Makespan minimization in online scheduling with machine eligibility
 Kangbok Lee,
 Joseph Y.T. Leung,
 Michael L. Pinedo
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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 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 several extensions in various directions. In the concluding section we describe the most important open problems in this particular area.
 Albers, S. (2003) Online algorithms: a survey. Mathematical Programming Series B 97: pp. 326
 Azar, Y., Naor, J., Rom, R. (1995) The competitiveness of online assignments. Journal of Algorithms 18: pp. 221237 CrossRef
 BarNoy, A., Freund, A., Naor, J. (2001) Online load balancing in a hierarchical server topology. SIAM Journal on Computing 31: pp. 527549 CrossRef
 Chassid, O., Epstein, L. (2008) The hierarchical model for load balancing on two machines. Journal of Combinatorial Optimization 15: pp. 305314 CrossRef
 Chen, B., Vestjens, A. P. A. (1997) Scheduling on identical machines: how good is LPT in an online setting?. Operations Research Letters 21: pp. 165169 CrossRef
 Dosa, G., Epstein, L. (2008) Preemptive scheduling on a small number of hierarchical machines. Information and Computation 206: pp. 602619 CrossRef
 Garg, N., Kumar, A. (2007) Minimizing average flowtime: upper and lower bounds. Proceedings of the 48th annual IEEE symposium on foundations of computer science. pp. 603613
 Glass, C. A., Mills, H. R. (2006) Scheduling unit length jobs with parallel nested machine processing set restrictions. Computers & Operations Research 33: pp. 620638 CrossRef
 Graham, R. L., Lawler, E. L., Lenstra, J. K., Rinnooy Kan, A. H. G. (1979) Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics 5: pp. 287326 CrossRef
 Hall, L. A., Schulz, A. S., Shmoys, D. B., Wein, J. (1997) Scheduling to minimize average completion time: offline and online approximation algorithms. Mathematics of Operations Research 22: pp. 513544 CrossRef
 Hong, K. S., Leung, J. Y.T. (1992) Online scheduling of realtime tasks. IEEE Transactions on Computers 41: pp. 13261331 CrossRef
 Hou, L., Kang, L. (2011) Online and semionline hierarchical scheduling for load balancing on uniform machines. Theoretical Computer Science 412: pp. 10921098 CrossRef
 Hou, L., Kang, L. (2012) Online scheduling on uniform machines with two hierarchies. Journal of Combinatorial Optimization 24: pp. 593612 CrossRef
 Hwang, H.C., Chang, S. Y., Hong, Y. (2004) A posterior competitiveness for list scheduling algorithm on machines with eligibility constraints. AsiaPacific Journal of Operational Research 21: pp. 117125 CrossRef
 Hwang, H.C., Chang, S. Y., Lee, K. (2004) Parallel machine scheduling under a grade of service provision. Computers & Operations Research 31: pp. 20552061 CrossRef
 Huo, Y., Leung, J. Y.T. (2010) Parallel machine scheduling with nested processing set restrictions. European Journal of Operational Research 204: pp. 229236 CrossRef
 Huo, Y., Leung, J. Y.T. (2010) Fast approximation algorithms for job scheduling with processing set restrictions. Theoretical Computer Science 411: pp. 39473955 CrossRef
 Jiang, Y. (2008) Online scheduling on parallel machines with two GoS levels. Journal of Combinatorial Optimization 16: pp. 2838 CrossRef
 Jiang, Y., He, Y., Tang, C. (2006) Optimal online algorithms for scheduling on two identical machines under a grade of service. Journal of Zhejiang University. Science A 7: pp. 309314 CrossRef
 Karhi, S., Shabtay, D. (2012) On the optimality of the TLS algorithm for solving the onlinelist scheduling problem with two job types on a set of multipurpose machines. Journal of Combinatorial Optimization.
 Lawler, E. L., Labetoulle, J. (1978) On preemptive scheduling of unrelated parallel processors by linear programming. Journal of the ACM 25: pp. 612619 CrossRef
 Lee, K., Leung, J. Y.T., Pinedo, M. (2009) Online scheduling on two uniform machines subject to eligibility constraints. Theoretical Computer Science 410: pp. 39753981 CrossRef
 Lee, K., Leung, J. Y.T., Pinedo, M. (2010) Makespan minimization in online scheduling with machine eligibility. 4OR 8: pp. 331364 CrossRef
 Lee, K., Leung, J. Y.T., Pinedo, M. (2011) Scheduling jobs with equal processing times subject to machine eligibility constraints. Journal of Scheduling 14: pp. 2738 CrossRef
 Lenstra, J. K., Shmoys, D. B., Tardos, E. (1990) Approximation algorithms for scheduling unrelated parallel machines. Mathematical Programming 46: pp. 259271 CrossRef
