A single machine scheduling problem where the objective is to minimize
the variance of job completion times is considered. The model is appl
icable to many environments where it is desirable to provide jobs, cus
tomers or computer files, with approximately the same service. It is s
hown that the problem can be formulated as a problem of maximizing a z
ero-one quadratic function which is a submodular function with a speci
al cost structure. It immediately follows from the cost structure that
value of the function for a sequence that minimizes total absolute de
viation about a common unrestrictive due date is at most 100% smaller
than the one for an optimal sequence for the completion time variance
problem. The Monge property holds for the costs. Other simple properti
es of the function are also presented. A pair of dynamic programs for
maximizing the function is proposed. The worst case time complexity of
the best of the pair is O (n(2)spt), where spt is the mean flow time
of an SPT-schedule for all jobs except the longest one.