Meeting due dates as a reflection of customer satisfaction is one of the scheduling criteria that is frequently encountered in today's manufacturing environments. The natural quantification of this qualitative goal involves tardiness related measures. In this study, we consider the dynamic job shop scheduling problem with the weighted tardiness criterion. After we present a comprehensive literature survey on the topic, we measure the long-run performances of more than 20 single-pass dispatching rules under various experimental conditions. In this study, we pay special attention to recently proposed dispatching heuristics such as CEXSPT, CR + SPT, S/RPT + SPT, and Bottleneck Dynamics (BD). We also investigate the effects of six resource pricing schemes proposed recently for ED. Moreover, we extend the earlier versions of inserted idleness and identify the conditions in which these techniques can be applied without incurring too much computational cost. Future research directions are also outlined in light of the computational results.