Fenchel cutting planes are based on the dual relationship between separation and optimization and can be applied in many instances where alternative cutting planes cannot. They are deep in the sense of providing the m...
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Fenchel cutting planes are based on the dual relationship between separation and optimization and can be applied in many instances where alternative cutting planes cannot. They are deep in the sense of providing the maximum separation between a point ($) over cap x and a polyhedron P as measured by an arbitrary norm which is specified in the process of generating a Fenchel cut. This paper demonstrates a number of fundamental convergence properties of Fenchel cuts and addresses the question of which norms lead to the most desirable Fenchel cuts. The strengths and weaknesses of the related class of 1-polar cuts are also examined.
Environmental integrated production and recycling planning is of great importance for the competitive position of production enterprises. Due to increasing disposal costs for industrial byproducts and waste as well as...
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Environmental integrated production and recycling planning is of great importance for the competitive position of production enterprises. Due to increasing disposal costs for industrial byproducts and waste as well as stronger emission standards. companies will be required to setup and control advanced, environmental friendly production technologies, so that emissions and byproducts will be reduced drastically. Nonavoidable byproducts and used products at the end of their lifetime have to be recycled by the producers. The complexity of the resulting decision problems requires adequate. operations research methods. The following paper deals with the development of sophisticated operations research models for two selected planning problems: recycling of industrial byproducts and dismantling and recycling of products at the end of their lifetime. The models have been applied successfully to large industrial problems in practice in the fields of recycling of demolition waste in a German-French region and byproduct management in the steel industry. The presentations of these two applications follow a case study point of view.
作者：
Bard, JFUNIV TEXAS
DEPT MECH ENGNGRAD PROGRAM OPERAT RESAUSTINTX 78712 USA
This paper reports on the results of an effort to design and analyse the rail car unloading area of Procter & Gamble's principal laundry detergent (soap powder) plant. In the first part of the study the design...
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This paper reports on the results of an effort to design and analyse the rail car unloading area of Procter & Gamble's principal laundry detergent (soap powder) plant. In the first part of the study the design team established daily requirements for the number of raw material rail cars unloaded per day. The related combinatorial optimisation problem of assigning rail cars to positions on the platform and unloading equipment to rail cars was modelled as a mixed-integer nonlinear program. The inability of two standard commercial codes to find optimal solutions led to the development of a greedy randomised adaptive search procedure (GRASP). Accounting for the operational and physical limitations of the system, GRASP was used to determine the maximum performance that could be achieved under normal conditions. In the second part of the study alternative designs were proposed for meeting an expected 14% increase in demand over the next few years. The analytic hierarchy process in conjunction with a standard scoring model was used to rank the evaluation criteria and to select the preferred alternative. A worst-case analysis of the top candidate confirmed its performance capabilities.
This paper presents a Hopfield artificial neural network for unit commitment and economic power dispatch. The dual problem of unit commitment and economic power dispatch is an example of a constrained mixed-integer co...
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This paper presents a Hopfield artificial neural network for unit commitment and economic power dispatch. The dual problem of unit commitment and economic power dispatch is an example of a constrained mixed-integer combinatorial optimization. Because of uncertainties in both the system load demand and unit availability, the unit commitment and economic power dispatch problem is stochastic. In this paper we model forced unit outages as independent Markov processes, and load demand as a normal Gaussian random variable. The (0,1) unit commitment-status variables and the hourly unit loading are modelled as sample functions of appropriate random processes. The problem variables over which the optimization is done are modelled as sample functions of random processes which are described by Ito stochastic differential equations. The method is illustrated by a simple example of a power system having three machines which are committed and dispatched over a four-hour period. In the method, unit commitment and economic dispatch are done simultaneously. (C) 1997 Elsevier Science S.A.
An optimization-based algorithm is presented for the short-term-scheduling of hydrothermal power systems using the Lagrangian relaxation technique. This paper concentrates on the solation methodology for hydro subprob...
