# Un-restricted Common Due-Date Problem with Controllable Processing Times - Linear Algorithm for a Given Job Sequence

### Abhishek Awasthi, Jörg Lässig, Oliver Kramer

#### Abstract

This paper considers the un-restricted case of the Common Due-Date (CDD) problem with controllable processing times. The problem consists of scheduling jobs with controllable processing times on a single machine against a common due-date to minimize the overall earliness/tardiness and the compression penalties of the jobs. The objective of the problem is to find the processing sequence of jobs, the optimal reduction in the processing times of the jobs and their completion times. In this work, we first present and prove an essential property for the controllable processing time CDD problem for the un-restricted case along with an exact linear algorithm for optimizing a given job sequence for a single machine with a run-time complexity of O(n), where n is the number of jobs. Henceforth, we implement our polynomial algorithm in conjunction with a modified Simulated Annealing (SA) algorithm and Threshold Accepting (TA) to obtain the optimal/best processing sequence while comparing the two heuristic approaches, as well. The implementation is carried out on appended CDD benchmark instances provided in the OR-library.

#### References

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#### Paper Citation

#### in Harvard Style

Awasthi A., Lässig J. and Kramer O. (2015). **Un-restricted Common Due-Date Problem with Controllable Processing Times - Linear Algorithm for a Given Job Sequence** . In *Proceedings of the 17th International Conference on Enterprise Information Systems - Volume 1: ICEIS,* ISBN 978-989-758-096-3, pages 526-534. DOI: 10.5220/0005398205260534

#### in Bibtex Style

@conference{iceis15,

author={Abhishek Awasthi and Jörg Lässig and Oliver Kramer},

title={Un-restricted Common Due-Date Problem with Controllable Processing Times - Linear Algorithm for a Given Job Sequence},

booktitle={Proceedings of the 17th International Conference on Enterprise Information Systems - Volume 1: ICEIS,},

year={2015},

pages={526-534},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005398205260534},

isbn={978-989-758-096-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Conference on Enterprise Information Systems - Volume 1: ICEIS,

TI - Un-restricted Common Due-Date Problem with Controllable Processing Times - Linear Algorithm for a Given Job Sequence

SN - 978-989-758-096-3

AU - Awasthi A.

AU - Lässig J.

AU - Kramer O.

PY - 2015

SP - 526

EP - 534

DO - 10.5220/0005398205260534