Best semi-online algorithms for unbounded parallel batch scheduling

Authors:
Jinjiang Yuan;C. T. Ng;T. C. E. Cheng
Affiliations:
Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, People's Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

We consider semi-online scheduling of an unbounded parallel batch machine to minimize the makespan where, at the present time instant t, information on the first longest job arriving after t is known. In this paper online means that jobs arrive over time, J^*(t) denotes the first longest job arriving after t, and p^*(t) and r^*(t) denote the processing time and arrival time of J^*(t), respectively. Given information p^*(t), we present an online algorithm with a competitive ratio (5-5)/2~1.382, and show that the algorithm is the best possible; furthermore, this algorithm generates at most two batches. This algorithm is also the best possible given information J^*(t). Given information r^*(t), we present an online algorithm with a competitive ratio 3/2, and show that any online algorithm cannot have a competitive ratio less than 33~1.442; furthermore, this algorithm generates at most three batches. Given information r^*(t) with the restriction that an online algorithm generates at most two batches, we present an online algorithm with a competitive ratio (5+1)/2~1.618, and show that the algorithm is the best possible.