Your software can solve transport matrices of more than 9000 cells of variables?

I am solving a problem that involves 59 factories and needs to be delivered to 146 different locations. When using solver in excel to minimize transportation costs, it tells me that the number of variables is too many. Through consultations they indicate to me that their software can solve these types of problems. Can you confirm if I can do it with your software? Thank you

[Jon]

I and probably others only have a vague idea of what is meant by "solve transport matrices". Please provide an exact mathematical description of the problem you are trying to solve and an example data set so we can try it in MATLAB. I Ithink you can also get a free trial in which case you could experiment yourself.

[APBALM]

Thaks Jan, I work for a transportation company that needs to reduce transportation costs for a client. Our job consists of transporting food from 56 production centers to 146 consumption points in the capital city. We normally use Excel (Solver) to define the optimal transport value in problems with fewer variables. Including this problem in Excel's Solver doesn't solve it for me because of the number of variables that need to be solved.

[Walter Roberson]

Is that a "capacitated vehicle routing problem" (CVRP)?

[John D'Errico]

It is not clear what your problem is. MATLAB is not a tool to explicitly solve specific problems, any more than is Excel. You will need to write the calls, and the code to call whatever solver is appropriate. You have not said enough for us to know the exact problem you would formulate.

Having said that, can MATLAB solve problems of similar size? Yes, with a caveat. We still don't know any specifics of what you need to solve.

Answer 1

[Walter Roberson]

Generally speaking:

There are some algorithms that require storage space that is linear in the number of variables being optimized.

There are other algorithms, such as algorithms that involve gradients or covariance matrices, that require storage space proportional to the square of the number of variables being optimized.

There are some algorithms, such as ones that deal with cross-correlation, that can involve storage space proportional to the 4th power of the number of variables being optimized.

The largest variable supported by MATLAB is:

junk = zeros(1,2^48-1, 'uint8');

Error using zeros
Requested 1x281474976710655 (262144.0GB) array exceeds maximum array size preference (30.9GB). This might cause MATLAB to become unresponsive.

If, hypothetically, you were operating on a system that had 2^48 bytes of memory, then MATLAB could use all of it (except one byte). It is, however, rather unlikely that you are using a system with that much memory. (HP has a server that can get pretty close to this.)

2^48 bytes is the limit of the Intel x64 architecture for all publicly known implementations -- the architecture is only defined to have 48 address lines. I wouldn't know if there is a secret government implementation with more address lines.

The realistic limit is the amount of physical memory on your system.

The amount of memory needed by your algorithm is something we do not know at the moment, as we do not know which algorithm you are using.

[Walter Roberson]

There are some links to some different VRP code at https://www.mathworks.com/matlabcentral/answers/11282-how-to-implement-an-aco-algorithm-for-vehicle-routing