Given bins of size B, non-negative values d and ∆, and a list L of items, each item e ∈ L with size se and class ce, we define a shelf as a subset of items packed inside a bin with total items size at most ∆ such that all items in this shelf have the same class. Two subsequent shelves must be separated by a shelf division of size d. The size of a shelf is the total size of its items plus the si...

Using simulation, we compare three offline packing heuristics for adjustable-size bins, a problem derived from operating room scheduling, on 500 days of generated data using different cost structures. Unlike classical bin-packing studies, we found that next-fit-decreasing is the best performing method. Subject Areas: Simulation, Bin Packing, OR and Scheduling.

We consider a variant of the generalized assignment problem (GAP) where the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (aminimum quantity). We provide several complexity results for different versions of the problem and give polynomial time exact algorithms and approximation algorithms for restricted cases. For the mo...

In variable sized bin packing, a number of bin types are given and the goal is to pack a list of items by choosing appropriate bins such that the total size of bins used is minimized. In this paper, we present absolute worst-case analysis for on-line algorithms. Then we consider an related problem: how to design k different bin sizes such that for any item list the waste space of bins used is m...

It is well known that the two simple algorithms for the classic bin packing problem, NF and WF both have an approximation ratio of 2. However, WF seems to be a more reasonable algorithm, since it never opens a new bin if an existing bin can still be used. Using resource augmented analysis, where the output of an approximation algorithm, which can use bins of size b > 1, is compared to an optima...

The two-dimensional discrete bin-packing problem (2BP ) consists in minimizing the number of identical rectangles used to pack a set of smaller rectangles. This problem is NP-complete. It occurs in industry if pieces of steel, wood, or paper have to be cut from larger rectangles. It belongs to the family of cutting and packing (C & P) problems, more precisely Two-Dimensional Single Bin Size Bin...

We introduce a novel variant of the well known d-dimensional bin (or vector) packing problem. Given a sequence of non-negative d-dimensional vectors, the goal is to pack these into as few bins as possible. In the classical problem the bin size vector is given and the sequence can be partitioned arbitrarily. We study a variation where the vectors have to be packed in the order in which they arri...

We are given a sequence of items that can be packed into m unit size bins. In the classical bin packing problem we x the size of the bins and try to pack the items in the minimum number of such bins. In contrast, in the bin-stretching problem we x the number of bins and try to pack the items while stretching the size of the bins as least as possible. We present two on-line algorithms for the bi...

We present the Generalized Bin Packing Problem (GBPP), a new packing problem where, given a set of items characterized by volume and profit and a set of bins with given volumes and costs, one aims to select the subsets of profitable items and appropriate bins to optimize an objective function which combines the cost of using the bins and the profit yielded by loading the selected items. The GBP...

The condensation and evaporation rates predicted by bin and bulk microphysics schemes in the same model framework are compared in a statistical way using simulations of non-precipitating shallow cumulus clouds. Despite other fundamental disparities between the bin and bulk condensation parameterizations, the differences in condensation rates are predominantly explained by accounting for the wid...