Scheduling jobs with equal processing times subject to machine eligibility constraints
We consider the problem of nonpreemptively scheduling a set of n jobs with equal processing times on m parallel machines so as to minimize the makespan. Each job has a prespecified set of machines on which it can be processed, called its eligible set. We consider the most general case of machine eligibility constraints as well as special cases of nested and inclusive eligible sets. Both online and offline models are considered. For offline problems we develop optimal algorithms that run in polynomial time, while for online problems we focus on the development of optimal algorithms of a new and more elaborate structure as well as approximation algorithms with good competitive ratios.
KeywordsParallel machine scheduling Eligibility constraint Nested and inclusive eligible sets Equal-processing-time jobs Online and offline scheduling Makespan Competitive ratio Worst-case ratio
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- Chen, B., Potts, C. N., & Woeginger, G. J. (1998). In D.-Z. Du & P. M. Pardalos (Eds.), Handbook of combinatorial optimization : Vol. 3. A review of machine scheduling: complexity, algorithms and approximability (pp. 21–169). Boston: Kluwer Academic. Google Scholar
- Garey, M. R., & Johnson, D. S. (1978). Strong NP-completeness results: Motivation, examples, and implications. Journal of the Association for Computing Machinery, 25, 499–508. Google Scholar
- Leung, J. Y.-T., & Li, C.-L. (2008). Scheduling with processing set restrictions: a survey. International Journal of Production Economics, 116, 251–262. Google Scholar
- Pinedo, M. L. (1995). Scheduling—theory, algorithms and systems. New York: Prentice Hall. Google Scholar