We consider the bicriteria scheduling problem of minimizing the number of tardy jobs and average flowtime on a single machine. This problem, which is known to be NP-hard, is important in practice, as the former criterion conveys the customer’s position, and the latter reflects the manufacturer’s perspective in the supply chain. We propose four new heuristics to solve this multiobjective scheduling problem. Two of these heuristics are constructive algorithms based on beam search methodology. The other two are metaheuristic approaches using a genetic algorithm and tabu-search. Our computational experiments indicate that the proposed beam search heuristics find efficient schedules optimally in most cases and perform better than the existing heuristics in the literature.