Abstract

Abstract
This paper presents a very special cutting path determination problem appearing in a high precision tools factory, and provides two new heuristics for its resolution. Particular features of both the cutting process, and of the material to be cut, bring in a set of unusual constraints, when compared with other cutting processes, which confer additional complexity and originality to the problem. In particular, this is a matter of practical and economic relevance, since the solution methods are intended to be implemented in a real-life industrial environment. The concept of dynamic graph is exploited to deal with the arc routing problem under study, which is modelled as a dynamic rural postman problem. The constructive heuristics developed, the "higher up vertex heuristic" (HUV) and the "minimum empty path heuristic" (MEP) are tested with real data sets.

Abstract
In this paper we present a new constructive algorithm for nesting problems. The layout is built by successively adding a new piece to a partial solution, i.e. to the set of pieces previously nested. Several criteria to choose the next piece Co place and its orientation are proposed and tested. Different objective functions are also proposed to evaluate and compare partial solutions. A total of 126 variants of the algorithm, generated by the complete set of combinations of criteria and objective functions, are computationally tested. The computational experiments are based on data sets published in the literature or provided by other authors. In some cases this new algorithm generates better solutions than the best known (published) solutions.

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.

Abstract
This work describes a real-world industrial problem of production planning and cutting optimization of reels and sheets, occurring at a Portuguese paper mill. It will focus on a particular module of the global problem, which is concerned with the determination of the width combinations of the items involved in the planning process: the main goal consists in satisfying an order set of reels and sheets that must be cut from master reels. The width combination process will determine the quantity/weight of the master reels to be produced and their cutting patterns, in order to minimize waste, while satisfying production orders. A two-phase approach has been devised, naturally dependent on the technological process involved. Details of the models and solution methods are presented. Moreover some illustrative computational results are included.

Abstract
When dealing with cutting problems, the generation of usable leftovers proved to be a good strategy for decreasing material waste. Focusing on practical applications, the main challenge in the implementation of this strategy is planning the cutting process to produce leftovers with a high probability of future use without complete information about the demand for any ordered items. We addressed the two-dimensional cutting stock with usable leftovers and uncertainty in demand, a complex and relevant problem recurring in companies due to the unpredictable occurrence of customer orders. To deal with this problem, a two-stage formulation that approximates the uncertain demand by a finite set of possible scenarios was proposed. Also, we proposed a matheuristic to support decision-makers by providing good-quality solutions in reduced time. The results obtained from the computational experiments using instances from the literature allowed us to verify the matheuristic performance, demonstrating that it can be an efficient tool if applied to real-life situations.