Makespan minimization in online scheduling with machine eligibility

In this paper we provide a survey of online scheduling in parallel machine environments with machine eligibility constraints and the makespan as objective function. We first give a brief overview of the different parallel machine environments and then survey the various types of machine eligibility constraints, including treehierarchical processing sets, Grade of Service processing sets, interval processing sets, and nested processing sets. We furthermore describe the relationships between the various different types of processing sets. We proceed with describing two basic online scheduling paradigms, namely online over list and online over time. For each one of the two paradigms we survey all the results that have been recorded in the literature with regard to each type of machine eligibility constraints. We obtain also This work is supported in part by the NSF Grant CMMI-0969830. M. L. Pinedo is supported in part by the NSF Grant CMMI-0969755. K. Lee Department of Supply Chain Management and Marketing Sciences, Rutgers Business School, 1 Washington Park, Newark, NJ 07102-3122, USA e-mail: [email protected] J. Y.-T. Leung Department of Computer Science, New Jersey Institute of Technology, Newark, NJ 07102, USA e-mail: [email protected] M. L. Pinedo (B) Department of Information, Operations and Management Sciences, Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012-1126, USA e-mail: [email protected]