{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T12:25:21Z","timestamp":1759667121984},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p> This paper investigates semi-online hierarchical scheduling problems on two identical machines, with the purpose of minimizing the [Formula: see text]-norm of the machines\u2019 loads. We consider two semi-online versions with knowing the total processing time [Formula: see text] of all jobs, or knowing the total processing time [Formula: see text] of the jobs of hierarchy [Formula: see text] for [Formula: see text] in advance. For the two semi-online versions, the best possible online algorithms are designed with competitive ratios of [Formula: see text] and [Formula: see text], respectively, where [Formula: see text] is the maximum value of the function [Formula: see text] in [Formula: see text]. When [Formula: see text], our results cover the known results for minimizing the makespan. <\/jats:p>","DOI":"10.1142\/s0217595919500027","type":"journal-article","created":{"date-parts":[[2018,11,6]],"date-time":"2018-11-06T21:01:08Z","timestamp":1541538068000},"page":"1950002","source":"Crossref","is-referenced-by-count":9,"title":["Semi-Online Hierarchical Scheduling on Two Machines for lp-Norm Load Balancing"],"prefix":"10.1142","volume":"36","author":[{"given":"Xianglai","family":"Qi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, Henan 450001, P. R. 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