scholarly journals Improved lower bounds for the online bin packing problem with cardinality constraints

2013 ◽  
Vol 29 (1) ◽  
pp. 67-87 ◽  
Author(s):  
Hiroshi Fujiwara ◽  
Koji Kobayashi
Keyword(s):  
Lower Bounds ◽  
Bin Packing ◽  
Packing Problem ◽  
Cardinality Constraints ◽  
Bin Packing Problem

Efficient lower bounds and heuristics for the variable cost and size bin packing problem

2011 ◽  
Vol 38 (11) ◽  
pp. 1474-1482 ◽  
Author(s):  
Teodor Gabriel Crainic ◽  
Guido Perboli ◽  
Walter Rei ◽  
Roberto Tadei
Keyword(s):  
Lower Bounds ◽  
Bin Packing ◽  
Packing Problem ◽  
Variable Cost ◽  
Bin Packing Problem

A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem

2018 ◽  
Vol 52 (2) ◽  
pp. 391-414 ◽  
Author(s):  
Mehdi Serairi ◽  
Mohamed Haouari
Keyword(s):  
Lower Bounds ◽  
Bin Packing ◽  
Computational Study ◽  
Packing Problem ◽  
Large Set ◽  
Two Dimensional ◽  
Bin Packing Problem ◽  
Benchmark Instances ◽  
Empirical Performance ◽  
Minimum Number

We address the two-dimensional bin packing problem with fixed orientation. This problem requires packing a set of small rectangular items into a minimum number of standard two-dimensional bins. It is a notoriously intractable combinatorial optimization problem and has numerous applications in packing and cutting. The contribution of this paper is twofold. First, we propose a comprehensive theoretical analysis of lower bounds and we elucidate dominance relationships. We show that a previously presented dominance result is incorrect. Second, we present the results of an extensive computational study that was carried out, on a large set of 500 benchmark instances, to assess the empirical performance of the lower bounds. We found that the so-called Carlier-Clautiaux-Moukrim lower bounds exhibits an excellent relative performance and yields the tightest value for all of the benchmark instances.

A bin packing game with cardinality constraints under the best cost rule

2019 ◽  
Vol 11 (02) ◽  
pp. 1950022
Author(s):  
Qingqin Nong ◽  
Jiapeng Wang ◽  
Suning Gong ◽  
Saijun Guo
Keyword(s):  
Cooperative Game ◽  
Bin Packing ◽  
Social Cost ◽  
Price Of Anarchy ◽  
Packing Problem ◽  
Cardinality Constraints ◽  
Bin Packing Problem ◽  
The Social ◽  
The Cost

We consider the bin packing problem with cardinality constraints in a non-cooperative game setting. In the game, there are a set of items with sizes between 0 and 1, and a number of bins each of which has a capacity of 1. Each bin can pack at most [Formula: see text] items, for a given integer parameter [Formula: see text]. The social cost is the number of bins used in the packing. Each item tries to be packed into one of the bins so as to minimize its cost. The selfish behaviors of the items result in some kind of equilibrium, which greatly depends on the cost rule in the game. We say a cost rule encourages sharing if for an item, compared with sharing a bin with some other items, staying in a bin alone does not decrease its cost. In this paper, we first show that for any bin packing game with cardinality constraints under an encourage-sharing cost rule, the price of anarchy of it is at least [Formula: see text]. We then propose a cost rule and show that the price of anarchy of the bin packing game under the rule is [Formula: see text] when [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document