The Analysis of Algorithm for Four Machines Scheduling under General Eligibility Constraint

In this paper we consider the on-line problem of scheduling on four identical machines under the machine eligibility constraints, where each job can be assigned to one of a subset of admissible machines. We propose the classical LS algorithm with competitive ratio of 3 which are shown to be optimal. Also the algorithm is optimal for the semi-online versions of the problem with the total or the longest processing time known in advance.