Manufacturing and service organizations routinely face the challenge of scheduling jobs, orders, or individual customers in a schedule that optimizes either (i) an aggregate efficiency measure, (ii) a measure of performance balance, or (iii) some combination of these two objectives. We address these questions for single-machine job scheduling systems with fixed or controllable due dates. We show that a large class of such problems can be optimized by solving either a single instance or a finite sequence of instances of the so-called (SQC) problem, in which the sum of general quasiconvex functions of the jobs' completion times is to be minimized. To solve a single instance of (SQC), we develop an efficient, though pseudopolynomial algorithm, based on dynamic programming. The algorithm generates a solution that is optimal among all schedules whose starting time is restricted to the points of a prespecified (arbitrary) grid. The algorithm is embedded in an iterative procedure, where in each iteration a specific instance of (SQC) is solved. Special attention is given to the simultaneous minimization of the mean and variance of completion times.