We consider a new load balancing model that arises in the processing of user requests for files located on a given set of servers. The optimization criterion is the total excess of actual load over the limit load. In order to redistribute the load and minimize the criterion, files can be moved between the servers. We show that if there are no other constraints related to the stage of moving the files, then this problem is equivalent to a problem previously considered in literature. For this special case of this problem, we propose a stochastic local search scheme that combines a special procedure for fast querying of the neighborhoods and a procedure of non-aggravating modification of intermediate solutions. Results of numerical experiments show that the proposed approach is able to find high-quality solutions for instances of large dimension under tight time constraints.