Annals of Operations Research

, Volume 204, Issue 1, pp 189-222

First online:

Makespan minimization in online scheduling with machine eligibility

  • Kangbok LeeAffiliated withDepartment of Supply Chain Management & Marketing Sciences, Rutgers Business School
  • , Joseph Y.-T. LeungAffiliated withDepartment of Computer Science, New Jersey Institute of Technology
  • , Michael L. PinedoAffiliated withDepartment of Information, Operations & Management Sciences, Stern School of Business, New York University Email author 

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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 tree-hierarchical 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 several extensions in various directions. In the concluding section we describe the most important open problems in this particular area.


Parallel machine scheduling Eligibility constraint Tree-hierarchical and GoS processing sets Interval and nested processing sets Online and semi-online scheduling Offline scheduling Makespan Competitive ratio