In this study we are concerned with the non-exact two-stage two-dimensional guillotine cutting problem considering usable leftovers, in which stock plates remainders of the cutting patterns (non-used material or trim loss) can be used in the future, if they are large enough to fulfill future demands of items (ordered smaller plates). This cutting problem can be characterized as a residual bin-p...

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...

Introduction. In this work we consider a special variant of a two-dimensional bin packing problem where a finite number of bins of different dimensions are given, and a given set of two-dimensional rectangular items must be packed into (a subset of) these bins. This problem obviously has many practical applications, e.g. in the wood, glass and metal industry. For this particular problem variant...

The 2-dimensional Bin Packing problem is a generalization of the classical Bin Packing problems and is defined as follows: Given a collection of rectangles specified by their width and height, the goal is to pack these into minimum number of square bins of unit size. Recently, the problem was proved to be APX-hard even in the asymptotic case, i.e. when the optimum solutions requires a large num...

We introduce the Generalized Bin Packing Problem, 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 combining the cost of using the bins and the profit yielded by loading the selected items. The Generalized B...

We introduce and study the batched bin packing problem (BBPP), a bin packing problem in which items become available for packing incrementally, one batch at a time. A batched algorithm must pack a batch before the next batch becomes known. A batch may contain several items; the special case when each batch consists of merely one item is the well-studied on-line bin packing problem. We obtain lo...