The worker assignment scheduling problem involves both the decisions of job scheduling and worker assignment. In this research, only the performance measure of total tardiness is investigated in the model of identical parallel machines with nonpreemptive jobs. Since the worker assignment scheduling problem in the selected model can be shown to be NP-complete, heuristics have been developed for minimising the total tardiness. The worker assignment scheduling problem is solved in two phases of job scheduling and worker assignment. The SES (SPT, EDD, SLACK) heuristic is used for the phase of job scheduling. For the phase of worker assignment, the largest marginal contribution (LMC) procedure is used to minimise the total tardiness. From the simulation conducted, 88 out of 100 simulated problems yielded optimal solutions while the others also obtained very good results. In conclusion, the heuristics developed have shown very impressive results in both effectiveness and efficiency aspects.