Dynamic job scheduling with strict deadline

Dynamic job scheduling on one processor is considered. In the problem, multiple types of jobs arrive randomly with deterministic processing time requirements, values and deadlines. If a job cannot be processed within its deadline, its value is lost. The objective is to schedule jobs so as to minimize the overall expected loss over an infinite horizon. The single processor scheduling problem is NP-hard. To solve the problem within a polynomial computation time, this study assumes that a job is to be scheduled upon its arrival and that it cannot bump previously scheduled ones. The problem is then solved within a stochastic dynamic programming framework. For I types of jobs the T units of initial time available, an algorithm of O(T²(I+1)) operations is developed to obtain the optimal policy. Using the algorithm, extensive numerical tests are performed to examine various properties of the optimal policy