The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan

Authors:
J. J. Yuan;Z. H. Liu;C. T. Ng;T. C. E. Cheng
Affiliations:
Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450052, People's Republic of China and Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong ...;Department of Mathematics, East China University of Science and Technology, Shanghai 200237, People's Republic of China and Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, ...;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China
Venue:
Theoretical Computer Science
Year:
2004

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Abstract

In this paper we consider the unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an O(n(n/m+1)m) time dynamic programming algorithm and an O(mkk-1p2k-1) time dynamic programming algorithm, where n is the number of jobs, m is the number of families, k is the number of distinct release dates and P is the sum of the processing times of all families. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme for the problem.