Semi-Online Scheduling on Two Identical Parallel Machines with Initial-Lookahead Information

Feifeng Zheng (), Yuhong Chen (), Ming Liu and Yinfeng Xu ()
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Feifeng Zheng: Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, P. R. China
Yuhong Chen: Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, P. R. China
Ming Liu: School of Economics and Management, Tongji University, Shanghai 200092, P. R. China
Yinfeng Xu: School of Management, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2024, vol. 41, issue 01, 1-20

Abstract: This work investigates a new semi-online scheduling problem with lookahead. We focus on job scheduling on two identical parallel machines, where deterministic online algorithms only know the information of k initial jobs (i.e., the initial-lookahead information), while the following jobs still arrive one-by-one in an over-list fashion. We consider makespan minimization as the objective. The study aims at revealing the value of knowing k initial jobs, which are used to improve the competitive performance of those online algorithms without such initial-lookahead information. We provide the following findings: (1) For the scenario where the k initial jobs are all the largest jobs with length Δ, we prove that the classical LIST algorithm is optimal with competitive ratio (k + 3)/(k + 2); (2) For the scenario where the total length of these k (> 1) jobs is at least Δ, we show that any online algorithm has a competitive ratio at least 3/2, implying that the initial-lookahead knowledge is powerless since there exists a 3/2-competitive online algorithm without such information; (3) For the scenario where the total length of these k (> α) jobs is at least αΔ (α ≥ 2), we propose an online algorithm, named as LPT-LIST, with competitive ratio of (α + 2)/(α + 1), implying that the initial-lookahead information indeed helps to improve the competitiveness of those online algorithms lacking such information.

Keywords: Parallel machine scheduling; semi-online algorithm; initial lookahead; competitive ratio; value of information (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0217595923500033

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