Abstract

Abstract
Real-world distribution problems raise some practical considerations that usually are not considered in a realistic way in more theoretical studies. One of these considerations is related to the vehicle capacity, not only in terms of cubic meters or weight capacity but also in terms of the cargo physical arrangements. In a distribution scene, two combinatorial optimization problems, the vehicle routing problem with time windows and the container loading problem, are inherently related to each other. This work presents a framework to integrate these two problems using two different resolution methods. The first one treats the problem in a sequential approach, while the second uses a hierarchical approach. To test the quality and efficiency of the proposed approaches, some test problems were created based on the well-known Solomon, Bischoff and Ratcliff test problems. The results of the integrated approaches are presented and compared with results of the vehicle routing problem with time windows and the container loading problem applied separately.

Abstract
The nesting (or placement) problem is an NP-hard combinatorial problem with important industrial applications, e.g. in apparel or footwear industry. This paper describes a hardware infrastructure to accelerate the processing of the underlying geometric information. The system consists of an FPGA-based reconfigurable platform enhanced by an ASIC for the processing of irregular polygons. The paper discusses the need for such a platform, establishes the main design guidelines and describes the architecture and modes of operation of both the reconfigurable infrastructure and the dedicated IC.

Abstract
This paper introduces a new upper bound to the problem of fitting identical circles into a rectangle. This problem is usually referred to as the ‘cylinder packing problem’ or ‘cylinder palletization’. In practice, it arises when it is desired to maximize the number of cylindrical items packed in an upright position onto a rectangle/pallet. The upper bound developed consists in determining the reduced pallet area by deducting a lower bound for the unused pallet area from the total area of the pallet. The upper bound for the number of identical circles to pack into the pallet is computed by the ratio reduced pallet area/circle area. The results obtained for five distinct sets of problems are analyzed and compared with previous bounds found in the published literature. International Federation of Operational Research Societies 2001.

Abstract
The nesting problem consists of defining the cutting plan of a piece of raw material in smaller irregular shapes, and has applications in the apparel and footwear industries. Due to its NP-hard nature, the optimal solution can only be guaranteed by exhaustively trying all possible solutions and choosing the best one. Because this is impractical in real-life industrial problems, automatic approaches are based on optimization meta-heuristics that search for sub-optimal but good enough solutions. These optimization techniques rely on the construction and evaluation of several solutions, thus requiring heavy geometric manipulation of the irregular polygons that constitute the problem data. Efficient processing of this geometric information is thus necessary to make effective fully automatic approaches to nesting problems in industrial environments. This paper describes Fafner, an FPGA-based custom computing machine that is used to accelerate the geometric operations, that are in the core of heuristic solutions to the nesting problem. The system is used as an auxiliary processor attached to a low cost personal computer, and combines a custom programmable processor with an array of custom circuits for the processing of irregular polygons.

Abstract
This paper deals with the two-dimensional cutting problem in which the pieces involved in the cutting process are rectangles and the number of times a piece may appear in a cutting pattern is bounded. A modified algorithm, which is an improved version of Wang's algorithm, is presented. The computational performance of both algorithms is illustrated and compared by tests applied to a large number of randomly generated problems. The algorithms were implemented in a microcomputer. © 1990.