In practice, the real problems don't have to get very large or complicated before just typing the problem into AMPL or clicking on SOLVE won't work -- that is,

In practice, the real problems don't have to get very large or complicated before just typing the problem into AMPL or clicking on SOLVE won't work -- that is, solver capacities may be exceeded or the running time can become absurdly long. Then you must exploit whatever special structure you can find in your problem and dig into the algorithms to make refined usage. So, maybe do some Lagrangian relaxation. Maybe find an embedded network flow problem and use a network flow version of the simplex algorithm.