Semi-online scheduling with known partial information about job sizes on two identical machines

Abstract

In this paper we consider the semi-online scheduling problem with known partial information about job sizes on two identical machines, where all the jobs have processing times in the interval [ p , t p ] ( p > 0 , t ≥ 1 ) and the maximum job size is t p . The objective is to minimize the makespan. For 1 ≤ t < 4 3 and t ≥ 2 , we obtain lower bounds t + 1 2 and 4 3 on the optimal solution, respectively, which match the upper bounds given by He and Zhang (1999) in [2]. For 4 3 ≤ t < 2 , we prove that a lower bound on the optimal solution is max { 4 t + 4 3 t + 4 , 2 t t + 1 } and design an algorithm with a competitive ratio equal to this lower bound.