Approximate algorithms for unrelated machine scheduling to minimize makespan

Abstract

We study two unrelated machine scheduling problems with machine dependent release dates to minimize the makespan.For the case with fixed processing time where processing job $j$ on machine $i$ requires time $p_{ij}$ and incurs a cost of $c_{ij}$,we derive a $2$-approximation algorithm. For the problem with variable processing times where the cost increases linearly as the processing time decreases, we propose a $(2+\epsilon)$-approximation algorithm.