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Integer linear programming models for the skiving stock problem
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DOI：10.1016/j.ejor.2015.11.005.png)
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Abstract
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We consider the one-dimensional skiving stock problem which is strongly related to 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 is an element of N smaller item lengths l(1,)...,l(m) with availabilities b(1),...,bm. For, this optimization problem, we present three new models (the arcflow model, the onestick model, and a model of Kantorovich-type) 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 the arcflow model, the onestick approach and the existing pattern-oriented standard model, In particular, this equivalence is shown to hold for the corresponding continuous relaxations, too. (C) 2015 Elsevier B.V. All rights reserved.
Keywords:
Packing
Skiving stock problem
Dual bin packing
Modeling
Continuous relaxation
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