The optimum two-dimensional allocation of irregular, multiply-connected shapes with linear, logical and geometric constraints

Abstract : The optimum two-dimensional allocation problem consists in taking some two-dimensional resource, such as a piece of cloth, a sheet of steel, or a parcel of land, and cutting it up into a number of two-dimensional forms, such as clothing patterns, sheet-metal parts, or parking spaces, in such a way that some objective, such as minimum waste of material or maximum total number of pieces, is achieved. This thesis describes the results of an investigation into methods of handling this type of problem when linear, logical, and geometric constraints, in addition to the usual area and nonoverlapping constraints, are imposed on the allocations. The investigation is concerned with two-dimensional shapes that can be irregular and either simply- or multiply-connected. (Author)