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 $$[1,\,t]$$[1,t] $$(t\ge 1)$$(t?1) and the jobs arrive in non-increasing order of their processing times. The objective is to minimize the makespan. For $$t\ge 1$$t?1, we obtain a lower bound $$\max _{N=1,2,3,\ldots }\left\{ \min \{\frac{4N+3}{4N+2}\,,\frac{Nt+N+1}{2N+1}\}\right\} $$maxN=1,2,3,?min{4N+34N+2,Nt+N+12N+1} and show that the competitive ratio of the $$LS$$LS algorithm achieves the lower bound.
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