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An optimization-based algorithm is presented for the short-term-scheduling of hydrothermal power systems using the Lagrangian relaxation technique. This paper concentrates on the solation methodology for hydro subproblems with cascaded reservoirs and discrete hydro constraints. Continuous reservoir dynamics and constraints, discontinuous operating regions, discrete operating states, and hydraulic coupling of cascaded reservoirs are considered in an integrated fashion. The key idea is to substitute oat the reservoir dynamics and to relax the reservoir level constraints by using another set of multipliers, making a hydro subproblem unit-wise and stage-wise decomposable. The optimal generation level for each operating state at each hour can be obtained simply by minimizing a single variable function. Dynamic programming is then applied to optimize the operating states across the planning horizon with a small number of well-structured transitions. A modified subgradient algorithm is used to update multipliers. After the dual problem converges, the feasible solution to the hydro power subsystem is obtained by using a network how algorithm with operating states obtained in the dual solutions, and possibly adjusted by heuristics. Numerical testing based on practical system data sets show that this method is efficient and effective for dealing with hydrothermal systems with cascaded reservoirs and discrete hydro constraints.
This note gives the complement of the class of 'generalized Bow cover' inequalities for a single-node structure as derived originally by Van Roy and Wolsey (1986). Despite the similarity with earlier results, ...
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This note gives the complement of the class of 'generalized Bow cover' inequalities for a single-node structure as derived originally by Van Roy and Wolsey (1986). Despite the similarity with earlier results, there are some elegant relationships between the original and the complementary class of generalized flow covers. It is demonstrated how this class can be of benefit when used in conjunction with the original one.
We give a new mixedintegerprogramming (MIP) formulation for the quadratic cost partition problem that is derived from a MIP formulation for maximizing a submodular function, Several classes of valid inequalities for...
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We give a new mixedintegerprogramming (MIP) formulation for the quadratic cost partition problem that is derived from a MIP formulation for maximizing a submodular function, Several classes of valid inequalities for the convex hull of the feasible solutions are derived using the valid inequalities for the node packing polyhedron. Facet defining conditions and separation algorithms are discussed and computational results are reported.
This paper presents the implementation of one element of a decision support system (DSS) for regional water quality management, applied to the Nitra River Basin in Slovakia. A model-based, aspiration-led methodology f...
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This paper presents the implementation of one element of a decision support system (DSS) for regional water quality management, applied to the Nitra River Basin in Slovakia. A model-based, aspiration-led methodology for multicriteria decision support has been used for the study. Several reusable, modular software tools have been developed and implemented: a problem-specific generator to produce the core part of the mathematical programming model, tools for the generation and interactive modification of multicriteria problems, and a solver for the resulting mixed-integer optimization problem. Provided in the paper are the following: a complete formulation of the mathematical model (including the imbedded water quality model), a summary of the aspiration-reservation-led multiple criteria optimization approach applied to decision support, and an overview of results that illustrate the applied approach and provide some interesting insights to the case study.
This paper considers the solution of systems of equations that are expressed by the two sets: a global rectangular system of equations involving more variables than equations, and a set of conditional equations that a...
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This paper considers the solution of systems of equations that are expressed by the two sets: a global rectangular system of equations involving more variables than equations, and a set of conditional equations that are expressed as disjunctions. The set of disjunctions are given by equations and inequalities, where the latter define the domain of validity of the equations. In this way the solution of such a system is defined by variables x satisfying the rectangular equations, and exactly one set of equations for each of the disjunctions. This paper focuses mainly in the solution of systems of linear disjunctive equations. Using a convex hull representation of the disjunctions, the disjunctive system of equations is converted into an MILP problem. A sufficient condition is presented under which the model is shown to be solvable as an LP problem. The extension of the proposed method to nonlinear disjunctive equations is also discussed. The application of the proposed algorithms are illustrated with several examples.
A new solution procedure for the discrete VAR optimization of a power distribution system is presented in this paper. In order to obtain an optimal discrete solution within a reasonable time, a mixed-integer programmi...
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A new solution procedure for the discrete VAR optimization of a power distribution system is presented in this paper. In order to obtain an optimal discrete solution within a reasonable time, a mixed-integer programming method combined with an expert system is proposed to achieve these requirements. The proposed expert system helps the system planning engineers to allocate an appropriate initial feasible solution, and to decide the position of transformer tap settings as well as the number of capacitor units. From three solution stages using the linear programming approach, the expert system approach, and the mixed-integer programming approach, the discrete VAR optimization problem is promptly solved. Numerical simulations of a small-scale system and a practical system are demonstrated with significant results. The results demonstrate the effectiveness and improvement of the proposed method to solve the VAR optimization problem in a power distribution system.
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