Semi-online scheduling problems on two identical machines with inexact partial information

Abstract

In semi-online scheduling problems, we always assume that some partial additional information is exactly known in advance. This may not be true in some applications. This paper considers semi-online scheduling problems on two identical machines with inexact partial information. Three versions are considered, where we know in advance that the total size of all jobs, the optimal value, and the largest job size are in given intervals, respectively, while their exact values are unknown. We give both lower bounds of the problems and competitive ratios of algorithms as functions of a so-called disturbance parameter r ∈ [ 1 , ∞ ) . We establish for which r the inexact partial information is useful to improve the performance of a semi-online algorithm with respect to its pure online problem. Optimal or near optimal algorithms are then obtained.