As the development and population of North America continues to grow, the demand for environmentally friendly or clean energy generation is becoming more of an issue. We present a model that addresses the energy techn...
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As the development and population of North America continues to grow, the demand for environmentally friendly or clean energy generation is becoming more of an issue. We present a model that addresses the energy technologies that may continue to be used and new clean energy technologies that should be introduced in energy generation. The approach involves a Stochastic mixed-integer Program (SMIP) that minimizes cost and emission levels associated with energy generation while meeting energy demands of a given region. The results provide encouraging outcomes with respect to cost, emission levels, and energy-technologies that should be utilized for future generation. (C) 2011 Elsevier Ltd. All rights reserved.
This paper presents a new data classification method based on mixed-integer programming. Traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi-class data classifi...
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This paper presents a new data classification method based on mixed-integer programming. Traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi-class data classification problems. The proposed approach is based on the use of hyper-boxes for defining boundaries of the classes that include all or some of the points in that set. A mixed-integer programming model is developed for representing existence of hyper-boxes and their boundaries. In addition, the relationships among the discrete decisions in the model are represented using propositional logic and then converted to their equivalent integer constraints using Boolean algebra. The proposed approach for multi-class data classification is illustrated on an example problem. The efficiency of the proposed method is tested on the well-known IRIS data set. The computational results on the illustrative example and the IRIS data set show that the proposed method is accurate and efficient on multi-class data classification problems. (c) 2005 Elsevier B.V. All rights reserved.
We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. ...
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We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP formulation is ideal, and uses exactly r integer variables and 2 x (#of spanning hyperplanes) general inequality constraints. We use this result to derive novel logarithmic-sized ideal MIP formulations for discontinuous piecewise linear functions and structures appearing in robotics and power systems problems. (C) 2019 Elsevier B.V. All rights reserved.
A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a)...
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A new mixed-integer programming (MIP) formulation is presented for the production planning of single-stage multi-product processes. The problem is formulated as a multi-item capacitated lot-sizing problem in which (a) multiple items can be produced in each planning period, (b) sequence-independent set-ups can carry over from previous periods, (c) set-ups can cross over planning period boundaries, and (d) set-ups can be longer than one period. The formulation is extended to model time periods of non-uniform length, idle time, parallel units, families of products, backlogged demand, and lost sales. (C) 2007 Elsevier Ltd. All rights reserved.
In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint...
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In this article, we consider a network of processors aiming at cooperatively solving mixed-integer convex programs subject to uncertainty. Each node only knows a common cost function and its local uncertain constraint set. We propose a randomized, distributed algorithm working under asynchronous, unreliable, and directed communication. The algorithm is based on a local computation and communication paradigm. At each communication round, nodes perform two updates: 1) A verification in which they check-in a randomized fashion-the robust feasibility of a candidate optimal point, and 2) an optimization step in which they exchange their candidate basis (the minimal set of constraints defining a solution) with neighbors and locally solve an optimization problem. As a main result, we show that processors can stop the algorithm after a finite number of communication rounds (either because verification has been successful for a sufficient number of rounds or because a given threshold has been reached) so that candidate optimal solutions are consensual. The common solution has proven to be-with high confidence-feasible and, hence, optimal for the entire set of uncertainty except a subset having an arbitrarily small probability measure. We show the effectiveness of the proposed distributed algorithm using two examples: a random, uncertain mixed-integer linear program and a distributed localization in wireless sensor networks. The distributed algorithm is implemented on a multicore platform in which the nodes communicate asynchronously.
This paper considers the class scheduling and timetabling problem faced at Kuwait University (KU). The principal focus is to design efficient class offering patterns while taking into consideration newly imposed gende...
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This paper considers the class scheduling and timetabling problem faced at Kuwait University (KU). The principal focus is to design efficient class offering patterns while taking into consideration newly imposed gender policies. We formulate a mathematical programming model that assigns offered classes to time-slots and addresses gender issues by defining appropriate surrogate constraints along with objective penalty terms. The model aims to enhance existing manual scheduling and timetabling approaches that are often accompanied with arduous combinatorial tasks such as resolving class conflicts, dealing with parking and traffic congestion, and ensuring an efficient utilization of facility and human resources. This modeling approach emphasizes the generation of flexible class timetables for students, and the efficient utilization of available facility resources. Computational results based on a number of case studies related to Kuwait University reveal that this approach yields improved schedules in terms of offering patterns and class conflicts. (c) 2006 Elsevier B.V. All rights reserved.
