Integer linear programming models for 2-staged two-dimensional Knapsack problems

@article{Lodi2003IntegerLP,
  title={Integer linear programming models for 2-staged two-dimensional Knapsack problems},
  author={Andrea Lodi and Michele Monaci},
  journal={Math. Program.},
  year={2003},
  volume={94},
  pages={257-278}
}
We are given a unique rectangular stock of material S, with height H and width W , and a list of m rectangular shapes to be cut from S. Each shape’s type i (i = 1, . . . ,m) is characterized by a height h̄i, a width w̄i, a profit p̄i, and an upper bound ubi indicating the maximum number of items of type i which can be cut. We refer to the Two-Dimensional Knapsack (TDK) as the problem of determining a cutting pattern of S maximizing the sum of the profits of the cut items. In particular, we… CONTINUE READING