In this paper, it is shown that dynamic optimization problems of first-order systems can be transformed into a static parametric programming problem, where the state plays the role of the parameter. Thus, an optimal f...
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In this paper, it is shown that dynamic optimization problems of first-order systems can be transformed into a static parametric programming problem, where the state plays the role of the parameter. Thus, an optimal feedback law is obtained. This concept is applied to the die-sinking electrical discharge machining, a highly time varying industrial process which necessitates adaptation of machining settings during operation. It is shown that the minimum-time operation of this process is equivalent to choosing the manipulated variables that maximizes the speed of machining at every position. (C) 2004 Elsevier B.V. All rights reserved.
We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a n...
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We present an algorithm for generating a subset of non-dominated vectors of multiple objective mixed integer linear programming. Starting from an initial non-dominated vector, the procedure finds at each iteration a new one that maximizes the infinity-norm distance from the set dominated by the previously found solutions. When all variables are integer, it can generate the whole set of non-dominated vectors. (c) 2006 Elsevier B.V. All rights reserved.
Most research work and refinery decision makers mainly focus on direct planning results such as the optimal combination of raw materials, unit loads, and production rates. There exists much more useful hidden informat...
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Most research work and refinery decision makers mainly focus on direct planning results such as the optimal combination of raw materials, unit loads, and production rates. There exists much more useful hidden information from an LP model such as marginal values of the feed stocks, the intermediate products, and the final products than direct planning results. One of the limitations of using marginal values is that they are only applied for stream flows at the solution point. We have no idea how these marginal values are changed beyond the solution. To tackle this problem, two analytical methods, namely sensitivity analysis ( SA) and parametric programming ( PP), are proposed and applied in MVA ( marginal value analysis). With these two analysis methods, MVA can be extended beyond the solution point and applied to process constraints. This article first uses a simple gasoline blending example to illustrate the required modeling techniques and procedures for performing these analyses. Then a multi-period refinery case study is presented to show how to interpret the results and apply the analyses to a real world refinery. The approach proposed here can be of great help for debottlenecking, retrofitting, pricing, and investment evaluation. The analytical methods proposed can also be generally applied to other chemical plants.
A method for obtaining continuous solutions to convex quadratic and linear programs with parameters in the linear part of the objective function and right-hand side of the constraints is presented. For parameter value...
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A method for obtaining continuous solutions to convex quadratic and linear programs with parameters in the linear part of the objective function and right-hand side of the constraints is presented. For parameter values for which the problem has nonunique solutions, the optimizer with the least Euclidean norm is selected. The normal cone optimality condition is utilized to obtain a unique polyhedral representation of the piecewise affine minimizer function.
Zero-wait (ZW) is a special type of batch operation in which products are processed without being stored in order to produce a number of low volume high value-added chemical products. Because of its economic impact, t...
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Zero-wait (ZW) is a special type of batch operation in which products are processed without being stored in order to produce a number of low volume high value-added chemical products. Because of its economic impact, there have been a number of studies on the scheduling of ZW processes. However, they are mainly focusing on formulating it into mathematical optimization problems assuming deterministic information. In reality, parameters in the ZW scheduling problem are subject to variation, which may make a fixed schedule suboptimal or even infeasible. Therefore. the scheduling problem has to be solved over and over again using the varying parameters. In order to overcome the inefficiency of such repeated computations, this paper introduces parametric programming technique for solving the ZW scheduling problem under uncertainty. The main advantage using the proposed technique is that a complete map of optimal schedules is obtained as a simple function of varying parameters. A new optimal schedule is thus obtained as a simple function evaluation instead of additional resource-expensive optimization computations. Computational experience with the proposed model and algorithm is presented in the form of two numerical examples. (c) 2006 Elsevier Ltd. All rights reserved.
In this paper two methods are presented for deriving the explicit model-based tracking optimal control law for constrained linear dynamic systems subject to persistent disturbances. The first scheme augments explicitl...
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In this paper two methods are presented for deriving the explicit model-based tracking optimal control law for constrained linear dynamic systems subject to persistent disturbances. The first scheme augments explicitly the model dynamics with a set of integral states that are then readily incorporated with a positive definite penalty in the system performance measure. The second scheme employs a state observer for estimating the value of the disturbance and then computes the new state target. Then it shifts accordingly the state and control values to ensure asymptotic tracking. The underlying controller structure in both approaches is derived off-line via parametric programming before any actual process implementation takes place. The proposed control schemes guarantee steady-state offset elimination and optimal performance in the presence of unknown constant uncertainties.
In this paper we present a solution method for fuzzy multiobjective integer nonlinear programming (FMOINLP) problems and the stability of this solution. An interactive stability compromise programming method for solvi...
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In this paper we present a solution method for fuzzy multiobjective integer nonlinear programming (FMOINLP) problems and the stability of this solution. An interactive stability compromise programming method for solving (FMOINLP) problems by using the compromise weights from the pay-off table of membership function for each objective function is presented. (c) 2005 Elsevier Inc. All rights reserved.
In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures;this wi...
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In some of the recently developed algorithms for convex parametric quadratic programs it is implicitly assumed that the intersection of the closures of two adjacent critical regions is a facet of both closures;this will be referred to as the facet-to-facet property. It is shown by an example, whose solution is unique, that the facet-to-facet property does not hold in general. Consequently, some existing algorithms cannot guarantee that the entire parameter space will be explored. A simple modification, applicable to several existing algorithms, is presented for the purpose of overcoming this problem. Numerical results indicate that, compared to the original algorithms for parametric quadratic programs, the proposed method has lower computational complexity for problems whose solutions consist of a large number of critical regions. (c) 2006 Elsevier Ltd. All rights reserved.
This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both prof...
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This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.
This paper investigates the consistency of efficiency frontier methods applied at the aggregate level. We estimate eight aggregate production frontiers on a sample of 93 countries, depending on three methodological ch...
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This paper investigates the consistency of efficiency frontier methods applied at the aggregate level. We estimate eight aggregate production frontiers on a sample of 93 countries, depending on three methodological choices for the specification of the frontier: the choice of the approach technique (stochastic frontier approach or data envelopment analysis), the specification of human capital as an input, and the nature of returns to scale. We observe some differences on the descriptive statistics of the distributions of the efficiency scores, but also a very high significant and positive correlation between scores rankings regardless of the methodological choices made. Our results tend then to suggest the consistency of the efficiency techniques at the aggregate level. (C) 2004 Elsevier B.V. All rights reserved.
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