ILP models for the skiving stock problem

We consider the one-dimensional skiving stock problem which is also known as the dual bin packing problem: find the maximum number of items with minimum length L that can be constructed by connecting a given supply of m ∈ N smaller item lengths l1, . . . , lm with availabilities b1, . . . , bm. For this optimization problem, we present three new models and investigate their relationships, especially regarding their respective continuous relaxations. To this end, numerical computations are provided. As a main result, we prove the equivalence between two of these approaches and the existing pattern-oriented standard model. In particular, this equivalence is shown to hold for the corresponding continuous relaxations, too.