Predicting Scheduling Success 

Fredric Messing 
Fredric_Messing@cscgt.gsfc.nasa.gov
NASA/CSC 

Abstract 
This paper provides an analytical formulation to predict the success in 
scheduling for a class of scheduling problems frequently referred to as activity 
scheduling. The principal assumption is that the activity start-times are 
randomly distributed over the available time in the time line. 
 
Each activity uses one of a set of equivalent resources. Each resource can be 
used to perform one and only one activity at any time. The activities are 
independent and have no predecessor relationships. Each activity has a specified 
duration and start-time although the possibility that the duration and start-time 
are flexible is also considered. 
 
Numerous approaches have been developed to produce schedules for such problems. 
The problems become challenging when not all of the activities can be scheduled 
due to conflicting demand for the resources. The results presented in this paper 
make it possible to estimate how much of the demand can be scheduled as a function 
of the demand, number of resources, activity duration, and activity flexibility. 
In addition to the formulation, the paper includes computed results for a variety 
of resource and flexibility conditions as a function of the demand. 
 
These results apply directly to scheduling space and ground system resources. 
They can be used to predict scheduling success for a variety of resource 
configurations and demand levels without the need for complex numerical 
simulations. The results demonstrate that even with highly flexible activities, 
it is difficult to schedule demand greater than 60 percent of resources without 
the use of optimization and conflict resolution capabilities in the scheduling 
system.