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What Is Cutting Stock? Essay

1289 words - 6 pages

This subset of cutting and packaging problem is NP-Hard in nature (Garey, M. R et al. (1979)). Dyckhoff
(1990) gave the first clear classification for cutting and packing problem. The characterization is based on the
fact that many are similar in their logical structure but different in application areas. There are various categories
in packing which includes cutting stock problem, knapsack, bin packing and loading problem. Cutting stock
involve cutting off available raw stock to meet customer demand such that trim loss is minimized. Knapsack is
mostly considered as a sub problem in many cases where certain weight is associated with the object. The
objective being to pack these objects in a fixed size larger container to maximize of overall weight. Bin packing
aim to pack items into bins, the dimensions are bounded, such that the remaining space in used bin is minimized
and overall bin required to pack all items is minimized. All these problems range from single to
multidimensions. Strip packing is considered in higher dimensions like two (2D) and three (3D).
The literature reveals that the rectangular strip packing is solved using many exact and inexact approaches.
Christofides et al. (1977), Beasley (1985), used tree search methods to solve guillotine and non-guillotine
variants of strip packing problem. Exact approaches like a branch and bound was used by Martello et al. (2003),
Lesh et al. (2004) modified the approach by adding pruning method with branch and bound to solve a small
subset of this problem. Another variant of branch and bound was presented by Kenmochi et al. (2009), where
the branching scheme is based on some placement scheme and bounding operation is governed by dynamic and
linear programming. However, a general observation follows with exact approach, which is as the number of
rectangles to be packed grow in number, they find difficult to get the optimal solution in acceptable time as the
time also grows exponentially. This behaviour of the exact motivates researcher to focus on heuristic and
metaheuristic approaches find optimal or near optimal solution. The benefit of using these approaches is their
ability to give approximate solutions in reasonable computing time. The most popular and common approach of
placement Bottom Left heuristic (BL) was given by Baker et al. (1980). This approach considered sequential
placement of rectangular blocks at the bottom left, where in the beginning each rectangle was placed at the top
right corner then slowly moved down till it a position where it cannot be further lowered, the block is then
shifted towards left ensuring that it resulted in no rectangular overlap. The heuristic was improved by Hopper
and Turton (2001) Bottom Left Fill (BLF) heuristic in which the gap that existed in between the already placed
rectangle was given preference while the placement of the new rectangle. The further improvement in these
strategies was observed by Asik et al. (2009) introduced Bidirectional...

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