Strip generation algorithms for constrained two-dimensional two-staged cutting problems [An article from: European Journal of Operational Research]

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Description:
The constrained two-dimensional cutting (C_TDC) problem consists of determining a cutting pattern of a set of n small rectangular piece types on a rectangular stock plate of length L and width W, as to maximize the sum of the profits of the pieces to be cut. Each piece type i, i=1,...,n, is characterized by a length l"i, a width w"i, a profit (or weight) c"i and an upper demand value b"i. The upper demand value is the maximum number of pieces of type i which can be cut on rectangle (L,W). In this paper, we study the two-staged fixed orientation C_TDC, noted FC_2TDC. It is a classical variant of the C_TDC where each piece is produced, in the final cutting pattern, by at most two guillotine cuts, and each piece has a fixed orientation. We solve the FC_2TDC problem using several approximate algorithms, that are mainly based upon a strip generation procedure. We evaluate the performance of these algorithms on instances extracted from the literature.