A critical measure of model quality for a mixed-integer program (MIP) is the difference, or gap, between its optimal objective value and that of its linear programming relaxation. In some cases, the right-hand side is...
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A critical measure of model quality for a mixed-integer program (MIP) is the difference, or gap, between its optimal objective value and that of its linear programming relaxation. In some cases, the right-hand side is not known exactly;however, there is no consensus metric for evaluating a MIP model when considering multiple right-hand sides. In this paper, we provide model formulations for the expectation and extrema of absolute and relative MIP gap functions over finite discrete sets. & COPY;2023 Elsevier B.V. All rights reserved.
Chemical centres provide great potential to tackle the worldwide energy and environmental issues via integrated chemical synthesis and heat and power generation. However, planning of chemical centres still involves ma...
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Chemical centres provide great potential to tackle the worldwide energy and environmental issues via integrated chemical synthesis and heat and power generation. However, planning of chemical centres still involves many formidable challenges, including locating production sites, arrangement of transportation, and selection of appropriate technologies. These problems become further complicated when considering the geographic situation of a region under study. In this paper, we propose a multi-period mixed-integer programming (MIP) approach to the optimal planning of chemical centres. The planning horizon is firstly divided into several time intervals, and the planning region is represented by a grid. Then a superstructure representation is developed to capture all available logistic and technical options. Based on the superstructure representation, an MIP problem is developed, and by solving it an optimal planning strategy can be obtained. A real-life case study for the UK follows, where the UK is divided into a grid of 34 cells. (C) 2011 Elsevier Ltd. All rights reserved.
The climate change emergency calls for a reduction in energy consumption in all human activities and production processes. The radio broadcasting industry is no exception. However, reducing energy requirements by unif...
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The climate change emergency calls for a reduction in energy consumption in all human activities and production processes. The radio broadcasting industry is no exception. However, reducing energy requirements by uniformly cutting the radiated power at every transmitter can potentially impair the quality of service. A careful evaluation and optimization study are in order. In this paper, by analyzing the Italian frequency modulation analog broadcasting service, we show that it is indeed possible to significantly reduce the energy consumption of the broadcasters without sacrificing the quality of the service, rather, even getting improvements.
Cloud manufacturing is an emerging service-oriented manufacturing paradigm that integrates and manages distributed manufacturing resources through which complex manufacturing demands with a high degree of customizatio...
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Cloud manufacturing is an emerging service-oriented manufacturing paradigm that integrates and manages distributed manufacturing resources through which complex manufacturing demands with a high degree of customization can be fulfilled. The process of service selection optimization and scheduling (SSOS) is an important issue for practical implementation of cloud manufacturing. In this paper, we propose new mixed-integer programming (MIP) models for solving the SSOS problem with basic composition structures (i.e., sequential, parallel, loop, and selective). Through incorporation of the proposed MIP models, the SSOS with a mixed composition structure can be tackled. As transportation is indispensable in cloud manufacturing environment, the models also optimize routing decisions within a given hybrid hub-and-spoke transportation network in which the central decision is to optimally determine whether a shipment between a pair of distributed manufacturing resources is routed directly or using hub facilities. Unlike the majority of previous research undertaken in cloud manufacturing, it is assumed that manufacturing resources are not continuously available for processing but the start time and end time of their occupancy interval are known in advance. The performance of the proposed models is evaluated through solving different scenarios in the SSOS. Moreover, in order to examine the robustness of the results, a series of sensitivity analysis are conducted on key parameters. The outcomes of this study demonstrate that the consideration of transportation and availability not only can change the results of the SSOS significantly, but also is necessary for obtaining more realistic solutions. The results also show that routing within a hybrid hub-and-spoke transportation network, compared with a pure hub-and-spoke network or a pure direct network, leads to more flexibility and has advantage of cost and time saving. The level of saving depends on the value of discount factor f
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