Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate fac...
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Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the points to be covered, or both, to be finite sets. In this work, we study the set-covering location problem when both candidate locations and demand points are continuous on a network. This variant has received little attention, and the scarce existing approaches have focused on particular cases, such as tree networks and integer covering radius. Here we study the general problem and present a mixedinteger Linear programming formulation (MILP) for networks with edge lengths no greater than the covering radius. The model does not lose generality, as any edge not satisfying this condition can be partitioned into subedges of appropriate lengths without changing the problem. We propose a preprocessing algorithm to reduce the size of the MILP, and devise tight big-M constants and valid inequalities to strengthen our formulations. Moreover, a second MILP is proposed, which admits edge lengths greater than the covering radius. As opposed to existing formulations of the problem (including the first MILP proposed herein), the number of variables and constraints of this second model does not depend on the lengths of the network's edges. This second model represents a scalable approach that particularly suits real-world networks, whose edges are usually greater than the covering radius. Our computational experiments show the strengths and limitations of our exact approach to both real-world and random networks. Our formulations are also tested against an existing exact method. & COPY;2023 Elsevier Ltd. All rights reserved.
Presolving is a critical component in modern mixed integer programming (MIP) solvers. In this paper, we propose a new and effective presolving method named inequation-based variable aggregation and develop a combined ...
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Presolving is a critical component in modern mixed integer programming (MIP) solvers. In this paper, we propose a new and effective presolving method named inequation-based variable aggregation and develop a combined variable aggregation (VA) technique with the advantage of significantly reducing the scales of MIP problems. This technique is particularly effective for problems involving semi -continuous variables, such as unit commitment problems. Extensive numerical experiments demonstrate that the combined VA technique can substantially accelerate the solution process of MIP problems. (c) 2024 Elsevier B.V. All rights reserved.
This paper challenges the traditional notion that mine planners need to plan production so as to incur the lowest mining cost. For a given mine configuration, a mine that increases its mining rate will incur increased...
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This paper challenges the traditional notion that mine planners need to plan production so as to incur the lowest mining cost. For a given mine configuration, a mine that increases its mining rate will incur increased mining costs. In an environment in which operations are fixated on cost reduction, a proposal that increases costs will not be readily accepted. Such a proposal requires financial justification-the increase in costs might be recuperated by the additional production. This paper evaluates the net present value (NPV) across a range of copper prices for two underground orebodies located at different depths, using a production rate of 300 kt per quarter and a scenario that introduces additional equipment and costs for 450 kt per quarter. The evaluation was based on the changes of NPV for the orebody located at a shallow depth compared with the orebody at a greater depth. Discrete event simulation combined with mixed integer programming was used for analysis. Unlike traditional sensitivity analysis, this study re-optimizes the mine plan for each commodity price at each production rate. The results show that, for the low mining rate at the final copper price, an NPV of A$ 1530.64 million is achieved, whereas an NPV of A$ 1537.59 million is achieved at a higher mining rate. Even though pushing mining rates beyond traditional limits may increase mining costs, this option may be beneficial at certain commodity prices, particularly when prices are elevated.
This paper presents a comparison of optimization methods applied to islanded micro-grids including renewable energy sources, diesel generators and battery energy storage systems. In particular, a comparative analysis ...
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This paper presents a comparison of optimization methods applied to islanded micro-grids including renewable energy sources, diesel generators and battery energy storage systems. In particular, a comparative analysis between an optimization model based on linear programming and a model based on mixed integer programming has been carried out. The general formulation of these models has been presented and applied to a real case study micro-grid installed in Somalia. The case study is an islanded micro-grid supplying the city of Garowe by means of a hybrid power plant, consisting of diesel generators, photovoltaic systems and batteries. In both models the optimization is based on load demand and renewable energy production forecast. The optimized control of the battery state of charge, of the spinning reserve and diesel generators allows harvesting as much renewable power as possible or to minimize the use of fossil fuels in energy production.
As awareness of the vulnerability of isolated regions to natural disasters grows, the demand for efficient evacuation plans is increasing. However, isolated areas, such as islands, often have characteristics that make...
