A note on minimizing the normalized sum of squared workload deviations on m parallel processors

In this note we provide a counter-example to a central result by Ho, Tseng, Ruiz-Torres, and López (2009) who proved that a schedule which minimizes the normalized sum of squared workload deviations is necessarily a makespan-optimal one. We explain why their proof is incorrect and present some computational results revealing the difference between workload balancing and makespan minimization.