A new algorithm for the minimal-area convex enclosure problem

Article Abstract:

An algorithm to solve the minimal-area convex enclosure problem is introduced. The problem, which is a special class of nesting problems usually encountered in the garment and sheet metal industries, computes the arrangement of two polygons in a module to minimize the area of their convex enclosure. The algorithm, which is implemented via an envelope-generation code, is unique in that the convex enclosure area is defined as a function of sliding distance and dynamically maintains the vertices of the convex enclosure.

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Solution approaches to irregular nesting problems

Article Abstract:

The one-dimensional cutting stock problem was numerically analyzed to determine whether it possesses the modified integer round-up property. The latter is inherent in linear integer minimization problems (IP) where the 'optimal value of any instance of IP is lesser than than the optimal value of the corresponding linear programming relaxation problems rounded up plus one.' The results were obtained via a procedure that may also be used as a heuristic to solve the cutting-stock problem.

Operations research, Management science, Linear programming, Case studies, Integer programming, Packing for shipment, Packing (Shipments)

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Compaction and separation algorithms for non-convex polygons and their applications

Article Abstract:

Algorithms for separating and compacting a tightly packed two-dimensional, non-overlapping layout of convex and non-convex polygons are developed. The compaction problem is solved via an algorithms using a velocity-based optimization model and a position-based optimization model, respectively. The latter, which improved the computational speed of the compaction algorithm, also led to an efficient separation algorithm.

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