Neste trabalho apresentamos um modelo de otimização para o planejamento agregado da produção de usinas de açúcar e álcool. Este modelo se baseia nos modelos clássicos de seleção de processos e ...dimensionamento de lotes para representar o sistema de produção de açúcar, álcool e melaço, incluindo decisões da etapa agrícola, das fases de corte, carregamento e transporte de cana e, principalmente, decisões de moagem, escolha do processo produtivo e estoque dos produtos finais. As decisões são tomadas em períodos semanais e o horizonte de planejamento são as semanas de safra. Para resolver o modelo de programação linear inteira mista resultante, utilizamos a linguagem de modelagem GAMS e o solver CPLEX. Um estudo de caso foi realizado em uma usina de açúcar e álcool do estado de Alagoas. Neste estudo foi possível verificar a adequação do modelo proposto quando aplicado para auxiliar nas decisões envolvidas no planejamento agregado da produção de empresas deste tipo. Resultados computacionais são apresentados resolvendo um exemplo com dados de uma safra típica.The main concern of this work is related to the presentation of an aggregate production planning model of a sugar and alcohol milling company. The mathematical model is based on the process selection model and the production lot-sizing model, and aims to help the decision makers in the production planning and control process of determining the quantity of sugarcane crushed, the selection of sugarcane suppliers, the selection of sugarcane transport system suppliers, the selection of industrial process used in the sugar, alcohol and molasses production and the storage decisions related to these final products. The decisions are taken on a weekly basis and the planning horizon is the whole sugarcane harvesting season. To solve the mixed integer mathematical problem found in this model, we applied the GAMS modeling language and the CPLEX solver. A case study was developed in a sugar and alcohol milling company located in Rio Largo, state of Alagoas, Brazil. The results of this case study helped us to verify the applicability of the proposed model in the aggregate production planning of a milling company. Computational results are presented in real data application.
Traditional mining selection methods focus on local estimates or loss functions that do not take into account the potential diversification benefits of financial risk that is unique to each location. ...A constrained efficient set model with a downside risk function is formulated as a solution. Estimates of this nonlinear mixed-integer combinatorial optimization problem are provided by a simulated annealing heuristic. A utility framework that is congruent with the proposed efficiency model is then used to choose the optimal set of local mining selections for a decision-maker with specific risk-averse characteristics. The methodology is demonstrated in a grade control environment. The results show that downside financial risk can be reduced by around 33% while the expected payoff is only reduced by 1% when compared to ore selections generated by traditional cut-off grade techniques.PUBLICATION ABSTRACT
The problems of scheduling and optimization of operational conditions in multistage, multiproduct continuous plants with intermediate storage are simultaneously addressed. An MINLP model, called ...TSPFLOW, which is based on the TSP formulation for product sequencing, is proposed to schedule the operation of such plants. TSPFLOW yields a one-order-of-magnitude CPU time reduction as well as the solution of instances larger than those formerly reported (Pinto and Grossmann, 1994). Secondly, processing rates and yields are introduced as additional optimization variables in order to state the simultaneous problem of scheduling with operational optimization. Results show that trade-offs are very complex and that the development of a straightforward (rule of thumb) method to optimally schedule the operation is less effective than the proposed approach.
The USDA Forest Service has a long-established program to identify areas in national forests for designation as protected Research Natural Areas (RNAs). One of the goals is to protect high quality ...examples of regional ecosystems for the purposes of maintaining biological diversity, conducting nonmanipulative research and monitoring, and fostering education. When RNA designation conflicts with other land uses, difficult choices must be made about the best number and location of sites. We addressed this problem by adapting a classic optimization formulation from the location science literature. The formulation was an integer optimization model for selecting the set of RNAs that maximized the number of regional ecosystems and natural communities represented subject to an upper bound on the total area covered by the sites in the selected set. We applied the formulation using 33 potential RNAs in the Superior National Forest in northeastern Minnesota. The 33 potential RNAs were chosen for our case study because they had been mapped and field-surveyed for the presence of natural communities. The use of those sites does not imply that other areas in the Superior National Forest do not merit further study as RNA candidates. The model quickly generated information about the trade-offs between different protection goals. We found multiple sets of potential RNAs, ranging from all 33 sites to a much smaller set of 21 sites, that attained the specified goals for natural community representation. Thus, the decision-maker can choose among sets of sites with a wide range of total areas without compromising the representation goal. We also found that requirements to choose a set of sites that represents a range of locally defined ecosystems or priority natural communities can limit the total number of natural communities that can be represented within a set of sites of a given area. Average solution times for different problems were less than 5 seconds on a personal computer, suggesting that integer optimization can readily facilitate investigation of the impacts of RNA selection goals.
