RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Semi on-line algorithms for the partition problem
Operations Research Letters
Ordinal algorithms for parallel machine scheduling
Operations Research Letters
Semi-online scheduling with decreasing job sizes
Operations Research Letters
Semi-on-line scheduling with ordinal data on two uniform machines
Operations Research Letters
Online scheduling with machine cost and rejection
Discrete Applied Mathematics
Online scheduling with general machine cost functions
Discrete Applied Mathematics
Semi-online algorithms for scheduling with machine cost
Journal of Computer Science and Technology
Information Sciences: an International Journal
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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-called List 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 known a 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. 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.