Optimal Semi-Online Algorithm for Scheduling on Two Parallel Batch Processing Machines

Ming Liu (), Feifeng Zheng (), Zhanguo Zhu () and Chengbin Chu ()
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Ming Liu: School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
Feifeng Zheng: Glorious Sun School of Business and Management, Donghua University, Shanghai 200092, P. R. China
Zhanguo Zhu: School of Economics and Management, Nanjing Agricultural University, Nanjing 210095, P. R. China;
Chengbin Chu: Laboratoire Génie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92295, Châtenay-Malabry Cedex, France

Asia-Pacific Journal of Operational Research (APJOR), 2014, vol. 31, issue 05, 1-10

Abstract: Batch processing machine scheduling in uncertain environment attracts more and more attention in the last decade. This paper deals with semi-online scheduling on two parallel batch processing machines with non-decreasing processing time of job. Jobs arrive over time in the online paradigm, and the processing time of any batch is equal to the length of the last arrival job in the batch. We study the unbounded model where each processing batch may contain an unlimited number of jobs, and the objective is to minimize the makespan. Given any job Jj together with its following job Jj+1, it is assumed that their processing times satisfy pj+1 ≥ αpj where α ≥ 1 is a constant. That is, jobs arrive in a non-decreasing order of processing times. We mainly propose an optimal ϕ-competitive online algorithm where ϕ ≥ 1 is a solution of equation ϕ3 + (α-1)ϕ2 + (α2 - α - 1)ϕ - α2 = 0.

Keywords: Scheduling; batch processing machines; competitive analysis; online algorithm (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0217595914500389

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