A SORTING IMPROVEMENT IN THE HEURISTIC BASED ON REMAINING AVAILABLE AND PROCESSING PERIODS TO MINIMIZE TOTAL TARDINESS IN PROGRESSIVE IDLING-FREE 1-MACHINE PREEMPTIVE SCHEDULING

Background. In preemptive job scheduling, which is a part of the flow-shop sequencing tasks, one most crucial goals to obtain schedule whose total tardiness would be minimal. Total minimization commonly reduced solving combinatorial problem becomes practically intractable as number jobs and numbers their processing periods increase. To cope with this challenge, heuristics are used. A heuristic, in decisive ratio reciprocal maximum pair remaining period available period, closely best one. However, heuristic may produce schedules few 25 % greater than minimum or even worse. Therefore, needs corrective branch further try minimize under certain conditions. Objective. The goal ascertain what corrected so that value could obtained lesser. will applied tight-tardy progressive idling-free 1-machine where release dates given ascending order starting from 1 jobs, due tightly set after dates. scheduling problem, inaccuracy finding minimal has strongest negative impact, almost worst case, defines accuracy limit positively serves just principle minimax guaranteeing decreasing losses Methods. sorts maximal ratios by dates, preference earliest job. achieve said goal, three other sorting approaches presented computational study carried out applying each four tardiness. For this, two series 266000 1064000 problems generated. Results. earliest-job ensures heuristically more 97.6 problems, but it fails no less 2.2 cases. Nevertheless, approach minimizing produces for any problem. If an exception occurs, “loses” very little. Moreover, exceptions quite rare been registered (out 31914 cases followed sole “win” version) achieved sorting. Conclusions. version uses periods. This, however, confirmed only case do not have priorities. when priority weights yet analyzed.