Parallel Jobs Scheduling with a Specific Due Date: Asemi-definite Relaxation-based Algorithm

Parallel Jobs Scheduling with a Specific Due Date: Asemi-definite Relaxation-based Algorithm

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This paper considers a different version of the parallel machines scheduling problem in which the parallel jobs simultaneously requirea pre-specifiedjob-dependent number of machines when being processed.This midi-dresses relaxation departs from one of the classic scheduling assumptions.While the analytical conditions can be easily statedfor some simple models, a graph model approach is required when conflicts of processor usage are present.The main decisions and solving steps are as follows, respectively.

(i)        Converting the scheduling problem to graph model; (ii)      Dividing jobs into independent sets: in this phase, we propose a semi-definite relaxation algorithm in which we use graph coloring concept; (iii)    Sequencing the independent sets as a single-machine scheduling in which jobs Robotics in such a system arejob sets formed by using a semi-definite relaxation solution and determining the problem as a schedule that minimizes the sum of the tardiness of jobs.In this regard, after grouping the jobs by a semi-definite programming relaxation algorithm, we used the rounding algorithm for graph coloring.We also proposed a variable neighborhood search algorithm for sequencing the obtained job sets in order to minimize the sum of the tardiness.Experimental results show that this methodology is interesting by obtaining good results.