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Application Mathematics and Informatics
The scheduling theory studying, in particular, minimization of the total weighted completion time, which refers to planning, organizing, and executing complex or multistep processes of assembling, manufacturing, building, dispatching, computing, etc., possesses both exact and heuristic approaches to the schedule computation. The computation time of the exact schedule approach grows immensely when the number of jobs is increased o just a few jobs (roughly, o 6 to 9, depending also on how jobs
... also on how jobs are divided into job parts). Therefore, a lot of heuristics are used to nd the approximate schedule but to obtain it much faster. The heuristics' approximate schedule is not always executed in the exactly minimal total weighted completion time, but the loss is commonly not so great. Moreover, when the number of jobs is of order of hundreds, the scheduling problems become intractable by any exact schedule approaches, and so the heuristics remain the single way to nd a schedule. Considering the preemptive scheduling problem by subsequent length-equal job importance growth, there are two ways to input the job release dates and the respective priority weights. On the one hand, the release dates can be given in ascending order; then the respective priority weights will be a set of, generally speaking, non-decreasing values. On the other hand, the release dates can be given in descending order; and then the respective priority weights will be a set of, generally speaking, non-increasing values. Having estimated the averaged time of obtaining the approximate schedule by both ascending and descending orders of inputting the job release dates, the heuristic's job order is revealed to be very signicant. Its signicance grows as the number of jobs increases. The inuence of the heuristic's job order also grows as the number of job parts increases. The descending job order has the growing advantage for scheduling about 300 jobs and more. In particular, the descending job order's advantage in scheduling 100000 jobs divided in two parts each is almost 42 %. So, for total weighted completion time minimization in the preemptive scheduling problem by subsequent length-equal job importance growth, the job release dates are to be input in the descending order. However, the heuristic's job order gain in scheduling a lesser number of jobs (a few tens and up to 100, 200, 300) remains uncertain due to considerable uctuations of the much shorter computation time.