COLUMN GENERATION TECHNIQUE FOR SOLVING TWO-DIMENSIONAL CUTTING STOCK PROBLEMS: METHOD OF STRIPE APPROACH

K. Novianingsih, R. Hadianti, S. Uttunggadewa

Abstract


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


Keywords


cutting stock problem, integer programming, mix integer programming, col- umn generation technique.

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DOI: https://doi.org/10.22342/jims.13.2.65.161-172

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Journal of the Indonesian Mathematical Society
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