The free “student” version of AMPL is limited to 300 variables (500 for linear problems) and a total of 300 objectives and constraints. However all other AMPL versions have no intrinsic limit on problem size; they are limited only by the resources available to the computer that is running AMPL.
In practice, memory is most often the limiting resource. The amount of memory used by AMPL necessarily depends on the numbers of variables and constraints, and on the number and complexity of the terms in the constraints — or in the case of linear programs, on the number of nonzero coefficients in the constraints. Memory use also depends on the size and complexity of the model’s sets and parameters. AMPL’s presolve phase may require additional memory to execute (though it may accomplish problem reductions that allow savings of memory later).
AMPL’s memory use for a linear program can be estimated crudely as 1000000 + 260 (m + n) + 50 nz bytes, where m is the number of constraints, n the number of variables, and nz the number of nonzeroes. A computer having 4GB or more of memory and running a 64-bit operating system can thus typically accommodate over a million variables and/or constraints. Memory required for a solver may have to be added, however, if the solver is to be run while AMPL remains active. See also our advice elsewhere in this FAQ for further comments on what to do (including running the solver separately) if you suspect a problem with insufficient memory.
Especially difficult problems may cause your solver to encounter its own resource limitations. Solvers that accept binary and integer variables, in particular, can consume impractical amounts of time and disk space as well as memory, even for problems of apparently modest size. Nonlinear problems can also be very time-consuming compared to linear programs in the same numbers of variables and constraints.
As a practical matter, there is no substitute for experimentation to determine the resource requirements of your particular problem. The best approach is usually to try out your model on progressively larger collections of data, so that you can record the trend in resource requirements as problem size increases.