期刊
ANNALS OF OPERATIONS RESEARCH
卷 179, 期 1, 页码 343-368出版社
SPRINGER
DOI: 10.1007/s10479-008-0456-5
关键词
Mathematical modeling; Cutting and packing; Phi-function; Geometry; Nofit polygon
资金
- Engineering and Physical Sciences Research Council [GR/S52421/01] Funding Source: researchfish
The article reviews the concept of and further develops phi-functions (I broken vertical bar-functions) as an efficient tool for mathematical modeling of two-dimensional geometric optimization problems, such as cutting and packing problems and covering problems. The properties of the phi-function technique and its relationship with Minkowski sums and the nofit polygon are discussed. We also describe the advantages of phi-functions over these approaches. A clear definition of the set of objects for which phi-functions may be derived is given and some exceptions are illustrated. A step by step procedure for deriving phi-functions illustrated with examples is provided including the case of continuous rotation.
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