Abstract: An apparatus and method is disclosed for scheduling a service (such as backup) in a complex computer installation given constraints of elapsed time and resource utilization. The apparatus form of the invention has two major components: a Modeler and a Scheduler. The Modeler calculates utilization of computer installation resources and elapsed time for the service for any subset of clients and/or networks using a model of the various client types, network types and their interconnections. The Scheduler invokes the Modeler with subsets of clients to find utilizations and elapsed times and adjusts the subsets to generate a schedule (if one exists) which is a list of subsets of clients which can be serviced concurrently without exceeding the utilization criterion or an elapsed time criterion. The Scheduler uses a heuristic involving client and network types to rapidly converge on the list of subsets of clients for the schedule to greatly improve over a trial and error approach.