Semi-online scheduling with machine cost

• Published in: Journal of computer science and technology Vol. 17; no. 6; pp. 781 - 787
• Main Authors: He, Yong, Cai, Shengyi
• Format: Journal Article
• Language: English
• Published: Beijing Springer Nature B.V 01.11.2002; Department of Mathematics, Zhejiang University, Hangzhou 310027, P.R. China%Department of Mathematics, Wenzhou Teachers' College, Wenzhou 325000, P.R. China
• Subjects: Algorithms; Competition; Computer aided scheduling; Computer simulation; Lower bounds; Mathematical models; On-line systems; Online; Operations research; Ratios; Schedules; Scheduling; Studies; competitive ratio; scheduling; machine cost; analysis of algorithm; semi-online
• ISSN: 1000-9000; 1860-4749
• DOI: 10.1007/BF02960768

For most scheduling problems the set of machines is fixed initially and remains unchanged for the duration of the problem. Recently Imreh and Nogaproposed to add the concept of machine cost to scheduling problems and considered the so-calledList Model problem. An online algorithm with a competitive ratio 1.618 was given while the lower bound is 4/3. In this paper, two different semi-online versions of this problem are studied. In the first case, it is assumed that the processing time of the largest job is knowna priori. A semi-online algorithm is presented with the competitive ratio at most 1.5309 while the lower bound is 4/3. In the second case, it is assumed that the total processing time of all jobs is known in advance. A semi-online algorithm is presented with the competitive ratio at most 1.414 while the lower bound is 1.161. It is shown that the additional partial available information about the jobs leads to the possibility of constructing a schedule with a smaller competitive ratio than that of online algorithms.