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

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 Go S 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 of9/5.(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.