What are some approaches/algorithms to solve the problem of supply-demand-price?

Question

Problem statement: transport some products from (A, B, C) to (D, E, F), each place has a specified amount of supply (from) and demand (to). Each route has multiple choices (multiple vendors) and each has a specified price. How to get the best prices?

I want to implement this in Python. The simplest way to make a loop but I know there are better approaches. I don't have historical data so machine learning is not a very good approach.

Answer 1

Sounds like a job for either the Maximum Flow algorithm, or the Stable Marriage algorithm. This really depends on the specifics, though. So I'd need you to provide the following clarifications:

1) Define "route" - can A transport directly to D, or are there intervening stops?

2) If the latter is true, do these stops have an associated cost?

3) Are supply and demand indicated in terms of quantity possessed/desired, or by dollar amount?

4) Can multiple vendors sell to the same buyer, or are vender-buyer partnerships exclusive?

5) Do buyers have price ceilings?

If you assume 1) is direct (no stops between), 3) is in $s, 4) is "exclusive", and 5) is true - you can solve with the stable marriage algorithm. In fact, if just one iteration of trading will take place, you can simply sort buyers by buying price (descending), vendors with selling price (ascending), and pair indexwise.

Else, you could turn the vendor - buyer data into a graph, calculate some metric for weights between nodes, and solve for maximum flow.

Do provide the additional information requested above, and perhaps I can help further!

Max Flow:

https://en.wikipedia.org/wiki/Minimum-cost_flow_problem

Stable Marriage:

https://en.wikipedia.org/wiki/Stable_marriage_problem