2016/05/24 by Mark Sh. Levin, Levin, Mark Sh.
Computer Science · Engineering · Mathematics · #68T20 #90B50 #93A13 #93B51 #Advanced Manufacturing and Logistics Optimization #Artificial Intelligence (cs.AI) #Computational Geometry and Mesh Generation #FOS: Computer and information sciences #FOS: Mathematics #I.2.8 #J.6 #K.4.3 #Optimization and Control (math.OC) #Optimization and Packing Problems #acm:68T20 #acm:90B50 #acm:93A13 #acm:93B51 #cs.AI #math.OC #msc:68T20 #msc:90B50 #msc:93A13 #msc:93B51
paper · pdf · doi:10.48550/arxiv.1605.07574
39 pages, 18 figures, 14 tables
arxiv created 2016/05/24 · openalex publication_date 2016/05/24 · arxiv updated 2016/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper described a generalized integrated glance to bin packing problems including a brief literature survey and some new problem formulations for the cases of multiset estimates of items. A new systemic viewpoint to bin packing problems is suggested: (a) basic element sets (item set, bin set, item subset assigned to bin), (b) binary relation over the sets: relation over item set as compatibility, precedence, dominance; relation over items and bins (i.e., correspondence of items to bins). A special attention is targeted to the following versions of bin packing problems: (a) problem with multiset estimates of items, (b) problem with colored items (and some close problems). Applied examples of bin packing problems are considered: (i) planning in paper industry (framework of combinatorial problems), (ii) selection of information messages, (iii) packing of messages/information packages in WiMAX communication system (brief description).