arXiv subjects

Washington A. Oliveira

Publications and source records attributed to Washington A. Oliveira.

3 recordsLinked to original sources

arXiv2019

A bi-integrated model for coupling lot-sizing and cutting-stock problems

In this paper, a framework that addresses the core of the papermaking process is proposed, starting from the production of jumbos and ending with the paper sheets used in daily life. The first phase of the process is modelled according to a lot-sizing problem, where the quantities of jumbos are determined in order to meet the demand of the entire chain. The second phase follows a one-dimensional cutting-stock formulation, where these jumbos are cut into smaller reels of predetermined lengths. Some of these are intended to fulfil a portfolio of orders, while others are used as raw material for the third phase of the process, when the reels are cut into sheets with specific dimensions and demands, following a two-dimensional cutting-stock problem. The model is called the Bi-Integrated Model, since it is composed of two integrated models. The heuristic method developed uses the Simplex Method with column generation for the two cutting-stock phases and applies the Relax-and-Fix technique to obtain the rounded-integer solution. Computational experiments comparing the solutions of the Bi-Integrated Model to other strategies of modelling the production process indicate average cost gains reaching 26.63%. Additional analyses of the model behaviour under several situations resulted in remarkable findings.

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arXiv2017

Local Pareto optimality conditions for vector quadratic fractional optimization problems

There are several concepts and definitions that characterize and give optimality conditions for solutions of a vector optimization problem. One of the most important is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. This condition ensures the existence of an arbitrary neighborhood that contains an local optimal solution. The present work we introduce an alternative concept to identify the local optimal solution neighborhood in vector optimization problems. The main aspect of this contribution is the development of necessary and sufficient Pareto optimality conditions for the solutions of a particular vector optimization problem, where each objective function consists of a ratio quadratic functions and the feasible set is defined by linear inequalities. We show how to calculate the largest radius of the spherical region centered on a local Pareto solution in which this solution is optimal. In this process we may conclude that the solution is also globally optimal. These conditions might be useful to determine termination criteria in the development of algorithms, including more general problems in which quadratic approximations are used locally.

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arXiv2017

Lot sizing problem integrated with cutting stock problem in a paper industry: a multiobjective approach

In this work, we use a multiobjective approach to address the lot sizing problem integrated with the cutting stock problem in a paper industry. We analyze the trade-offs and correlations which exist among the costs and their decision variables. Considering some of our computational results, if we decrease the production costs, then we increase the waste of material of the cutting process and vice versa. Thereby we show the importance of the multiobjective approach in allowing multiple answers to the decision maker, using Pareto optimal solutions set. Several tests were performed to check the quality of our approach.

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