Problem Size and Numerical Stability

Because of their structural simplicity, the main limitations on the size of LP problems which can be solved are time, memory, and the possibility of numerical "instabilities" which are the cumulative result of the small errors intrinsic to finite precision computer arithmetic. The larger the model, the more likely it is that numerical instabilities will be encountered in solving it.

Most large LP models are sparse in nature: While they may include thousands of decision variables and constraints, the typical constraint will depend upon only a few of the variables. This sparsity can be exploited to save memory and gain speed in solving the problem.