 Leung, J. Y.T., Li, C.L. (2008) Scheduling with processing set restrictions: a survey. International Journal of Production Economics 116: pp. 251262 CrossRef
 Lim, K., Lee, K., Chang, S. Y. (2011) Improved bounds for online scheduling with eligibility constraints. Theoretical Computer Science 412: pp. 52115224 CrossRef
 Liu, M., Xu, Y., Chu, C., Zheng, F. (2009) Online scheduling on two uniform machines to minimize the makespan. Theoretical Computer Science 410: pp. 20992109 CrossRef
 Liu, M., Chu, C., Xu, Y., Zheng, F. (2011) Semionline scheduling on 2 machines under a grade of service provision with bounded processing times. Journal of Combinatorial Optimization 21: pp. 138149 CrossRef
 Mandelbaum, M., Shabtay, D. (2011) Scheduling unit length jobs on parallel machines with lookahead information. Journal of Scheduling 14: pp. 335350 CrossRef
 McNaughton, R. (1959) Scheduling with deadlines and loss functions. Management Science 6: pp. 112 CrossRef
 Muratore, G., Schwarz, U. M., Woeginger, G. J. (2010) Parallel machine scheduling with nested job assignment restrictions. Operations Research Letters 38: pp. 4750 CrossRef
 Noga, J., Seiden, S. S. (2001) An optimal online algorithm for scheduling two machines with release times. Theoretical Computer Science 268: pp. 133143 CrossRef
 Ou, J., Leung, J. Y.T., Li, C.L. (2008) Scheduling parallel machines with inclusive processing set restriction. Naval Research Logistics 55: pp. 328338 CrossRef
 Park, J., Chang, S. Y., Lee, K. (2006) Online and semionline scheduling of two machines under a grade of service provision. Operations Research Letters 34: pp. 692696 CrossRef
 Pruhs, K., Sgall, J., Torng, E. Online scheduling. In: Leung, J. Y.T. eds. (2004) Handbook of scheduling: algorithms, models, and performance analysis. CRC Press, Boca Raton
 Sgall, J. (1998) Online scheduling. Lecture notes in computer science. pp. 196231
 Shabtay, D., Karhi, S. (2012) Online scheduling of two job types on a set of multipurpose machines with unit processing times. Computers & Operations Research 39: pp. 405412 CrossRef
 Shabtay, D., & Karhi, S. (2012b, submitted). Online scheduling of two job types on a set of multipurpose machines (Working Paper).
 Shchepin, E. V., Vakhania, N. (2005) An optimal rounding gives a better approximation for scheduling unrelated machines. Operations Research Letters 33: pp. 127133 CrossRef
 Shmoys, D. B., Wein, J., Williamson, D. P. (1995) Scheduling parallel machines online. SIAM Journal on Computing 24: pp. 13131331 CrossRef
 Tan, Z., Zhang, A. (2010) A note on hierarchical scheduling on two uniform machines. Journal of Combinatorial Optimization 20: pp. 8595 CrossRef
 Tan, Z., Zhang, A. (2011) Online hierarchical scheduling: an approach using mathematical programming. Theoretical Computer Science 412: pp. 246256 CrossRef
 Wang, Z., Xing, W. (2010) Worstcase analysis for online service polices. Journal of Combinatorial Optimization 19: pp. 107122 CrossRef
 Wang, Z., Xing, W., Chen, B. (2009) Online service scheduling. Journal of Scheduling 12: pp. 3143 CrossRef
 Wu, Y., Ji, M., Yang, Q. (2012) Optimal semionline scheduling algorithms on two parallel identical machines under a grade of service provision. International Journal of Production Economics 135: pp. 367371 CrossRef
 Zhang, A., Jiang, Y., & Tan, Z. (2008). Optimal algorithms for online hierarchical scheduling on parallel machines (Technical Report). Zhejiang University.
 Zhang, A., Jiang, Y., Tan, Z. (2009) Online parallel machines scheduling with two hierarchies. Theoretical Computer Science 410: pp. 35973605 CrossRef
 Title
 Makespan minimization in online scheduling with machine eligibility
 Journal

Annals of Operations Research
Volume 204, Issue 1 , pp 189222
 Cover Date
 20130401
 DOI
 10.1007/s1047901212716
 Print ISSN
 02545330
 Online ISSN
 15729338
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Parallel machine scheduling
 Eligibility constraint
 Treehierarchical and GoS processing sets
 Interval and nested processing sets
 Online and semionline scheduling
 Offline scheduling
 Makespan
 Competitive ratio
 Industry Sectors
 Authors

 Kangbok Lee ^{(1)}
 Joseph Y.T. Leung ^{(2)}
 Michael L. Pinedo ^{(3)}
 Author Affiliations

 1. Department of Supply Chain Management & Marketing Sciences, Rutgers Business School, 1 Washington Park, Newark, NJ, 071023122, USA
 2. Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, 07102, USA
 3. Department of Information, Operations & Management Sciences, Stern School of Business, New York University, 44 West 4th Street, New York, NY, 100121126, USA