An embodiment of a method of scheduling computer processing begins with a first step of receiving job properties for a plurality of jobs to be processed in a multi-processor computing environment. At least some of the jobs each comprise a plurality of stages, one or more tasks for each stage, and precedence constraints among the stages. The method continues with a second step of determining a schedule for processing at least a subset of the plurality of jobs on processors within the multi-processor computing environment from a solution of a mathematical program that provides a near maximal completion reward. The schedule comprises a sequence of tasks for each processor. In a third step, the computer processing jobs are processed on the processors according to the sequence of tasks for each processor.