A branch-and-price algorithm for the two-dimensional vector packing problem

Lijun Wei, Minghui Lai, Andrew Lim and Qian Hu

European Journal of Operational Research, 2020, vol. 281, issue 1, 25-35

Abstract: The two-dimensional vector packing problem is a well-known generalization of the classical bin packing problem. It considers two attributes for each item and bin. Two capacity constraints must be satisfied in a feasible packing solution for each bin. The objective is to minimize the number of bins used. To compute optimal solutions for the problem, we propose a new branch-and-price algorithm. A goal cut that sets a lower bound to the objective is used. It is effective in speeding up column generation by reducing the number of iterations. To efficiently solve the pricing problem, we develop a branch-and-bound method with dynamic programming, which first eliminates conflicts between two items through branching, and then solves the two-constraint knapsack problem at leaf nodes through dynamic programming. Extensive computational experiments were conducted based on 400 test instances from existing literature. Our algorithm significantly outperformed the existing branch-and-price algorithms. Most of the test instances were solved within just a few seconds.

Keywords: Packing; Two-dimensional vector packing problem; Exact algorithm; Branch-and-price (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:281:y:2020:i:1:p:25-35

DOI: 10.1016/j.ejor.2019.08.024

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