In this thesis, we consider the bicriteria scheduling problem of minimizing 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 two new heuristics to solve this multiobjective scheduling problem. These two heuristics are constructive algorithms which are based on beam search methodology. We compare these proposed algorithms with three existing heuristics in the literature and two new meta-heuristics. Our computational experiments illustrate that proposed heuristics find efficient schedules optimally in most of the cases and perform better than the other heuristics.