1.State Key Laboratory of Software Development Environment, Beihang University, Beijing 100191, China; 
2.School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

Packing problem has been proved to be an NP-hard problem. Many algorithms such as simula- tion annealing algorithm, genetic algorithm and other heuristic algorithms have been proposed to solve two- dimensional and three-dimensional packing problem. To solve the cube packing problem with time schedule, this paper first introduces some concepts such as packing level, space distance and average neighbor birth order and then proposes a greedy algorithm. The algorithm tries every feasible corner greedily to calculate the space utilization, packing level, space distance, average neighbor birth order of this placement, and chooses the best placement according to these criteria. Theoretical analysis indicates that the time complexity of this algorithm is O(A²B²C²T²n⁵). The experiments show that the average space utilization of non-guillotine cutting test cases is 98.81%, and the average space utilization of guillotine cutting test cases achieves 99.87%. Furthermore, optimal solutions of more than half cases are achieved by this algorithm. The experimental results show that this algorithm can solve the problem of cube packing with time schedule effectively and efficiently.

This work was supported by the National Basic Research Program of China (Grant No. 2005CB321903), and the National High-Tech Research & Development Program of China (Grant No. 2007AA010301).