Monte Carlo generator programs are commonly used to model physics processes. They provide samples of single events with their full set of initial state, intermediate and final state particles which follow distributions as predicted by the underlying QCD calculation. The fact that single physics events can be analyzed gives particular strength to Monte Carlo simulations: Both parton and hadron-level are accessible and detector effects, which lead to finite resolutions for the measurement of the particles, can be simulated by feeding the generated list of particles through detector simulation programs.
At HERA, the most commonly used Monte Carlo programs for the
modeling of heavy quark physics are: PYTHIA [108],
RAPGAP [124], AROMA [103]
and HERWIG [125].
These programs are based on the DGLAP evolution
equations [59] and provide leading order calculations
of the cross sections.
Recently, the Monte Carlo program CASCADE [104] was introduced
which contains an implementation of the 
factorization
approach using the CCFM evolution equation [65], described
in section 2.5.
In most Monte Carlo programs, and also in CASCADE, the formation of hadrons is simulated using the LUND string model [108] as implemented in JETSET [107]. Optionally, for heavy quarks, the Peterson fragmentation function [109] can be used. In HERWIG, a cluster algorithm is used to form hadrons from clusters of quark-antiquark states in a color-singlet configuration.
Factorization