Optimal dispatching of two-priority job streams to two nonidentical machines

The following control problem in manufacturing is addressed. Jobs of two priority classes, C/sub 1/ and C/sub 2/, arrive at a system with two non-identical machines. Class C/sub 1/ jobs with higher priority have dispatch preference over C/sub 2/ jobs with lower priority. The problem is to dispatch appropriate fractions of class C/sub 1/ jobs to machines 1 and 2 so that the average flow time of C/sub 1/ jobs is minimized and neither C/sub 1/ jobs nor C/sub 2/ jobs are lost. The analytical solution to the problem is derived for various system disciplines, including: nonpreemptive priorities, preemptive priorities with resumption, preemptive priorities with resumption and setup and nonpreemptive priorities with multiple vacations.<
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