Background: Bin packing is an NP hard optimization problem of packing items of given sizes into minimum number of capacity limited bins. Besides the basic problem, numerous other variants of bin packing exist. The cardinality constrained bin packing adds an additional constraint that the number of items in a bin must not exceed a given limit Nmax. Objectives: Goal of the paper is to present a p...

case performance bounds for simple one-dimensional packing algorithms. SIAM J. A better algorithm for an ancient scheduling problem. Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems. A new algorithm for on-line bin-packing. 44 43] G. Galambos and J. B. G. Frenk. A simple proof of Liang's lower bound for on-line bin packing and the extension to the ...

Flow reasoning has been successfully used in CP for more than a decade. It was originally introduced by Régin in the well-known Alldifferent and Global Cardinality Constraint (GCC) available in most of the CP solvers. The BinPacking constraint was introduced by Shaw and mainly uses an independent knapsack reasoning in each bin to filter the possible bins for each item. This paper considers the ...

In this paper we present a dual approximation scheme for the class constrained shelf bin packing problem. In this problem, we are given bins of capacity 1, and n items of Q different classes, each item e with class ce and size se. The problem is to pack the items into bins, such that two items of different classes packed in a same bin must be in different shelves. Items in a same shelf are pack...

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the pr...

Let $A$ and $B$ be two unital $C^{*}$-algebras and $varphi:A rightarrow B$ be a linear map. In this paper, we investigate the structure of linear maps between two $C^{*}$-algebras that preserve a certain property or relation. In particular, we show that if $varphi$ is unital, $B$ is commutative and $V(varphi(a)^{*}varphi(b))subseteq V(a^{*}b)$ for all $a,bin A$, then $varphi$ is a $*$-homomorph...

The state-of-the-art global constraint for bin packing is due to Shaw. We compare two linear continuous relaxations of the bin packing problem, based on the DP-flow and Arc-flow models, with the filtering of the bin packing constraint. Our experiments show that we often obtain significant improvements in runtime. The DP-flow model is a novel formulation of the problem.

This paper studies a variant of the three-dimensional bin packing problem (3D-BPP), where the bin height can be adjusted to the cartons it packs. The bins and cartons to be packed are assumed rectangular in shape. The cartons are allowed to be rotated into any one of the six positions that keep the carton edges parallel to the bin edges. This greatly increases the difficulty of finding a good s...