COLUMN GENERATION TECHNIQUE FOR SOLVING TWO-DIMENSIONAL CUTTING STOCK PROBLEMS: METHOD OF STRIPE APPROACH
| Autor: | R. Hadianti, Saladin Uttunggadewa, Khusnul Novianingsih |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Mathematical optimization
Cutting stock problem Branch and price lcsh:Mathematics cutting stock problem integer programming mix integer programming col- umn generation technique Column generation Change-making problem Pattern generation lcsh:QA1-939 Integer programming Branch and cut Stock (geology) Mathematics |
| Zdroj: | Journal of the Indonesian Mathematical Society, Vol 13, Iss 2, Pp 161-172 (2012) |
| ISSN: | 2460-0245 2086-8952 |
| Popis: | We consider two-dimensional cutting stock problems where single rectangular stocks have to be cut into some smaller rectangular so that the number of stocks needed to satisfy the demands is minimum. In this paper we focus our study to the problem where the stocks have to be cut with guillotine cutting type and fixed orientation of finals. We formulate the problem as an integer programming, where the relaxation problem is solved by column generation technique. New pattern generation is formulated based on method of stripe. In obtaining the integer solution, we round down the optimal solution of the relaxation problem and then we derive an extra mix integer programming for satisfying the unmet demands. The optimal solution of the original problem is the combination of the round-down solution and the optimal solution of the extra mix integer programming.A numerical example of the problem is given in the end of this paper.DOI : http://dx.doi.org/10.22342/jims.13.2.65.161-172 |
| Databáze: | OpenAIRE |
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