Consider the following problem: You have 2 distributors offering the exact same product, and there are multiple producers. At each time you know the total number of units each distributor has available, but this number can be made up from the distributors own inventory as well as units available from selected producers. The 2 distributors might share one or multiple producers, which are unknown.
The task is to identify the shared producer(s), in order to estimate the total number of units available on the market (the 2 distributors).
What approach would you take to solve this? I've mainly been modelling it as a set of stochastic processes and taking the MLE of these, but the difficulties I've had is that the part of each distributor's available units is not proportional to the producer.
I wonder if anyone has any better suggestions for this, as the "real" problem has 10+ distributors and an unknown number of producers leading to a large number of parameters.