Joseph Y.-T. Leung New Jersey Institute of Technology 33.

In the recent paper [2] we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a “good and fast” packing or covering. In that paper we mainly dealt with only one possible online BP/CD model, and proposed a new method that we call the “Evolution of Algorithms”. In case of such met...

The vector bin packing problem (VBP) is a generalization of bin packing with multiple constraints. In this problem we are required to pack items, represented by p-dimensional vectors, into as few bins as possible. The multiple-choice vector bin packing (MVBP) is a variant of the VBP in which bins have several types and items have several incarnations. We present an exact method, based on an arc...

Given a set of identical capacitated bins, a set of weighted items and a set of precedences among such items, we are interested in determining the minimum number of bins that can accommodate all items and can be ordered in such a way that all precedences are satisfied. The problem, denoted as the Bin Packing Problem with Precedence Constraints (BPP-P), has a very intriguing combinatorial struct...

We study a variant of the classical bin-packing problem, the ordered open-end bin-packing problem, where first a bin can be filled to a level above 1 as long as the removal of the last piece brings the bin’s level back to below 1 and second, the last piece is the largest-indexed piece among all pieces in the bin. We conduct both worst-case and average-case analyses for the problem. In the worst...

The analytical calculation of the area moments inertia used for special mechanical tests in materials science and further generalizations different orders broader symmetry properties has led to a new type trigonometric power sums. corresponding generalized equations are presented, proven, their characteristics discussed. Although sums have basic form, results quite properties, dependent on valu...

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 ...