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Complexity of single machine scheduling subject to nonnegative inventory constraints

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  • Briskorn, Dirk
  • Choi, Byung-Cheon
  • Lee, Kangbok
  • Leung, Joseph
  • Pinedo, Michael

Abstract

This paper focuses on single machine scheduling subject to inventory constraints. Jobs either add items to an inventory or remove items from that inventory. Jobs that have to remove items cannot be processed if the required number of items is not available. We consider scheduling problems on a single machine with the minimization of the total weighted completion time, the maximum lateness, and the number of tardy jobs, respectively, as objective and determine their computational complexity. Since the general versions of our problems turn out to be strongly NP-hard, we consider special cases by assuming that different jobs have certain parameter values in common. We determine the computational complexity for all special cases when the objective is either to minimize total completion time or to minimize maximum lateness and for several special cases when the objective is either to minimize total weighted completion time or to minimize the number of tardy jobs.

Suggested Citation

  • Briskorn, Dirk & Choi, Byung-Cheon & Lee, Kangbok & Leung, Joseph & Pinedo, Michael, 2010. "Complexity of single machine scheduling subject to nonnegative inventory constraints," European Journal of Operational Research, Elsevier, vol. 207(2), pages 605-619, December.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:605-619
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    Cited by:

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    6. Buijs, Paul & Vis, Iris F.A. & Carlo, Héctor J., 2014. "Synchronization in cross-docking networks: A research classification and framework," European Journal of Operational Research, Elsevier, vol. 239(3), pages 593-608.
    7. Györgyi, Péter & Kis, Tamás, 2017. "Approximation schemes for parallel machine scheduling with non-renewable resources," European Journal of Operational Research, Elsevier, vol. 258(1), pages 113-123.
    8. Péter Györgyi & Tamás Kis, 2015. "Approximability of scheduling problems with resource consuming jobs," Annals of Operations Research, Springer, vol. 235(1), pages 319-336, December.
    9. Saeid Rezaei & Amirsaman Kheirkhah, 2018. "A comprehensive approach in designing a sustainable closed-loop supply chain network using cross-docking operations," Computational and Mathematical Organization Theory, Springer, vol. 24(1), pages 51-98, March.
    10. Gehring, Marco & Volk, Rebekka & Schultmann, Frank, 2022. "On the integration of diverging material flows into resource‐constrained project scheduling," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1071-1087.
    11. Davari, Morteza & Ranjbar, Mohammad & De Causmaecker, Patrick & Leus, Roel, 2020. "Minimizing makespan on a single machine with release dates and inventory constraints," European Journal of Operational Research, Elsevier, vol. 286(1), pages 115-128.

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