Abstract: An improved scheduling system is effective to schedule resources in a resource constrained environment. The first step in the process is initialization wherein the set of requests to be scheduled and the processing controls are input to the system. A primary sort is done to determine the order of request processing according to an "importance" ranking. Next, the feasible segments are determined. This determination defines the times where the request could conceivably be scheduled with respect to constraints and resource availabilities. A dynamic laxity determination implements a set of heuristics which models a request's allocation possibilities by taking into account the remaining unscheduled requests with which it conflicts. Account is taken of those requests which require multiple concurrent resources by combining multiple resources. A worthiness determination is made which defines a function indicating advantageous start times admitting high worth values.