Abstract
We consider the well-known d-dimensional Orthogonal Packing Problem (OPP-d). Using the toolset of conservative scales introduced by Fekete and Schepers we are able to change items’ sizes of the initial instance to obtain an equivalent instance with the same solution. In this paper, we present efficient algorithm for building equivalent instances with certain properties.We also consider the so-called raster model for OPP-d introduced by Belov, Kartak, Rohling and Scheithauer. It is a 0/1 ILP model in which the number of variables and constraints depends on the total number of raster points over all dimensions. Using our algorithm, we construct equivalent instances with a reduced number of raster points. We also present an algorithm to find a lower bound on the minimum possible number of raster points over all equivalent instances. Numerical results are presented.
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