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Scheduling of inventory releasing jobs to satisfy time-varying demand: an analysis of complexity

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Abstract

This paper studies a new class of single-machine scheduling problems, which are faced by Just-in-Time-suppliers satisfying a given demand. In these models the processing of jobs leads to a release of a predefined number of product units into inventory. Consumption is triggered by predetermined time-varying, and product-specific demand requests. While all demands have to be fulfilled, the objective is to minimize the resulting product inventory. We investigate different subproblems of this general setting with regard to their computational complexity. For more restricted problem versions strongly polynomial time algorithms are presented. In contrast to this, NP-hardness in the strong sense is proven for more general problem versions. Moreover, for the most general version, even finding a feasible solution is shown to be strongly NP-hard.

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References

  • Bock, S. (2010). Real-time control of freight forwarder transportation networks integrating multimodal transports and multiple transshipments. European Journal of Operational Research, 200, 733–746.

    Article  Google Scholar 

  • Boysen, N., & Bock, S. (2011). Scheduling just-in-time part supply for mixed-model assembly lines. European Journal of Operational Research, 211, 15–25.

    Article  Google Scholar 

  • Boysen, N., & Fliedner, M. (2010). Cross dock scheduling: classification, literature review and research agenda. Omega, 38, 413–422.

    Article  Google Scholar 

  • Briskorn, D., Choi, B.-C., Lee, K., Leung, J., & Pinedo, M. (2010). Complexity of single machine scheduling subject to nonnegative inventory constraints. European Journal of Operational Research, 207, 605–619.

    Article  Google Scholar 

  • Bülbül, K., Kaminsky, P., & Yano, C. (2004). Flow shop scheduling with earliness, tardiness, and intermediate inventory holding cost. Naval Research Logistics, 51, 407–445.

    Article  Google Scholar 

  • Chand, S., & Schneeberger, H. (1988). Single machine scheduling to minimize weighted earliness subject to no tardy jobs. European Journal of Operational Research, 34, 221–230.

    Article  Google Scholar 

  • Frederickson, G. (1983). Scheduling unit-time tasks with integer release times and deadlines. Information Processing Letters, 16, 171–173.

    Article  Google Scholar 

  • Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of np-completeness. San Francisco: Freeman.

    Google Scholar 

  • 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, 4, 287–326.

    Article  Google Scholar 

  • Kellerer, H., Kotov, V., Rendl, F., & Woeginger, G. J. (1998). The stock size problem. Operations Research, 46, S1–S12.

    Article  Google Scholar 

  • Lenstra, J. K., Rinnooy Kan, A. H. G., & Brucker, P. (1979). Complexity of machine scheduling problems. Annals of Discrete Mathematics, 1, 343–362.

    Article  Google Scholar 

  • Park, M.-W., & Kim, Y.-D. (2000). A branch and bound algorithm for a production scheduling problem in an assembly system under due date constraints. European Journal of Operational Research, 123, 504–518.

    Article  Google Scholar 

  • Monma, C. L. (1980). Sequencing to minimize the maximum job cost. Operations Research, 28, 942–951.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Operations Management, Friedrich-Schiller-Universität Jena, Carl-Zeiß-Straße 3, 07743, Jena, Germany

    Nils Boysen & Malte Fliedner

  2. Lehrstuhl für Wirtschaftsinformatik und Operations Research, Bergische Universität Wuppertal, Gaußstraße 20, 42097, Wuppertal, Germany

    Stefan Bock

Authors
  1. Nils Boysen
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  2. Stefan Bock
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  3. Malte Fliedner
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Correspondence to Nils Boysen.

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Boysen, N., Bock, S. & Fliedner, M. Scheduling of inventory releasing jobs to satisfy time-varying demand: an analysis of complexity. J Sched 16, 185–198 (2013). https://doi.org/10.1007/s10951-012-0266-0

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