Managing uncertainty has been a challenging task for market operations. This paper first reviews the current practice of managing uncertainties at MISO. A framework of using robust optimization based approach on MISO ...
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(纸本)9781479964161
Managing uncertainty has been a challenging task for market operations. This paper first reviews the current practice of managing uncertainties at MISO. A framework of using robust optimization based approach on MISO Look-Ahead commitment (LAC) is then introduced. The numerical results show that this type of approaches are promising and yet with challenges to overcome in order to be practical for real world application.
In the fixed-charge transportation problem, the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or, equivalently, to opening an arc in the underlying...
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In the fixed-charge transportation problem, the goal is to optimally transport goods from depots to clients when there is a fixed cost associated to transportation or, equivalently, to opening an arc in the underlying bipartite graph. We further motivate its study by showing that it is both a special case and a strong relaxation of the big-bucket multi-item lot-sizing problem, and a generalization of a simple variant of the single-node flow set. This paper is essentially a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We give a O(n(3))-time optimization algorithm and a O(n(2))-size linear programming extended formulation. We describe a new class of inequalities that we call "path-modular" inequalities. We give two distinct proofs of their validity. The first one is direct and crucially relies on sub-and super-modularity of an associated set function. The second proof is by showing that the projection of the extended linear programming formulations onto the original variable space yields exactly the polyhedron described by the path-modular inequalities. Thus we also show that these inequalities suffice to describe the convex hull of the set of feasible solutions.
We consider the problem of decomposing Intensity Modulated Radiation Therapy (IMRT) fluence maps using rectangular apertures. A fluence map can be represented as an integer matrix, which denotes the intensity profile ...
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We consider the problem of decomposing Intensity Modulated Radiation Therapy (IMRT) fluence maps using rectangular apertures. A fluence map can be represented as an integer matrix, which denotes the intensity profile to be delivered to a patient through a given beam angle. We consider IMRT treatment machinery that can form rectangular apertures using conventional jaws, and hence, do not need sophisticated multi-leaf collimator (MLC) devices. The number of,apertures used to deliver the fluence map needs to be minimized in order to treat the patient efficiently. From a mathematical point of view, the problem is equivalent to a minimum cardinality matrix decomposition problem. We propose a combinatorial Benders decomposition approach to solve this problem to optimality. We demonstrate the efficacy of our approach on a set of test instances derived from actual clinical data. We also compare our results with the literature and solutions obtained by solving a mixed-integer programming formulation of the problem. (C) 2011 Elsevier Ltd. All rights reserved.
Focusing on the HIV-1 subtype B epidemic, the most frequent HIV variant in Brazil, we extend our work on HIV modeling and propose a practical decision-making framework for the design of individualized HIV-1 drug chemo...
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Focusing on the HIV-1 subtype B epidemic, the most frequent HIV variant in Brazil, we extend our work on HIV modeling and propose a practical decision-making framework for the design of individualized HIV-1 drug chemotherapy strategies relying on patient-specific genotyping test data. The methodology is applied to 9 real-world problem instances regarding a set of 15 antiretroviral drugs and a set of 62 amino acid mutations along 45 positions of the HIV-1 pol gene. Optimized strategies are compared with current guidelines from the Brazilian standard HIV/AIDS treatment protocol. Computational results show that distinct optimal treatment strategies are produced for different patients and we conclude that relevant opportunities are to be promptly exploited on an individual basis through a better management of HIV-1 mutations in the long-term, which can be achieved by frequently changing the HAART scheme over time in response to and in anticipation of the emergence of drug-resistant strains. (C) 2013 Elsevier Ltd. All rights reserved.
A novel efficient agent-based method for scheduling network batch processes in the process industry is proposed. The agent-based model is based on the resource-task network. To overcome the drawback of localized solut...
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A novel efficient agent-based method for scheduling network batch processes in the process industry is proposed. The agent-based model is based on the resource-task network. To overcome the drawback of localized solutions found in conventional agent-based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function value by simulating another cloned agent-based model. Global information is obtained, and the solution quality is improved. The solution quality of this approach is validated by detailed comparisons with the mixed-integer programming (MIP) methods. A solution close to the optimal one can be found by the agent-based method with a much shorter computational time than the MIP methods. As a scheduling problem becomes increasingly complicated with increased scale, more specifications, and uncertainties, the advantages of the agent-based method become more evident. The proposed method is applied to simulated industrial problems where the MIP methods require excessive computational resources. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 2884-2906, 2013
This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible...
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This paper considers the problem of scheduling n jobs on a single machine. A fixed processing time and an execution interval are associated with each job. Preemption is not allowed. The objective is to find a feasible job sequence that minimizes the number of tardy jobs. On the basis of an original mathematical integerprogramming formulation, this paper shows how good-quality lower and upper bounds can be computed. Numerical experiments are provided for assessing the proposed approach.