This paper describes a modeling and optimization of operation for small compressed-air energy systems (CAES) in the range of kW, typical of small and medium enterprises (SME) and energy intensive ...industry. These CAES are equipped with air storage. This paper analyzes how those systems may provide flexibility for electrical Demand Response (DR) in city districts. The paper presents first, the modeling of a CAES system. The system design, such as compressor and storage size is then performed based on the modeling results. The mixed-integer linear optimization model for using CAES is explained afterwards. The optimization is an offline day-ahead optimization for planning operation purposes. The approach is analyzed in terms of flexibility within a test case for optimizing the CAES of a typical German car repair shop.
The superpixels provided by an unsupervised segmentation algorithm are sets of neighboring pixels homogeneous in some sense. Therefore it is very likely that, in a classification problem, most pixels ...in a superpixel belong to the same class, namely if the homogeneity criterion is compatible with the class statistics. Superpixels are, therefore, a powerful device to express spatial contextual information. However, the exploitation of superpixels in a principled way is not straightforward. Recent efforts attack this problem under a discrete optimization framework, by including regularization terms promoting consistence of the labels in the superpixels and computing approximate labelings with graph-cut algorithms. The well known hardness of integer optimization problems is a major limitation of this line of attack. In this paper, we introduce a new strategy, based on convex relaxation, to include the spatial information provided by superpixels in classification problems. The convex relaxation of an integer optimization problem opens a door to include extra information, such as spatial partitioning information given by over-segmented superpixels. The convex optimization problem thus obtained is solved by using SALSA algorithm. Experimental results with the ROSIS Pavia University dataset illustrate the effectiveness of the proposed framework.
Robust optimization, as a powerful paradigm for optimization under uncertainty, has recently attracted increasing attention in power system operations. In particular, adaptive robust optimization ...models have been proposed for the day-ahead unit commitment as well as real-time economic dispatch problems in power systems with a high penetration level of renewable energy sources. In this paper, we review the recent advances in this area and propose some new ideas in uncertainty modeling and robust optimization formulations.
The lifetime of a wireless sensor network (WSN) is limited by the lifetime of the individual sensor nodes. A promising technique to extend the lifetime of the nodes is wireless energy transfer. The ...WSN lifetime can also be extended by exploiting the redundancy in the nodes' deployment, which allows the implementation of duty-cycling mechanisms. In this paper, the joint problem of optimal sensor node deployment and WET scheduling is investigated. Such a problem is formulated as an integer optimization whose solution is challenging due to the binary decision variables and non-linear constraints. To solve the problem, an approach based on two steps is proposed. First, the necessary condition for which the WSN is immortal is established. Based on this result, an algorithm to solve the node deployment problem is developed. Then, the optimal WET scheduling is given by a scheduling algorithm. The WSN is shown to be immortal from a networking point of view, given the optimal deployment and WET scheduling. Theoretical results show that the proposed algorithm achieves the optimal node deployment in terms of the number of deployed nodes. In the simulation, it is shown that the proposed algorithm reduces significantly the number of nodes to deploy compared to a random-based approach. The results also suggest that, under such deployment, the optimal scheduling and WET can make WSNs immortal.
Stochastic mixed-integer programs (SMIPs) deal with optimization under uncertainty at many levels of the decision-making process. When solved as extensive formulation mixed-integer programs, problem ...instances can exceed available memory on a single workstation. To overcome this limitation, we present PIPS-SBB: an exact distributed-memory parallel stochastic MIP solver that takes advantage of parallelism at multiple levels of the optimization process. We show promising results on instances from the SIPLIB benchmark by combining methods known for accelerating Branch and Bound (B&B) methods with new ideas that leverage the structure of SMIPs. We expect the performance of PIPS-SBB to improve further as more functionality is added in the future.
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