Abstract
In this paper we investigate two single machine scheduling problems. The first problem addresses a class of the two-stage scheduling problem in which the first stage is job production and the second stage is job delivery. For the case that jobs are processed on a single machine and delivered by a single vehicle to one customer area, with the objective of minimizing the time when all jobs are completed and delivered to the customer area and the vehicle returns to the machine, an approximation algorithm with a worst-case ratio of 5/3 is known and no approximation can have a worst-case of 3/2 unless P = NP. We present an improved approximation algorithm with a worst-case ratio of 53/35, which only leaves a gap of 1/70. The second problem is a single machine scheduling problem subject to a period of maintenance. The objective is to minimize the total completion time. The best known approximation algorithm has a worst-case ratio of 20/17. We present a polynomial time approximation scheme.
Research supported by the TRAPOYT of China and NSFC (10271110, 60021201).
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© 2005 Springer-Verlag Berlin Heidelberg
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He, Y., Zhong, W., Gu, H. (2005). Improved Algorithms for Two Single Machine Scheduling Problems. In: Megiddo, N., Xu, Y., Zhu, B. (eds) Algorithmic Applications in Management. AAIM 2005. Lecture Notes in Computer Science, vol 3521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496199_9
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DOI: https://doi.org/10.1007/11496199_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26224-4
Online ISBN: 978-3-540-32440-9
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