Semi-online scheduling with combined information on two identical machines in parallel

Abstract

This paper is concerned with a semi-online scheduling problem with combined information on two identical parallel machines to minimize the makespan, where all the jobs have processing times in the interval $[1,\,t]$  $(t\ge 1)$ and the jobs arrive in non-increasing order of their processing times. The objective is to minimize the makespan. For $t\ge 1$, we obtain a lower bound $\max _{N=1,2,3,\ldots }\left\{ \min \{\frac{4N+3}{4N+2}\,,\frac{Nt+N+1}{2N+1}\}\right\}$ and show that the competitive ratio of the $LS$ algorithm achieves the lower bound.