By Gleb Belov, Guntram Scheithauer, Cláudio Alves, José M. Valério de Carvalho (auth.), Andreas Bortfeldt, Jörg Homberger, Herbert Kopfer, Giselher Pankratz, Reinhard Strangmeier (eds.)

This anthology includes contributions addressing present demanding situations and ways of clever choice aid in companies. the most foci are on:
- quantitative choice difficulties in transportation, construction, finance and marketing
- enterprise strategy optimization and data structures layout
- specified difficulties of clever choice help that have their resource in parts resembling human assets administration, info administration and fiscal concept.
greater than 50 authors from Germany and overseas representing varied learn fields starting from desktop technology over arithmetic to monetary idea have contributed to this anthology that's released at the get together of the sixty fifth birthday of Hermann Gehring, Professor of data structures on the collage in Hagen, Germany.

Die Beiträge dieses Sammelbandes behandeln aktuelle Probleme und Lösungsansätze der intelligenten Entscheidungsunterstützung in Unternehmen. Die Schwerpunkte sind:
- Quantitative Entscheidungsprobleme aus delivery, Produktion, Finanzierung und Marketing
- Optimierung von Geschäftsprozessen und Gestaltung von Informationssystemen
- spezielle Aspekte intelligenter Entscheidungsunterstützung, die u. a. den Gebieten der Personalwirtschaft, des Informationsmanagement und der Volkswirtschaftslehre entstammen
Über 50 Vertreter verschiedener Fachgebiete der Wirtschaftswissenschaft sowie der Informatik und Mathematik aus dem In- und Ausland haben zu dem Sammelband beigetragen, der aus Anlass des sixty five. Geburtstages von Hermann Gehring, Professor für Wirtschaftsinformatik an der FernUniversität in Hagen, herausgegeben wird.

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Oliveira As this algorithm is quite complex, we will present a small step by step example to better illustrate its application. Fig. 11 to Fig. 16 illustrate the application of Fekete and Scheper’s algorithm to a packing problem of five rectangles. Let the OPP-2 P=(V,w) be defined by 0 1 V={0,1,2,3,4} w (0) = (4,4), w (1) = (5,5), w (2) = (4,5), w (3) = (2,4), w (4) = (3,4), w (Container ) = (9,9) 3 2 4 4 Fig. 11. Data example of a packing. e. the edges ( b,c ) where wi ( b ) + wi ( c ) > wi ( C ) .

6 presents one unfeasible packing pattern where property P1 fails. By the theorem of Gilmore and Hoffman this graph is not an interval graph because there is a C4; therefore it does not satisfy property P1. Node 2 sees nodes 0, 1 and 3; node 4 sees the nodes 0 and 1. Node 0 sees nodes 2 and 4, but this is only feasible if node 0 sees node 1, as we can see in Fig. 6. 2 Unfeasible visibility graph Fails P1 1 4 0 0 2 4 1 3 3 G0 projection xx Fig. 6. G0 Example in which P1 fails. Property P2: A stable set S of Gi.

It is then possible to overcome this shortcome without applying Fekete and Schepers’ construction algorithm? Why does this happen? The only property that places any constraints on the dimensions of the packing is P2, limiting the size of each stable set of the graphs to fit in the container. Nevertheless, one must not forget that a visibility graph represents only the overlapping projections of the rectangles on one given direction. In an actual packing, the graphs may induce empty space between some rectangles in the container (which is not directly represented in the graphs) and therefore the computed size of the stable set is only lower bound for the size of the actual stable set.

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