AbstractIn this paper, a number of non-regular bicriteria penalty functions of completion times on a single machine are studied. In each function, one criterion is a measure of central tendency (CT) of completion times, for example, mean or median, and the other is a measure of completion time dispersion (DSP). Five different DSP measures are considered in the paper. We discuss the characterizations of optimal sequences for some new functions and summarize previous results when appropriate for the pure bicriteria problem as well as for the convex combination of CT and DSP. Further, in the context of minimizing a dispersion measure, a comparison is made between the two dispersion measures of variance of completion times and total absolute deviations of completion times (TADC).