Computers and Operations Research
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Recently, a new approximation algorithm for the nonpreemptive scheduling of independent jobs on $m$ identical parallel processors has appeared in the literature. The algorithm, named $MPS$ (MultiProcessor Scheduling), combines partial solutions which satisfy suitable properties. Its performance ratio is bounded by $\frac{z+1}{z}-\frac{1}{mz}$, where $z$ represents the number of initial partial solutions provided by the algorithm. This note presents an advanced estimate of $z$ and, consequently, an improved worst-case performance ratio of the $MPS$ algorithm.