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

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,tp] (p>0,t<1) and the maximum job size is tp. The objective is to minimize the makespan. For 1≤t<43 and t<2, we obtain lower bounds t+12 and 43 on the optimal solution, respectively, which match the upper bounds given by He and Zhang (1999) in [2]. For 43≤t<2, we prove that a lower bound on the optimal solution is max4t+43t+4,2tt+1 and design an algorithm with a competitive ratio equal to this lower bound.