An Exact Algorithm for Constrained Two-Dimensional Two-Staged Cutting Problems

Authors:
Mhand Hifi;Rym M'Hallah
Affiliations:
-;-
Venue:
Operations Research
Year:
2005

Citing 0
Cited 9

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Abstract

Theconstrained two-dimensional cutting (C_TDC) problem consists of determining acutting pattern of a set ofn small rectangular piece types on a rectangular stock plateS with lengthL and widthW, to maximize the sum of the profits of the pieces to be cut. Each piece typei,i=1,..., n, is characterized by a lengthl i , a widthw i , a profit (or weight)c i , and an upper demand valueb i . The upper demand value is the maximum number of pieces of typei that can be cut onS. In this paper, we study the two-staged C_TDC problem, noted C_2TDC. It is a classical variant of the C_TDC where each piece is produced, in the final cutting pattern, by at most two cuts. We solve the C_2TDC problem using an exact algorithm that is mainly based on a bottom-up strategy. We introduce new lower and upper bounds and propose new strategies that eliminate several duplicate patterns. We evaluate the performance of the proposed exact algorithm on problem instances extracted from the literature and compare it to the performance of an existing exact algorithm.