Systems reliability plays an important role in systems design, operation and management. Systems reliability can be improved by adding redundant components or increasing the reliability levels of subsystems. Determina...
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Systems reliability plays an important role in systems design, operation and management. Systems reliability can be improved by adding redundant components or increasing the reliability levels of subsystems. Determination of the optimal amount of redundancy and reliability levels among various subsystems under limited resource constraints leads to a mixed-integer nonlinear programming problem. The continuous relaxation of this problem in a complex system is a nonconvex nonseparable optimization problem with certain monotone properties. In this paper, we propose a convexification method to solve this class of continuous relaxation problems. Combined with a branch-and-bound method, our solution scheme provides an efficient way to find an exact optimal solution to integer reliability optimization in complex systems.
A multi-product, multi-stage, and multi-period production and distribution planning model is proposed in this paper to tackle the compromised sales prices and the total profit problem of a multi-echelon supply chain n...
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A multi-product, multi-stage, and multi-period production and distribution planning model is proposed in this paper to tackle the compromised sales prices and the total profit problem of a multi-echelon supply chain network with uncertain sales prices. This model is constructed as a mixed-integer nonlinear programming problem to achieve a maximum total profit of the whole network and to guarantee the maximum satisfactory levels of sellers' and buyers' preference on sales prices. For the purpose that a compensatory solution among all participants of the supply chain can be achieved, a fuzzy decision-making method is proposed and, by means of applying it to a numerical example, proved effective in providing a compromised solution in a multi-echelon supply chain network.
The production system using kanban was pioneered by Toyota Motor Company in Japan and subsequently it was adopted by numerous other Japanese and US companies for applying the just-in-time manufacturing principles. Thi...
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The production system using kanban was pioneered by Toyota Motor Company in Japan and subsequently it was adopted by numerous other Japanese and US companies for applying the just-in-time manufacturing principles. This research studies a single-stage supply chain system that is controlled by kanban mechanism. The supply chain system is modelled as a mixed-integer nonlinear programming (MINLP) problem. It is solved optimally by branch-and-bound method to determine the number of kanbans, batch size, number of batches, and the total quantity over one period. Meanwhile. the kanban operation between two adjacent plants is worked out considering the factors of loading and unloading time. and transport time. Coupled with plant-wide efforts for cost control and management commitment to enhance other measures of performance, a logistics system for controlling the production as well,is the supply chain system is developed. which results in minimizing the total cost of the supply chain system. The results show that the improvements in reduction of inventory, wasted labour, and customer service in a supply chain are accomplished through the kanban mechanism.
A multi-product, multi-stage, and multi-period scheduling model is proposed in this paper to deal with multiple incommensurable goals for a multi-echelon supply chain network with uncertain market demands and product ...
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A multi-product, multi-stage, and multi-period scheduling model is proposed in this paper to deal with multiple incommensurable goals for a multi-echelon supply chain network with uncertain market demands and product prices. The uncertain market demands are modeled as a number of discrete scenarios with known probabilities, and the fuzzy sets are used for describing the sellers' and buyers' incompatible preference on product prices. The supply chain scheduling model is constructed as a mixed-integer nonlinear programming problem to satisfy several conflict objectives, such as fair profit distribution among all participants, safe inventory levels, maximum customer service levels, and robustness of decision to uncertain product demands, therein the compromised preference levels on product prices from the sellers and buyers point of view are simultaneously taken into account. The inclusion of robustness measures as part of objectives can significantly reduce the variability of objective values to product demand uncertainties. For purpose that a compensatory solution among all participants of the supply chain can be achieved, a two-phase fuzzy decision-making method is presented and, by means of application of it to a numerical example, proved effective in providing a compromised solution in an uncertain multi-echelon supply chain network. (C) 2003 Elsevier Ltd. All rights reserved.
A multi-product, multi-stage, and multi-period scheduling model is proposed in this paper to deal with multiple incommensurable goals for a multi-echelon supply chain network with uncertain market demands and product ...
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A multi-product, multi-stage, and multi-period scheduling model is proposed in this paper to deal with multiple incommensurable goals for a multi-echelon supply chain network with uncertain market demands and product prices. The uncertain market demands are modeled as a number of discrete scenarios with known probabilities, and the fuzzy sets are used for describing the sellers' and buyers' incompatible preference on product prices. The supply chain scheduling model is constructed as a mixed-integer nonlinear programming problem to satisfy several conflict objectives, such as fair profit distribution among all participants, safe inventory levels, maximum customer service levels, and robustness of decision to uncertain product demands, therein the compromised preference levels on product prices from the sellers and buyers point of view are simultaneously taken into account. The inclusion of robustness measures as part of objectives can significantly reduce the variability of objective values to product demand uncertainties. For purpose that a compensatory solution among all participants of the supply chain can be achieved, a two-phase fuzzy decision-making method is presented and, by means of application of it to a numerical example, proved effective in providing a compromised solution in an uncertain multi-echelon supply chain network. (C) 2003 Elsevier Ltd. All rights reserved.
