Scheduling on parallel identical machines with late work criterion: Offline and online cases

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• 作者：Xin Chen ; Malgorzata Sterna ; Xin Han ; Jacek Blazewicz
• 关键词：Online and offline scheduling ; Identical parallel machines ; Late work ; NP ; hardness ; Competitive ratio
• 刊名：Journal of Scheduling
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：19
• 期：6
• 页码：729-736
• 全文大小：487KB
• 刊物类别：Business and Economics
• 刊物主题：Operation Research/Decision Theory; Calculus of Variations and Optimal Control; Optimization; Optimization; Artificial Intelligence (incl. Robotics); Supply Chain Management;
• 出版者：Springer US
• ISSN：1099-1425
• 卷排序：19

文摘

In the paper, we consider the problem of scheduling jobs on parallel identical machines with the late work criterion and a common due date, both offline and online cases. Since the late work criterion has not been studied in the online mode so far, the analysis of the online problem is preceded by the analysis of the offline problem, whose complexity status has not been formally stated in the literature yet. Namely, for the offline mode, we prove that the two-machine problem is binary NP-hard, and the general case is unary NP-hard. In the online mode we assume that jobs arrive in the system one by one, i.e., we consider the online over list model. We give an algorithm with a competitive ratio being a function of the number of machines, and we prove the optimality of this approach for two identical machines.