We introduce a new problem that was motivated by a (more complicated) problem arising in a robotized assembly environment. The bin coloring problem is to pack unit size colored items into bins, such that the maximum number of different colors per bin is minimized. Each bin has size B ∈ N. The packing process is subject to the constraint that at any moment in time at most q ∈ N bins are partiall...

The bin-packing problem is to partition a multiset of n numbers into as few bins of capacity C as possible, such that the sum of the numbers in each bin does not exceed C. We compare two existing algorithms for solving this problem: bin completion (BC) and branch-and-cut-and-price (BCP). We show experimentally that the problem difficulty and dominant algorithm are a function of n, the precision...

Bin packing is a well known problem which has a large number of applications. Classical bin packing is a simple model where all bins are identical. In the bin packing problem with variable sized bins, we are given a supply of a variety of sizes. This latter model assumes, however, that the cost of a bin is always defined to be its exact size. In this paper we study the more general problem wher...

A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the numbe...

by shouldering the burden of a big chunk of global production, and giving shelter to half of the world’s population, currently cities play an important role in national economies. benefits of agglomeration in cities have played a major role in the process of economic development of different countries, however, the expansion of urbanization has produced some problems including environmental and...

The following online bin packing problem is considered: Items with integer sizes are given and variable sized bins arrive online. A bin must be used if there is still an item remaining which fits in it when the bin arrives. The goal is to minimize the total size of all the bins used. Previously, a lower bound of 5 4 on the competitive ratio of this problem was achieved using jobs of size S and ...

We explore a novel theoretical model for studying the performance of distributed storage management systems where the data-centers have limited capacities (as compared to storage space requested by the users). Prior schemes such as Balls-into-bins (used for load balancing) neither consider bin (consumer) capacities (multiple balls into a bin) nor the future performance of the system after, ball...