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 presents two new solution procedures for a deterministic lot size problem, a matrix algorithm and a heuristic matrix method. The algorithm is based on the dual of a linear programming model formulation of the lot size problem, and it provides optimal solutions even in the general case of time-varying parameters. A comparison of the efficiency of the new solution procedures with well-known methods is developed. New applications of the techniques described within the fields of engineering (optimal design of a pump-pipe system) and economics (a model for import-planning) are referred to. © 1984 Taylor & Francis Group, LLC.

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 reports the main results relative to a project concerning the development of a simulation-based scheduler (System SABE - Sistema de Apoio an Balanceamento e Escalonamento) for a manufacturing system, in a large Portuguese footwear industry. The physical system under consideration is, basically, a flexible flow line (the Transporter) and an automatic warehouse, which supplies the line with boxes containing the mix of components. The implementation of such a system is a response to the need of technological innovation to face new challenges in this fashion industrial sector. The flexibility of the line allows the system to manufacture simultaneously various products in lower quantities, but it also increases the complexity of the line balancing and the automatic selection of the boxes, from the warehouse - therefore the relevance of a software system to support production scheduling in the lines. The simulation model is described and it is explained that it may be used to analyse an ongoing production plan and to effectively support and guide the scheduling of all the operations in the line. The simulation package used is SIMPLE ++. The main results, which can be obtained by the system SABE, are presented. Conclusions are drawn, in particular the practical advantages reported by the footwear industry.

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.