A space-indexed formulation of packing boxes into a larger box
Sam D. Allen, Edmund K.Burke, Jakub Marecek
TL;DR
This paper introduces a novel relaxation method for the box packing problem that enables solving larger instances more efficiently than traditional integer programming approaches.
Contribution
It proposes an alternative relaxation formulation for packing problems, improving the scalability of solving larger instances.
Findings
Successfully solves larger packing instances than previous methods
Outperforms Chen/Padberg relaxation in computational experiments
Enables practical applications of packing optimization
Abstract
Current integer programming solvers fail to decide whether 12 unit cubes can be packed into a 1x1x11 box within an hour using the natural relaxation of Chen/Padberg. We present an alternative relaxation of the problem of packing boxes into a larger box, which makes it possible to solve much larger instances.
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