Three-stage heuristic algorithm for three-dimensional irregular packing problem

•This paper studies a new practical problem.•New problem includes three three-dimensional packing problems.•The mathematical models of each sub-problem are defined.•A three-stage heuristic algorithm is proposed to solve this new problem.•Computational results indicate that our proposed algorithm is efficient and can yield satisfactory results. This paper studies a new practical problem which can be decomposed into three three-dimensional packing problems: three-dimensional irregular packing with variable-size cartons problem, three-dimensional variable-size bin packing problem, and the single container loading problem. Since the three sub-problems are NP-hard, searching a good solution becomes more difficult. In this paper, mathematical models of each sub-problem are developed and three-stage heuristic algorithms are proposed to solve this new problem. Experiments are conducted with random instances generated by real-life case. Computational results indicate that the proposed algorithm is efficient and can yield satisfactory results.