For large, complex reacting systems, computational efficiency becomes a critical issue in process simulation, optimization, and model-based control. Mechanism simplification is often a necessity to improve computation...
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For large, complex reacting systems, computational efficiency becomes a critical issue in process simulation, optimization, and model-based control. Mechanism simplification is often a necessity to improve computational speed. We present a novel approach to reaction mechanism simplification that formulates the model reduction problem as a mixed-integer nonlinear programming problem and solves it using DICOPT + + (discrete and continuous optimizer). Two formulations of the mechanism simplification problem are considered, one involving the elimination of reactions and the other the elimination of species. Both steady-state and dynamic problem formulations are developed. Solutions for example problems having six reactions and six species are presented. (C) 2000 Elsevier Science Ltd. All rights reserved.
This paper addresses the solution of mixed-integernonlinear mathematical programs in which the number of linear constraints far exceed the number of nonlinear constraints, and with most variables participating in the...
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This paper addresses the solution of mixed-integernonlinear mathematical programs in which the number of linear constraints far exceed the number of nonlinear constraints, and with most variables participating in the nonconvex terms. Some computer-aided molecular design models have these features. A branch-and-bound (BB) algorithm is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of branching functions, which depend linearly on the search variables. The branching functions are determined from a special tree function (STF) representation of both the objective function and constraints. In order to construct the corresponding linear underestimators, we have developed the Sweep method. The proposed algorithm scales well with problem size. Specifically, as the problem size increases, the computational effort increases almost linearly. The computational efficiency of the algorithm is demonstrated by solving a molecular design problem to global optimality. (C) 2002 Elsevier Science Ltd. All rights reserved.
This paper examines alternative models for the economic optimization of multicomponent distillation columns. Different column representations are modeled involving rigorous mixedintegernonlinearprogramming (MINLP) ...
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This paper examines alternative models for the economic optimization of multicomponent distillation columns. Different column representations are modeled involving rigorous mixedintegernonlinearprogramming (MINLP) and General Disjunctive programming (GDP) formulations. The different representations involve various ways of representing the choices for the number of trays and feed tray location. Also, alternatives are considered for modeling the heat exchange when the number of trays of the column must be determinated. A preprocessing procedure developed in a previous paper [Ind. Eng. Chem. Res. (2002a)] is extended in this work to provide good initial values and bounds for the variables involved in the economic models. This initialization scheme increases the robustness and usefulness of the optimization models. Numerical results are reported on problems involving the separation of zeotropic and azeotropic mixtures. Trends about the behavior of the different proposed alternative models are discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.
This paper addresses the relaxations in alternative models for disjunctions, big-M and convex hull model, in order to develop guidelines and insights when formulating mixed-integer Non-Linear programming (MINLP), Gene...
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This paper addresses the relaxations in alternative models for disjunctions, big-M and convex hull model, in order to develop guidelines and insights when formulating mixed-integer Non-Linear programming (MINLP), Generalized Disjunctive programming (GDP), or hybrid models. Characterization and properties are presented for various types of disjunctions. An interesting result is presented for improper disjunctions where results in the continuous space differ from the ones in the mixed-integer space. A cutting plane method is also proposed that avoids the explicit generation of equations and variables of the convex hull. Several examples are presented throughout the paper, as well as a small process synthesis problem, which is solved with the proposed cutting plane method. (C) 2002 Elsevier Science Ltd. All rights reserved.
In this study, we have introduced a fuzzy decision-making approach to design a multi-objective optimal design problem of a multiproduct batch chemical plant. In the crisp decision-making approach, the designer is firs...
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In this study, we have introduced a fuzzy decision-making approach to design a multi-objective optimal design problem of a multiproduct batch chemical plant. In the crisp decision-making approach, the designer is first to solve the multi-objective optimization problem, and then to check whether each optimal objective function value satisfies the rigid preference goal. In real world application, the preference goal for each objective function is an interval bound not a rigid value so that the problem becomes a fuzzy goal optimization problem. A monotonic increasing or decreasing membership function is used to define the degree of satisfaction for each objective function so that the fuzzy goal optimization problem is then represented as an augmented minimax problem formulated as mixed-integer nonlinear programming (MINLP) models. To obtain a unique solution, we have introduced the mixed-integer hybrid differential evolution (MIHDE) to solve the MINLP problems. The MIHDE can straightforwardly solve the problem without any mathematical model transformation. Two examples were used to illustrate the applicability of the proposed interactive algorithm. (C) 2002 Elsevier Science Ltd. All rights reserved.
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