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Approximation schemes for single machine scheduling with non-renewable resource constraints

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Abstract

In this paper we discuss exact and approximation algorithms for scheduling a single machine with additional non-renewable resource constraints. Given the initial stock levels of some non-renewable resources (e.g., raw materials, fuel, money), and time points along with replenishment quantities, a set of resource consuming jobs has to be scheduled on the machine such that there are enough resources for starting each job, and the makespan is minimized. We show that the problem admits a pseudo-polynomial time algorithm when the number of replenishments is not part of the input, and also present an FPTAS when there is only a single resource, and it is replenished only once. We also describe a PTAS for the problem with a constant number of replenishments.

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References

  • Blazewicz, J., Lenstra, J. K., & Rinnooy Kan, A. H. G. (1983). Scheduling subject to resource constraints: classification and complexity. Discrete Applied Mathematics, 5, 11–24.

    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 

  • Briskorn, D., Jaehn, F., & Pesch, E. (2012) : Exact algorithms for inventory constrained scheduling on a single machine. Journal of scheduling (in press).

  • Carlier, J., & Rinnooy Kan, A. H. G. (1982). Scheduling subject to nonrenewable resource constraints. Operations Research Letters, 1, 52–55.

    Article  Google Scholar 

  • Carlier, J. (1984). Problèmes d’ordonnancements à contraintes de ressources: algorithmes et complexité, Thèse d’état.

  • Carlier, J. (1989). Scheduling under financial constraints. In R. Slowiński & J. Weglarz (Eds.), Advances in project scheduling (pp. 187–224). Amsterdam: Elsevier.

  • Chekuri, C., & Khanna, S. (2006). A polynomial time approximation scheme for the multiple knapsack problem. SIAM Journal on Computing, 35, 713–728.

    Article  Google Scholar 

  • Drótos, M., & Kis, T. (2013). Scheduling of inventory releasing jobs to minimize a regular objective function of delivery times. Journal of Scheduling, 16, 337–346.

    Google Scholar 

  • Gafarov, E. R., Lazarev, A. A., & Werner, F. (2011). Single machine scheduling problems with financial resource constraints: Some complexity results and properties. Mathematical Social Sciences, 62, 7–13.

    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, 5, 287–326.

    Article  Google Scholar 

  • Grigoriev, A., Holthuijsen, M., & van de Klundert, J. (2005). Basic scheduling problems with raw material constraints. Naval Research of Logistics, 52, 527–553.

    Article  Google Scholar 

  • Neumann, K., & Schwindt, C. (2002). Project scheduling with inventory constraints. Mathematical Methods of Operations Research, 56, 513–533.

    Article  Google Scholar 

  • Slowinski, R. (1984). Preemptive scheduling of independent jobs on parallel machines subject to financial constraints. European Journal of Operational Research, 15, 366–373.

    Article  Google Scholar 

  • Toker, A., Kondakci, S., & Erkip, N. (1991). Scheduling under a non-renewable resource constraint. Journal of the Operational Research Society, 42, 811–814.

    Google Scholar 

Download references

Acknowledgments

The authors are grateful to the AE and to the reviewers for constructive comments that helped to improve the presentation. This work has been supported by the research Grant ”Digital, real-time enterprises and networks”, OMFB-01638/2009. The research of Tamás Kis has been supported by the János Bólyai research grant BO/00412/12/3 of the Hungarian Academy of Sciences.

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Authors and Affiliations

  1. Department of Operations Research, Loránd Eötvös University, Pázmány Péter sétány 1/C, 1117 , Budapest, Hungary

    Péter Györgyi

  2. Computer and Automation Research Institute, Hungarian Academy of Sciences, Kende Str. 13–17, 1111 , Budapest, Hungary

    Tamás Kis

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  1. Péter Györgyi
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  2. Tamás Kis
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Correspondence to Tamás Kis.

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Györgyi, P., Kis, T. Approximation schemes for single machine scheduling with non-renewable resource constraints. J Sched 17, 135–144 (2014). https://doi.org/10.1007/s10951-013-0346-9

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  • DOI: https://doi.org/10.1007/s10951-013-0346-9

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