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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 twomachine 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.

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International Handbooks on Information Systems is a series of volumes offering state-of-the-art surveys on selected topics of information theory and applications.The scope of the series comprises topics such as architectures of information systems, enterprise architecture, data management in information systems, electronic commerce, knowledge management, ontologies and others. To date more than a dozen volumes have been published, some of them in multiple editions.The objective is to involve contributors who are the authoritative figures in this area of information systems in each volume in order to provide a reference source for problem solvers in business, industry, and government, which can also be used by professional researchers and graduate students.

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