The classical Particle Swarm Optimization (PSO) algorithm is a powerful method to find the mini- mums of numerical functions on a continuous definition domain.It has been a very important optimization tool in many research fields.So far,papers on the application of PSO algorithm to multilevel lot-sizing (MLLS) problems can not be seen often.In view of this,a PSO algorithm combined with the mutation operator of Ge- netic algorithm (GA) is come up with to solve MLLS problems.Our aim is to expand t...