Towards Bin Packing (preliminary problem survey, models with multiset estimates)

TL;DR

This paper offers a comprehensive overview and new formulations for bin packing problems, emphasizing multiset estimates and systemic viewpoints, with applications in industry and communication systems.

Contribution

It introduces a systemic framework for bin packing problems, including new models with multiset estimates and a broad survey of related literature.

Findings

New problem formulations for multiset estimates of items

Application examples in paper industry and WiMAX communication

A systemic viewpoint on bin packing problems

Abstract

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).