the goal is to find the shortest distance between a source and a sink node. The distances given in the network diagram can be either time or cost. The objective is to minimize the total cost. This is a specific example of a binary integer program.

Further references:

Complete module:

[jafacam]

Hello.

Thank you for putting up your shortest path solution. I am trying to do something similar-but-more complex, and am having trouble, and I was wondering if you could give me some guidance.

What I want to in Excel with shortest paths is:
1) layout a large m-by-n matrix of nodes, with distances in meters between them. I'll use pseudo-chess-board nomenclature with one axis being A-Z and one axis being numbered 1-n (calling nodes "A1", "C3", "F7", etc)
2) have the ability to request multiple shortest paths from (say) B3->F8, G2->A14, F2->R23, etc
3) partially congest a route based on previous paths. For example, if a route is found it may be tagged as 25% congested between two nodes. Another route may add to this. Eventually the route would be congested, and an alternative shortest path would have to be found.
4) ideally I'd like to make it iteratively optimise, but I realise that may be impossible to do in Excel, so the above congestion may have be sequentially built in

Do you know of any examples where such a thing has been done?

Thank you in advance,

Adam