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

Abstract
Assortment selection problems with cutting policies play an important role in several industries but, possibly due to their combinatorial characteristics, they did not receive as much attention as cutting stock problems did, though the two problems are closely related. In this paper we graph several examples of cost functions of one and two-dimensional problems which reveal that many local optima with cost close to optimum exist. Several implementations of known meta-heuristics are tested with a real problem. Two different neighbourhood structures are considered and the different performance of the implemented heuristics is briefly discussed.

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
The integrated planning of several activities implicated in paper production can lead to remarkable gains in terms of raw materials and resource usage. However, activities such as order assignment, production sequencing and cutting planning are usually addressed separately while ignoring the interactions among these processes. But the quality of the solution resulting from the juxtaposition of the partial solutions is not guaranteed, and may have a significant impact in terms of inefficiency of global performance. This article considers production planning in a pulp and paper industry in order to meet a set of orders of diverse types of products, admitting the possibility of producing simultaneously in two or more paper machines with their own features. The developed approach, ASC-3Steps, considers not only cutting optimisation but also extends itself to the processes of assigning orders to paper machines and production sequencing at each machine. Minimisation of wasted paper is assumed to be the overall goal. A set of computational results based on real data is presented.