We address a dynamic single-machine scheduling problem where the objective is to minimize the weighted absolute deviation of completion times from the due dates. This objective approximates a decisionmaker's goal in a just-in-time environment which is the primary motivation for the problem. Several heuristics are developed and tested. We use a novel approach to heuristic development by designing it in modules. At each decision epoch, the front end provides a lookahead feature, the main theme develops a sequence, and the balancing routine determines the schedule. The performance of the heuristics as well as modules of the heuristics are tested by simulation experiments across several classes of problems. By analysing the results we develop some guidelines for operational decisions.