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.

Abstract

Abstract
This paper presents an application of the maximum principle and the generalized maximum principle (a recent extension of that principle) to a discrete-time model of consumer choice behaviour. The model includes two brands in a market and uses a non-stationary first-order Markov chain. The optimization is carried out by algorithms based on the above mentioned principles. These algorithms are described, and their performances are discussed and compared both with and without fulfilment of the directional convexity property.

Abstract
A two-phase roll cutting problem appearing in the iron and steel industry is considered in this paper. It consists of optimizing the planning of roll cutting that, for technological reasons, is effected in two phases, i.e., each raw material roll is cut into intermediate primary rolls, which in turn are cut to obtain the constituent rolls of the final product. Apart from an inherent complexity to the cutting problem resulting from the large variety of final product dimensions, other supplementary difficulties also exist. These are related to the existence of numerous restrictions involved in the whole process and the link between the two cutting phases. A heuristic was developed and tested, that is based on an automatic sequential search with defined objectives, so as to obtain a good compromise between pattern usage and trim loss, respecting the various technological impositions. Finally, a real example taken from the steel industry together with the solution obtained from a computerized version developed for microcomputers, is presented. © 1990.

Abstract
A problem consisting of the optimal design of a segmented wall on a surface having a nonlinear slope contour is considered. It is formulated as an optimal control problem and a solution procedure based on the Discrete Maximum Principle is developed. An application to a real case, which previously had been solved by a Dynamic Programming based method, is included together with some critical comments on the above-mentioned technique.

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.