Annals of Operations Research

, Volume 271, Issue 2, pp 1079–1085 | Cite as

A note: minimizing total absolute deviation of job completion times on unrelated machines with general position-dependent processing times and job-rejection

  • Baruch Mor
  • Gur MosheiovEmail author
Short Note


We study a scheduling problem with the objective of minimizing total absolute deviation of completion times (TADC). TADC is considered here in the most general form studied so far: the machine setting is that of parallel unrelated, job processing time are assumed to be position-dependent with no restrictions on the functional form, and the option of processing only a subset of the jobs (i.e., job-rejection) is allowed. We show that minimizing TADC in this very general form remains polynomially solvable in the number of jobs.


Scheduling Unrelated machines Total absolute deviation of completion times Position-dependent processing times Job-rejection 



This research was supported by the Israel Science Foundation (Grant No. 1286/14). The second author was also supported by the Charles I. Rosen Chair of Management, and by The Recanati Fund of The School of Business Administration, The Hebrew University, Jerusalem, Israel.


  1. Agnetis, A., Billaut, J.-C., Gawiejnowicz, S., Pacciarelli, D., & Soukhal, A. (2014). Multiagent scheduling: Models and algorithms. Berlin: Springer.CrossRefGoogle Scholar
  2. Agnetis, A., & Mosheiov, G. (2017). Scheduling with job-rejection and position-dependent processing times on proportionate flowshops. Optimization Letters, 11, 885–892.CrossRefGoogle Scholar
  3. Ben-Yehoshua, Y., Hariri, E., & Mosheiov, G. (2015). A note on minimising total absolute deviation of job completion times on a two-machine no-wait proportionate flowshop. International Journal of Production Research, 53, 5717–5724.CrossRefGoogle Scholar
  4. Chen, S. H., Mani, V., & Chen, Y. H. (2015). Bi-criterion single machine scheduling problem with a past-sequence-dependent setup times and learning effect. In Proceedings of the 2015 IEEE IEEM (pp. 185–189).Google Scholar
  5. Gawiejnowicz, S. (2008). Time-dependent scheduling. Berlin, Heidelberg: Springer.CrossRefGoogle Scholar
  6. Gerstl, E., Mor, B., & Mosheiov, G. (2017). Minmax scheduling with acceptable lead-times: Extensions to position-dependent processing times, due-window and job rejection. Computers and Operations Research, 83, 150–156.CrossRefGoogle Scholar
  7. Gerstl, E., & Mosheiov, G. (2017). Single machine scheduling problems with generalized due-dates and job-rejection. International Journal of Operations Research, 55, 3164–3172.Google Scholar
  8. Huang, X., & Wang, M. Z. (2011). Parallel identical machines scheduling with deteriorating jobs and total absolute differences penalties. Applied Mathematical Modeling, 35, 1349–1353.CrossRefGoogle Scholar
  9. Ji, M., & Cheng, T. C. E. (2010). Scheduling with job-dependent learning effects and multiple rate-modifying activities. Information Processing Letters, 110, 460–463.CrossRefGoogle Scholar
  10. Kanet, J. (1981). Minimizing variation of flow time in single machine systems. Management Science, 27, 1453–1459.CrossRefGoogle Scholar
  11. Koulamas, C., & Kyparisis, G. J. (2008). Single machine scheduling problems with past-sequence-dependent setup times. European Journal of Operational Research, 187, 1045–1049.CrossRefGoogle Scholar
  12. Li, Y., Li, G., Sun, L., & Xu, Z. (2009). Single machine scheduling of deteriorating jobs to minimize total absolute differences in completion times. International Journal of Production Economics, 118, 424–429.CrossRefGoogle Scholar
  13. Mani, V., Chang, P. C., & Chen, S. H. (2011). Single-machine scheduling with past-sequence-dependent setup times and learning effects: A parametric analysis. International Journal of Systems Science, 42, 2097–2102.CrossRefGoogle Scholar
  14. Mor, B., & Mosheiov, G. (2011). Total absolute deviation of job completion times on uniform and unrelated machines. Computers and Operations Research, 38, 660–665.CrossRefGoogle Scholar
  15. Mor, B., & Mosheiov, G. (2016). Minimizing maximum cost on a single machine with two competing agents and job rejection. Journal of The Operational Research Society, 67, 1524–1531.CrossRefGoogle Scholar
  16. Mosheiov, G. (2008). Minimizing total absolute deviation of job completion times: Extensions to position-dependent processing times and parallel identical machines. Journal of the Operational Research Society, 59, 1422–1424.CrossRefGoogle Scholar
  17. Mosheiov, G., & Strusevich, V. (2017). Determining optimal sizes of bounded batches with rejection via quadratic min-cost flow. Naval Research Logistics, 64, 217–224.CrossRefGoogle Scholar
  18. Oron, D. (2008). Single machine scheduling with simple linear deterioration to minimize total absolute deviation of completion times. Computers and Operations Research, 35, 2071–2078.CrossRefGoogle Scholar
  19. Ou, J., Zhong, X., & Wang, G. (2015). An improved heuristic for parallel machine scheduling with rejection. European Journal of Operational Research, 241, 653–661.CrossRefGoogle Scholar
  20. Pei, J., Cheng, B., Liu, X., Pardalos, P. M., & Kong, M. (2017). Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time. Annals of Operations Research.
  21. Rudek, R. (2012). Scheduling problems with position dependent job processing times: Computational complexity results. Annals of Operations Research, 196, 491–516.CrossRefGoogle Scholar
  22. Shabtay, D., Gaspar, N., & Kaspi, M. (2013). A survey on offline scheduling with rejection. Journal of Scheduling, 16, 3–28.CrossRefGoogle Scholar
  23. Stirzaker, D. (1994). Elementary probability. Cambridge: Cambridge University Press.Google Scholar
  24. Sun, L.-H., Cui, K., Chen, J.-H., Wang, J., & He, X.-C. (2013). Research on permutation flow shop scheduling problems with general position-dependent learning effects. Annals of Operations Research, 211, 473–480.CrossRefGoogle Scholar
  25. Thevenin, S., Zufferey, N., & Widmer, M. (2015). Metaheuristics for a scheduling problem with rejection and tardiness penalties. Journal of scheduling, 18, 89–105.CrossRefGoogle Scholar
  26. Wang, D. J., Yin, Y., & Liu, M. (2016). Bicriteria scheduling problems involving job rejection, controllable processing times and rate-modifying activity. International Journal of Production Research, 54, 3691–3705.CrossRefGoogle Scholar
  27. Yang, D. L., & Kuo, W. H. (2009). Single machine scheduling with both deterioration and learning effects. Annals of OR, 172, 315–327.CrossRefGoogle Scholar
  28. Yang, D. L., & Kuo, W. H. (2010). Some scheduling problems with deteriorating jobs and learning effects. Computers & Industrial Engineering, 58, 25–28.CrossRefGoogle Scholar
  29. Zhong, X., Pan, Z., & Jiang, D. (2017). Scheduling with release times and rejection on two parallel machines. Journal of combinatorial Optimization, 33, 934–944.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Economics and Business AdministrationAriel UniversityArielIsrael
  2. 2.School of Business AdministrationThe Hebrew UniversityJerusalemIsrael

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