I am working within the transport sector and have got someone to program me a logic for a project I am working on. The code works like a charm, so it is as such not a technical questions as to what type of coding language or what to write he should use. What I am looking for is more meta.
I have time series prices for 6 different regions wherein there are 5 different destination options (i.e. if you are in zone A, you can choose to go to zone B/C/D/E/F - if zone E is the best paying, the logic will then choose whether to go to A/B/C/D/F, etc etc etc until it reaches the end of the times series).
In mathematics, this logic is is similar to maximum flow model but in this case the segment is bidirectional (e.g. zone A travel to zone B and vice versa), compared to most optimization problems where segments are unidirectional and there is a source and a sink (e.g. finding the most profitable flow from California to New York given different stopovers).
I am looking to see how historically one could have choosen which transport routes that yield achieve superior income over the full time series. I am looking for ways which I could improve the logic to achieve and even higher income. There is an assumption in this logic that I can predict in 4-5 weeks what the best paying zone is, but the purpose of this model is to find the superior logic - and then reverse engineer my research to predict 4-5 weeks out.
My logic is the following for calculating maximum historical theoretical income on transport assets:
choose a starting zone
list all options from zone, calculate average income per destination zone
list all options in destination zone options
choose the highest paying trip in each destination zone
get the average of each source zone-destination zone option pairing
choose the highest average and move asset 4-5-6 weeks down the time series
repeat steps 1-6 until time series end
I would be happy to hear if anyone can come up with a smarter logic that yields a greater profit.
The logic is made in Excel with VBA.
What I am seeking input on is how to find a maximum on a maximum flow model?