n independent jobs are to be scheduled nonpreemptively on a single machine so as to minimize some performance measure. Federgruen and Mosheiov (F and M) show that a large class of such scheduling problems can be optimized by solving either a single instance or a finite sequence of instances of the so-called SQC problem, in which all the jobs have a fixed or controllable common due date and the sum of general quasiconvex functions of the job completion times is to be minimized. In this note the authors point out that this is not always true. In particular, they show that the algorithm proposed by F and M does not always find a global optimal schedule to the problem of minimizing the weighted sum of the mean and variance of job completion times.
