This paper extends previous research on multi-objective additive manufacturing (AM) scheduling by introducing a comprehensive tri-objective mixed-integer linear programming (MILP) model that simultaneously optimizes makespan, energy consumption, and material waste in integrated AM and post-processing operations. Unlike existing approaches that focus primarily on printing operations, our model considers the complete production cycle including post-processing activities such as support removal, surface finishing, and quality inspection. The proposed framework addresses heterogeneous multi-machine environments with different AM technologies (FDM, SLA, SLS) and incorporates dynamic job arrivals with precedence constraints between printing and post-processing operations. We introduce novel material waste calculation methods that account for support structures, failed prints, and material preparation losses. The model is formulated as a tri-objective optimization problem using augmented \(\varepsilon \) -constraint and weighted Tchebycheff methods to generate well-distributed Pareto frontiers. Extensive computational experiments on 45 benchmark instances demonstrate that our integrated approach can reduce material waste by up to 21.3% and total energy consumption by up to 11.4% compared to sequential optimization approaches, while maintaining competitive makespan performance with only a 3.1% average increase. The results provide valuable insights for sustainable AM production planning and highlight the importance of considering post-processing operations in scheduling decisions.