Analyzing data - what tools should I use?


I am analyzing data of seat distribution among different types of rail wagons. I have m types of wagons and n seats. What I want to achieve is to find the sets M of m and N of n where M.N->max. And in addition, which is the most important, I need to know exactly which are the objects in the sets - the wagons in M and the seats in N.

I have uploaded an excel table with information about the seats and the wagons. You have the seat number in the first column and the wagon types in the first row. The content of the table represent whether this seat number is physically available on certain type of wagon or not(e.g. seat number 9 is physically available only in wagon type "2563-1").

I think I have found the value of N.M->max but I am not sure if it is so, because I have done this by visually rearranging the rows so I can decide if it is the best option. I have chose among 4 different options that I have considered.

The results are put in the second sheet. The best option I have chosen is M=13, N= 36 where M.N=468.

I need to describe this results with some mathematical method. So if you can help me with the tools that I should be using here and the tests to convey.

Thank you!

I have been working on it and I have realized that is more optimization problem than statistical. So I would rather look for other tools. As far as I have thought about the problem I could represent it like a graph. No clear view yet on how it will happen :)