Abstract
This paper presents the identical parallel machine’s scheduling problem when the jobs are submitted over time. This problem consists of assigning N various jobs to M identical parallel machines to reduce the workload imponderables among the different machines. We generalized the mixed-integer linear programming approach to decrease the workload imbalance between the different machines, and that is done by converting the problem to the mathematical model. The studied cases are presented for different problems, and it indicates to an online system, and this system does not know the arrival times of the jobs before and reduce Makespan criterion is not well appropriate to describe the utilization for this online problem. The obtained results proved good solutions for the scheduling problem compared with standard algorithms.
Highlights
Parallel manufacturing body is one of the solutions for enhancing the processing capability of a manufacturing system
This paper aims to generalize the mixed-integer linear programming approach to decrease the difference between the greats and smallest machine's workload in the definition of the appropriate functions of the approximate resolution algorithms proposed in the literature, and we selected actual the online problems where the times of jobs are not known in advance and minimizing the Makespan is not suitable away to evaluate the utilization of the online problems
We note that for the small scale instances with 7 jobs in table 4.3, both longest processing time (LPT) algorithm and MILP2R approach are similarity in difference between maximum and minimum Makespan that it is equal to one unit time but in large scale instances that show in table 4.4,4.5, 4.6 and 4.7, the MILP2R approach are better than LPT algorithm, we obtain the optimal solution in the case 3 and in case 2,4 and 5 the maximum workload imbalance obtained by LPT algorithm is equal to 2,21and 11 time units while MILP2R approach obtains an optimal solution with two time unit in case 2 and one time unit of workload imbalance in case 4 and 5
Summary
Parallel manufacturing body is one of the solutions for enhancing the processing capability of a manufacturing system. Workload balancing is serious for both the service, and manufacturing industries. In the manufacturing industry, balancing the workload among the machines is serious to minimize the idle times and work-in-process, Y. Addressed the workload balancing problem using various priorities basics such as random, the shortest processing times and longest processing times. The authors used the proportional variation of imbalance to evaluate the performances of these various strategies In their pamphlet, Rajakumar et al [14], the authors proposed a genetic algorithm (GA) that outperforms these various strategies. Raghavendra and Murthy [1] made overworks to decrease the imbalance in a random type of parallel machines addressing the loading problem in an elastic manufacturing system. Raghavendra et al [4] proposed a GA based approach with short processing time (SPT) and longest processing time (LPT) rules for a decrease in the imbalance
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