The analysis of algorithm for three machines scheduling with general eligibility

Online parallel machine scheduling problems have been studied by many researchers and enormous results are appeared in the last 40 years. With the development of scheduling theory and application, new online scheduling problems where the partial information is known in advance, that is, semi-online, gained much interest due to their increased application in practice. So we consider the online scheduling of three machines with general eligibility and its semi-online variant where the total processing time is known in advance. For the online and semi-online problems, we develop algorithms with competitive ratio of 5/2 which are shown to be optimal.