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A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines

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Solving Computationally Expensive Engineering Problems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 97))

Abstract

This chapter presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing times but a common due-date. The objective of the problem is to minimize the total penalty incurred due to earliness or tardiness of the job completions. This work presents exact polynomial algorithms for optimizing a given job sequence for single and identical parallel machines with the run-time complexities of O(nlogn) for both cases, where n is the number of jobs. Besides, we show that our approach for the parallel machine case is also suitable for non-identical parallel machines. We prove the optimality for the single machine case and the run-time complexities of both. Henceforth, we extend our approach to one particular dynamic case of the CDD and conclude the chapter with our results for the benchmark instances provided in the OR library.

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Notes

  1. 1.

    J and J ′ are two disjoint sets of jobs, hence J + J ′ is the union of two sets maintaining the job sequences in each set.

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Acknowledgements

The research project was promoted and funded by the European Union and the Free State of Saxony, Germany. The authors take the responsibility for the content of this chapter.

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Authors and Affiliations

  1. Department of Computer Science, University of Applied Sciences Zittau/Görlitz, Görlitz, Germany

    Abhishek Awasthi & Jörg Lässig

  2. Department of Computing Science, Carl von Ossietzky University of Oldenburg, Oldenburg, Germany

    Oliver Kramer

Authors
  1. Abhishek Awasthi
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  2. Jörg Lässig
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  3. Oliver Kramer
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Corresponding author

Correspondence to Abhishek Awasthi .

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Editors and Affiliations

  1. Engineering Optimization & Modeling Center, School of Science & Engineering, Reykjavik University, Reykjavik, Iceland

    Slawomir Koziel

  2. Engineering Optimization & Modeling Center, School of Science & Engineering, Reykjavik University, Reykjavik, Iceland

    Leifur Leifsson

  3. School of Science and Technology, Middlesex University, London, United Kingdom

    Xin-She Yang

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Awasthi, A., Lässig, J., Kramer, O. (2014). A Novel Approach to the Common Due-Date Problem on Single and Parallel Machines. In: Koziel, S., Leifsson, L., Yang, XS. (eds) Solving Computationally Expensive Engineering Problems. Springer Proceedings in Mathematics & Statistics, vol 97. Springer, Cham. https://doi.org/10.1007/978-3-319-08985-0_13

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