A note on Lehtonen’s schedule on parallel processors

In this note a stochastic scheduling problem on parallel processors to minimize total flowtime as considered by Lehtonen is dealt with. Lehtonen has given an optimal schedule when job contents are exponentially distributed. However, it is observed that the result is much stronger in the sense that it holds good even in the more general case, i.e., when the random job contents can be ordered in likelihood ratio.