Security-constrained unit commitment (SCUC), as one of key components in power system operation, is being widely applied in vertically integrated utilities and restructured power systems. The efficient solution framew...
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Security-constrained unit commitment (SCUC), as one of key components in power system operation, is being widely applied in vertically integrated utilities and restructured power systems. The efficient solution framework is to implement iterations between a master problem (unit commitment) and subproblems (network security evaluations). In industrial applications, both Lagrangian relaxation and mixed-integer programming are commonly applied for the unit commitment problem, and both linear sensitivity factor and Benders cut methods are used to generate additional constraints in the phase of network security evaluations. This paper evaluates capabilities and performances of each algorithm through technical discussion and numerical testing. Special topics on the large-scale SCUC engine development are also discussed in this paper, such as input data screening, inactive constrains elimination, contingency management, infeasibility handling, parallel computing, and model simplification. This paper will benefit academic researchers, software developers, and system operators when they design, develop and assess effective models and algorithms for solving large-scale SCUC problems.
The p-hub center problem has extensive applications in various real-world fields such as transportation and telecommunication systems. This paper presents a new risk aversion p-hub center problem with fuzzy travel tim...
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The p-hub center problem has extensive applications in various real-world fields such as transportation and telecommunication systems. This paper presents a new risk aversion p-hub center problem with fuzzy travel times, in which value-at-risk (VaR) criterion is adopted in the formulation of objection function. For trapezoidal and normal fuzzy travel times, we first turn the original VaR p-hub center problem into its equivalent parametric mixed-integer programming problem, then develop a hybrid algorithm by incorporating genetic algorithm and local search (GALS) to solve the parametric mixed-integer programming problem. In our designed GALS, the GA is used to perform global search, while LS strategy is applied to each generated individual (or chromosome) of the population. Finally, we conduct two sets of numerical experiments and discuss the experimental results obtained by general-purpose LINGO solver, standard GA and GALS. The computational results show that the GALS achieves the better performance than LINGO solver and standard GA. (C) 2012 Elsevier B. V. All rights reserved.
The modeling of time plays a key role in the formulation of mixed-integer programming (MIP) models for scheduling, production planning, and operational supply chain planning problems. It affects the size of the model,...
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The modeling of time plays a key role in the formulation of mixed-integer programming (MIP) models for scheduling, production planning, and operational supply chain planning problems. It affects the size of the model, the computational requirements, and the quality of the solution. While the development of smaller continuous-time scheduling models, based on multiple time grids, has received considerable attention, no truly different modeling methods are available for discrete-time models. In this paper, we challenge the long-standing belief that employing a discrete modeling of time requires a common uniform grid. First, we show that multiple grids can actually be employed in discrete-time models. Second, we show that not only unit-specific but also task-specific and material-specific grids can be generated. Third, we present methods to systematically formulate discrete-time multi-grid models that allow different tasks, units, or materials to have their own time grid. We present two different algorithms to find the grid. The first algorithm determines the largest grid spacing that will not eliminate the optimal solution. The second algorithm allows the user to adjust the level of approximation;more approximate grids may have worse solutions, but many fewer binary variables. Importantly, we show that the proposed models have exactly the same types of constraints as models relying on a single uniform grid, which means that the proposed models are tight and that known solution methods can be employed. The proposed methods lead to substantial reductions in the size of the formulations and thus the computational requirements. In addition, they can yield better solutions than formulations that use approximations. We show how to select the different time grids, state the formulation, and present computational results. (C) 2013 Elsevier Ltd. All rights reserved.
In this paper, we analyse a service provider's mixed bundling problem for services such as sporting events or holiday packages. Pursuing the objective of maximising total revenue, the service provider has to deter...
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In this paper, we analyse a service provider's mixed bundling problem for services such as sporting events or holiday packages. Pursuing the objective of maximising total revenue, the service provider has to determine static prices for each single product at the beginning of the selling period. Additionally, an optimal package price has to be chosen for the bundle that comprises one unit of each single product. Because of capacity constraints, the availability of products can change over time such that consumers are forced to switch from their preferred subset of products to an alternative following dynamic substitution. We propose two mixed-integer linear programmes based on reservation prices that appropriately model the consumer choice process to address the bundling problem. It becomes evident that the determination of the optimal prices is computationally expensive even for small problem classes. Therefore, we develop metaheuristics using variable neighbourhoods. To evaluate their performance, we propose the following new approach: our extensive computational study is performed using especially generated scenarios for which the optimal product prices are known. For this purpose, we present a set of conditions for the generation of reservation prices that guarantee the optimality of the predefined prices. Based on our computational results, managerial insights are derived. (C) 2013 Elsevier B.V. All rights reserved.
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