Fuzzy chance constrained linear programming model for optimizing the scrap charge in steel production (original) (raw)
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Operational Strategies for Increasing Secondary Materials in Metals Production Under Uncertainty
Journal of Sustainable Metallurgy, 2016
Increased use of secondary raw materials in metals production offers several benefits including reduced cost and lowered energy burden. The lower cost of secondary or scrap materials is accompanied by an increased uncertainty in elemental composition. This increased uncertainty for different scraps, if not managed well, results in increased risk that the elemental concentrations in the final products fall outside customer specifications. Previous results show that incorporating this uncertainty explicitly into batch planning can modify the potential use of scrap materials while managing risk. Chance constrained formulations provide one approach to uncertainty-aware batch planning; however typical formulations assume normal distributions to represent the compositional uncertainty of the materials. Compositional variation in scrap materials has been shown to have a skewed distribution and, therefore, the performance of these models, in terms of their ability to provide effective planning, may then be heavily influenced by the structure of the compositional data used. To address this issue, this work developed several approximations for skewed distributional forms within chance constrained formulations. We explored a lognormal approximation based on Fenton's method; a convex approximation based on Bernstein inequalities; and a linear approximation using fuzzy set theory. Each of these methods was formulated 2 and case studies executed using compositional data from an aluminum remelter. Results indicate that the relationship between the underlying structure/distribution of the compositional data and how these distributions are formulated in batch planning can modify the use of secondary raw materials.
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Soft Computing, 2017
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Resources, Conservation and Recycling, 2007
Operational uncertainties create disincentives for use of recycled materials in metal alloy production. One that greatly influences remelter batch optimization is variation in the raw material composition, particularly for secondary materials. Currently, to accommodate compositional variation, firms commonly set production targets well inside the window of compositional specification required for performance reasons. Window narrowing, while effective, does not make use of statistical sampling data, leading to sub-optimal usage of recycled materials. This paper explores the use of a chance-constrained optimization method, which allows explicit consideration of statistical information on composition. The framework and a case study of cast and wrought production with available scrap materials are presented. Results show that it is possible to increase the use of recycled material without compromising the likelihood of batch errors, when using this method compared to conventional window narrowing. This benefit of the chance-constrained method grows with increase in compositional uncertainty and is driven by scrap portfolio diversification.
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We investigate various types of fuzzy linear programming problems based on models and solution methods. First, we review fuzzy linear programming problems with fuzzy decision variables and fuzzy linear programming problems with fuzzy parameters (fuzzy numbers in the definition of the objective function or constraints) along with the associated duality results. Then, we review the fully fuzzy linear programming problems with all variables and parameters being allowed to be fuzzy. Most methods used for solving such problems are based on ranking functions, α-cuts, using duality results or penalty functions. In these methods, authors deal with crisp formulations of the fuzzy problems. Recently, some heuristic algorithms have also been proposed. In these methods, some authors solve the fuzzy problem directly, while others solve the crisp problems approximately.
Global Journal of Research In Engineering, 2016
This paper studies the vehicle spare parts production problem to obtain the optimum production rate under fuzzy capital budget. We applied the integer goal programming technique to determine the best compromise solution. There are two goals in our case study. These goals are minimization of the uncertain capital budget and maximization of the uncertain expected profits. The case study is a factory which produces different types of vehicle heat exchangers. The results indicate that the problem solution depends on the membership function and the α- cut. The optimum quantities of heat exchangers’ production are found to be biased to the lower limit of production.
Currently, with regard to the increasing complexities in the industrial and organizational environments, the mathematical programming methods of the creation type used in the past do not meet the demands of the decision-makers of technical and managerial fields. As a result, making use of a combination of mathematical programming models and fuzzy set theory has led to creating further flexible methods and producing more reliable results for optimization problems. Thus, the main objective of applying the methods is to use the limited uncertainties in the decision-making model through the use of fuzzy logic. In the present article, a practical managerial case has been chosen to investigate how to obtain the optimum value for nonlinear programming problems using fuzzy techniques in models with uncertain resource constraints in the optimization of manufacturing and production dimensions. The modelling for this problem has led to creating a fuzzy nonlinear programming model and convertin...
Soft Computing
Linear programming (LP) has long proved its merit as the most flexible and most widely used technique for resource allocation problems in various fields. To solve an LP problem, we have traditionally considered crisp values for the parameters, which are unrealistic in real-world decision-making under uncertainty. The fuzzy set theory has been used to model the imprecise parameter values in LP problems to overcome this shortcoming, resulting in a fuzzy LP (FLP) problem. This paper proposes a new method for solving fuzzy variable linear programming (FVLP) problems in which the decision variables and resource vectors are fuzzy numbers. We show how to use the standard simplex algorithm to solve this problem by converting the fuzzy problem into a crisp one once a linear ranking function is chosen. The novelty of the proposed model resides in that it requires less effort on fuzzy computations as opposed to the existing fuzzy methods. Furthermore, to solve the FVLP problem using the existing methods, fuzzy arithmetic operations and the solution to fuzzy systems of equations are required. By contrast, only arithmetic operations of real numbers and the solution to crisp systems of equations are required to solve the same problem with the method proposed in this study. Finally, a transportation case study in the coal industry is presented to demonstrate the applicability of the proposed algorithm.