We propose exact algorithms for the 2-dimensional strip packing problem (2SP) with and without 90 degrees rotations. We first focus on the perfect packing problem (PP), which is a special case of 2SP, wherein all given rectangles are required to be packed without wasted space, and design branch-and-bound algorithms introducing several branching rules and bounding operations. A combination of th...

We consider a Two-Bar Charts Packing Problem (2-BCPP), in which it is necessary to pack two-bar charts (2-BCs) unit-height strip of minimum length. The problem generalization the Bin Problem. Earlier, we proposed an $$O(n^2)$$ –time algorithm that constructs packing n arbitrary 2-BCs, whose length at most $$2\cdot OPT+1$$ , where OPT This paper proposes two new 3/2–approximate algorithms based ...

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infin...

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cuttin...

This article aims to tackle a practical three-dimensional packing problem, where a number of cartons of diverse sizes are to be packed into a bin with fixed length and width but open height. Each carton is allowed to be packed in any one of the six orientations, and the carton edges are parallel to the bin edges. The allowance of variable carton orientations exponentially increases the solution...

In this paper we propose a new exact procedure for the two-dimensional orthogonal packing problem, based on F. Clautiaux et al. approach [4]. The principle consists in searching first the positions of the items on the horizontal axis, so as that, at each position, the sum of the heights of the items does not exceed the height of the bin. Each time a valid placement of all the items is encounter...