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As awareness of the vulnerability of isolated regions to natural disasters grows, the demand for efficient evacuation plans is increasing. However, isolated areas, such as islands, often have characteristics that make conventional methods, such as evacuation by private vehicle, impractical to infeasible. Mathematical models are conventional tools for evacuation planning. Most previous models have focused on densely populated areas, and are inapplicable to isolated communities that are dependent on marine vessels or aircraft to evacuate. This paper introduces the Isolated Community Evacuation Problem (ICEP) and a corresponding mixed integer programming formulation that aims to minimize the evacuation time of an isolated community through optimally routing a coordinated fleet of heterogeneous recovery resources. ICEP differs from previous models on resource-based evacuation in that it is highly asymmetric and incorporates compatibility issues between resources and access points. The formulation is expanded to a two-stage stochastic problem that allows scenario-based optimal resource planning while also ensuring minimal evacuation time. In addition, objective functions with a varying degree of risk are provided, and the sensitivity of the model to different objective functions and problem sizes is presented through numerical experiments. To increase efficiency, structure-based heuristics to solve the deterministic and stochastic problems are introduced and evaluated through computational experiments. The results give researchers and emergency planners in remote areas a tool to build optimal evacuation plans given the heterogeneous resource fleets available, which is something they have not been previously able to do and to take actions to improve the resilience of their communities accordingly.
Correspondence analysis (CA) is a dimension reduction technique for categorical data in a two-way contingency table. The low-dimensional CA solution optimally depicts the relationship between the categorical variables...
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Correspondence analysis (CA) is a dimension reduction technique for categorical data in a two-way contingency table. The low-dimensional CA solution optimally depicts the relationship between the categorical variables. We consider the inverse correspondence analysis (ICA) problem, where we use the low-dimensional representation in order to retrieve the original data table. We propose a mixed integer programming formulation for the ICA problem based on transition formulas, which link the row and column coordinates in a CA solution. We show that our formulation has better theoretical characteristics than the existing formulation in the literature and is able to model a generalised ICA problem, which requires less input. In addition, we introduce an iterative method, which uses the fit of individual points in the low-dimensional CA solution. By incorporating statistical information on the quality of CA solutions into our methodology, we are able to retrieve the original data for larger ICA instances.
Rice production in Arkansas usually involves intensive tillage. No-till rice has been studied, but the focus has been limited to impacts on yields and per acre returns. This study uses mixed integer programming to mod...
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Rice production in Arkansas usually involves intensive tillage. No-till rice has been studied, but the focus has been limited to impacts on yields and per acre returns. This study uses mixed integer programming to model optimal machinery selection and evaluate whole-farm profitability of no-till management for rice-soybean farms. Results indicate that lower machinery ownership expenses combined with lower fuel and labor expenses do enhance the profitability of no-till management, but the monetary gains appear to be modest, implying that other incentives may be necessary to entice producers to use the practice.
Since the appearance of computers, engineers recognized their potential. Due to this fact, engineers are utilizing computer usage during their daily tasks. When it comes to analysis, simulation is one of the most valu...
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Since the appearance of computers, engineers recognized their potential. Due to this fact, engineers are utilizing computer usage during their daily tasks. When it comes to analysis, simulation is one of the most valuable tools an engineer can apply. In this paper a mixed integer programming-based description and a discrete event-based model is presented. The mathematical approach is used for rough checking, while the more detailed event-based simulation is used to examine the effects of certain parameters of the assembly cell. Based on the results, the bottleneck of the line and the possibly over-capacitated buffers were identified. Furthermore, a worker regrouping strategy is determined with the help of the models.
This “proof of concept” paper describes parallel solution of general mixedinteger programs by a branch-and-bound algorithm on the CM-5 multiprocessing system. It goes beyond prior parallel branch-and-bound work by ...
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This “proof of concept” paper describes parallel solution of general mixedinteger programs by a branch-and-bound algorithm on the CM-5 multiprocessing system. It goes beyond prior parallel branch-and-bound work by implementing a reasonably realistic general-purpose mixed integer programming algorithm, as opposed to a specialized method for a narrow class of problems. It shows how to use the capabilities of the CM-5 to produce an efficient parallel implementation employing centrally controlled search, achieving near-linear speedups using 64–128 processors on a variety of difficult problems derived from real applications. In concrete terms, a problem requiring half an hour to solve on a SPARC-2 workstation might be solved in 15–20 seconds, and a problem originally taking a week might be reduced to about an hour. Central search control does have limitations, and some final computational experiments begin to address the merits of more decentralized options.
In this study, we develop an extended multi-objective mixed integer programming (EMOMIP) approach for water resources management under uncertainty, in which the parameters are fuzzy random variables while the decision...
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In this study, we develop an extended multi-objective mixed integer programming (EMOMIP) approach for water resources management under uncertainty, in which the parameters are fuzzy random variables while the decision variables are interval variables. Furthermore, some alternatives are considered to retrieve the difference between the quantities of promised water-allocation targets and the actual allocated water. Then, the proposed EMOMIP for the problem is solved by a new method using fuzzy random chance-constrained programming based on the idea of possibility theory. This method can satisfy both optimistic and pessimistic decision makers simultaneously. Finally, a real example is given to explain the proposed method.
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