Improved Algorithms for Two Single Machine Scheduling Problems

• Published in: Algorithmic Applications in Management pp. 66 - 76
• Main Authors: He, Yong, Zhong, Weiya, Gu, Huikun
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Knapsack Problem; Manufacturing System; Mathematical programming; Operational research and scientific management; Operational research. Management science; Polynomial Time Algorithm; Schedule Problem; Scheduling, sequencing; Single Machine; Theoretical computing; Delivery (good); Polynomial approximation; Worst case method; Algorithmics; Best approximation; Scheduling; Makespan; Maintenance; Approximation algorithm; Single machine; Mathematical programming; Polynomial time
• ISBN: 3540262245; 9783540262244
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11496199_9

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.