This paper presents the use of genetic algorithms (GA) for solving the dual bin packing problem using fuzzy objectives. In bin packing problems, a list, L of items is to be packed into a minimum number of bins. In dual bin packing the items are packed into a maximum number of bins, assuring a minimum weight for each bin. We consider a class which we call dynamic dual bin packingg. Similar to th...

We consider the two-dimensional bin packing problem (BPP): given a set of rectangular items, find the minimal number of rectangular bins needed to pack all items. Rotation of the items is not permitted. We show for any integer k ≥ 3 that at most k − 1 bins are needed to pack all items if every item fits into a bin and if the total area of items does not exceed k/4-times the bin area. Moreover, ...

Following the work of Anily et al., we consider a variant of bin packing, called BIN PACKING WITH GENERAL COST STRUCTURES (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However,...

2 West Central Research and Outreach Center, University of Minnesota, Morris; 3 Iowa State University, Ames, 4 Minnesota Extension Regional Office, Mankato; 5 Department of Animal Science, University of Minnesota, St. Paul II. Abstract: Two experiments were conducted to evaluate the effects of feed bin design and the use of passive agitators on flowability of feed containing 40% dried distiller...

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...