Takustr. 7 Zuse Institute Berlin 14195 Berlin Germany FELIX PRAUSE1,KAI HOPPMANN-BAUM2,BORIS DEFOURNY3,THORSTEN KOCH4 The Maximum Diversity Assortment Selection Problem 1 0000-0001-9401-3707 2 0000-0001-9184-8215 3 0000-0003-0405-5538 4 0000-0002-1967-0077 ZIB Report 20-34 (Dezember 2020) Zuse Institute Berlin Takustr. 7 14195 Berlin Germany Telephone: +49 30-84185-0 Telefax: +49 30-84185-125 E-mail:
[email protected] URL: http://www.zib.de ZIB-Report (Print) ISSN 1438-0064 ZIB-Report (Internet) ISSN 2192-7782 The Maximum Diversity Assortment Selection Problem Felix Prause1[0000−0001−9401−3707], Kai Hoppmann-Baum1;2[0000−0001−9184−8215], Boris Defourny3[0000−0003−0405−5538], and Thorsten Koch1;2[0000−0002−1967−0077] 1 Zuse Institute Berlin, Takustr. 7, 14195 Berlin, Germany {prause,hoppmann-baum,koch}@zib.de 2 TU Berlin, Chair of Software and Algorithms for Discrete Optimization, Str. des 17. Juni 135, 10623 Berlin, Germany 3 Lehigh University, Department of Industrial and Systems Engineering, 200 W Packer Ave, Bethlehem, PA, 18015, USA
[email protected] Abstract. In this paper, we introduce the Maximum Diversity Assort- ment Selection Problem (MADASS), which is a generalization of the 2-dimensional Cutting Stock Problem (2CSP). Given a set of rectan- gles and a rectangular container, the goal of 2CSP is to determine a subset of rectangles that can be placed in the container without overlap- ping, i.e., a feasible assortment, such that a maximum area is covered. In MADASS, we need to determine a set of feasible assortments, each of them covering a certain minimum threshold of the container, such that the diversity among them is maximized.