Online and offline packing cylinders in a cylindrical container

This paper addresses the Single Cylindrical Packing Problem with Cylindrical Items (SCPP-CI), which packs cylindrical items into a cylindrical container to maximize the volume utilization. Two variants of the problem are considered: the online version, where items are coming sequentially and need to be packed immediately once coming, and the offline version, where all items are given at once. A deterministic greedy heuristic algorithm is proposed for both the online and offline problems, using two special operators to obtain dense placements and evaluate the quality of feasible placements. In addition, a top-local search algorithm is introduced that considers future benefits for the offline problem. To evaluate the performance of the proposed algorithms, we first degrade the 3D problem to a corresponding packing problem of circles and then compare our results with those found (1) by the CPLEX solver, and (2) by the known heuristic for 2D benchmark instances. We generate 10 groups of the SCPP-CI problem instances (100 instances in each group) with increasing heterogeneity, and compare the results found by our approach with those found by the CPLEX solver for these instances. Computational results show that both our algorithms significantly outperform the baselines for both 2D and 3D problems, indicating the excellent performance of the proposed approach.