Abstract
In this paper, we address multiple container loading problems, consisting of placing rectangular boxes, orthogonally and without overlapping, inside containers in order to optimize a given objective function, generally maximizing the value of the packed boxes or minimizing the number of containers required to pack all available boxes. Four techniques to enumerate the possible locations of boxes inside a container, some of them not yet tested in the literature, are evaluated. We also propose new techniques to obtain primal and dual bounds for these problems. In addition, we study the constraints related to box orientation, load stability, and separation of boxes. Detailed analysis on well-known benchmark instances shows that our method is very competitive, generating mathematical models containing significantly fewer variables and constraints than the traditional approach existing in the literature. We test our methods on five different benchmark sets. We provide a detailed comparison with different approaches from the CLP literature, proving new optimal solutions and improving the best-known results for several instances.
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