Abstract
A possibility of speeding up the job scheduling by a heuristic based on the shortest processing period approach is studied in the paper. The scheduling problem is such that the job volume and job priority weight are increasing as the job release date increases. Job preemptions are allowed. Within this model, the input for the heuristic is formed by either ascending or descending job order. Therefore, an estimator of relative difference in duration of finding an approximate schedule by these job orders is designed. It is ascertained that the job order results in different time of computations when scheduling at least a few hundred jobs. The ascending-order solving becomes on average by 1 % to 2.5 % faster when job volumes increase steeply. As the steepness of job volumes decreases, this gain vanishes and, eventually, the descending-order solving becomes on average faster by up to 4 %. The gain trends of both job orders slowly increase as the number of jobs increases.
Highlights
TO PYRAMIDAL PREEMPTIVE JOBSCHEDULING PROBLEMSOptimal scheduling is a very important means to efficiently executing multistage processes of manufacturing, assembling, building, rendering, dispatching, etc
Job scheduling problems (JSPs), where the schedule is commonly considered without idle time intervals, are segregated in two classes, one of which allows a job to preempt, and another one does not support any preemptions [1], [3]
One of them constitutes Preemptive JSPs (PJSPs), wherein the job volume and job priority weight are increasing as the job release date increases [4], [5]
Summary
Preemptive Job Scheduling Problems for Total Weighted Completion Time Minimization. Abstract – A possibility of speeding up the job scheduling by a heuristic based on the shortest processing period approach is studied in the paper. Keywords – Heuristic, job order, job parts, job scheduling, preemption, total weighted completion time minimization. Variables or parameters, it is effectively solved by the shortest processing period approach (SPPA) [5], [8] This is a heuristic trying to minimize TWCT by executing the most expensive job first if it has the fewest parts to do [9]. When PJSPs are not pyramidal but all the jobs instead have the same volume [10], the heuristic finds an approximate schedule faster if the release dates are given in descending order (along with non-increasing priority weights) [5]. The descending job order input (DJOI) has a 1 % relative advantage in scheduling more than jobs for such non-pyramidal PJSPs. With increasing the number of jobs off 1000, this advantage has a slight tendency to increase. The question is whether a similar gain could be obtained in solving PPJSPs
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