Heuristics for Online Scheduling on Identical Parallel Machines with Two GoS Levels

摘要

This paper considers the online scheduling problem on m (m ≥ 3) parallel machines (the first k machines with grade 1 and the remaining m-k machines with grade 2) with two GoS levels and makespan as the objective function.The jobs arrive over time with grade 1 or 2 and an arrival job can be assigned to a machine only when the grade of the job is no less than the grade of the machine.Three cases are considered:(i) For k =1,the authors present an online algorithm with competitive ratio of 9/5.(ii) For 1 ＜ k ＜ m-1,an online algorithm with competitive ratio of 2.280 is proposed.(iii) For k =m-1,an online algorithm is presented with competitive ratio of 2.All the three algorithms are based on greedy algorithm with a similar structure.At last,numerical instances are given and the average competitive ratios of the instances show good performance of the proposed algorithms.