Title: A faster exact method for large-scale knapsack problems with setup costs and times

Authors: Tomiyasu Ichimura; Ryuichi Yokoyama; Hideki Magori

Addresses: Solutions Business Division, Energy Solutions Business Unit, Fujitsu Limited, 17-25, Shin-Kamata 1-chome, Ota-ku, Tokyo, Japan ' Graduate School of Environment and Energy Engineering, Waseda University, 4-1, Okubo 3-chome, Shinjuku-ku, Tokyo, Japan ' ARK Information Systems, Inc., 4-2, Gobancho, Chiyoda-ku, Tokyo, Japan

Abstract: A class of 0-1 knapsack problems having both setup costs and setup times in the classified item groups is treated. This class emerged relatively newly among many variants of the knapsack problems, and its fast solution methods for the large-scale instances are not yet published to the authors' best knowledge. From this viewpoint, the authors have proposed an extended exact method to tackle the large-scale ones much faster than that of the latest published. The proposed method can solve the instances with 10,000 groups and 1,000,000 items in a few seconds at the best performance. Some computational results are also given.

Keywords: 0-1 knapsack problems; setup times; setup costs; large-scale knapsack problems; branch and bound; relaxation; heuristics; pegging.

DOI: 10.1504/IJOR.2012.047517

International Journal of Operational Research, 2012 Vol.14 No.4, pp.485 - 504

Available online: 25 Jun 2012 *

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