The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the ...
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The global supply chain for liquid helium presents a complex structure due to increasing foreign demand, elaborate recovery techniques, and costly forms of distribution. Although the problem contains parallels to the liquid natural gas supply chain, supply requirements and problem specific network constraints require a unique optimization model. We develop a large-scale, discrete time, path-based integer-programming model which solves optimally with CPLEX. Computational results implementing a rolling horizon structure and testing based on historical data are presented. A detailed sensitivity analysis demonstrates the effective use of our model, testing a variety of realistic parameter settings for the liquid helium supply chain.
Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing me...
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Metro maps are schematic diagrams of public transport networks that serve as visual aids for route planning and navigation tasks. It is a challenging problem in network visualization to automatically draw appealing metro maps. There are two aspects to this problem that depend on each other: the layout problem of finding station and link coordinates and the labeling problem of placing nonoverlapping station labels. In this paper, we present a new integral approach that solves the combined layout and labeling problem (each of which, independently, is known to be NP-hard) using mixed-integer programming (MIP). We identify seven design rules used in most real-world metro maps. We split these rules into hard and soft constraints and translate them into an MIP model. Our MIP formulation finds a metro map that satisfies all hard constraints (if such a drawing exists) and minimizes a weighted sum of costs that correspond to the soft constraints. We have implemented the MIP model and present a case study and the results of an expert assessment to evaluate the performance of our approach in comparison to both manually designed official maps and results of previous layout methods.
Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for t...
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Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound. Solutions are repaired by performing a projection and a shift to ensure all constraints are satisfied;bound computations are accelerated by reusing structural information through the branch-and-bound tree. We demonstrate this method to be widely applicable and faster than solving a sequence of exact LPs. Several variations of the algorithm are described and computationally evaluated in an exact branch-and-bound algorithm within the mixed-integer programming framework SCIP (Solving Constraint integerprogramming).
This paper proposes an innovative reverse logistics network (RLN) to manage kitchen waste (KW) transportation and resource treatment. The network employs battery electric (BE) trucks for transportation, and the challe...
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This paper proposes an innovative reverse logistics network (RLN) to manage kitchen waste (KW) transportation and resource treatment. The network employs battery electric (BE) trucks for transportation, and the challenge lies in determining the distribution of various KW treatment centers and establishing the optimal transportation routes for KW and its residues. The proposed RLN is self-sufficient, because the electricity produced by the centers within the network is adequate to power the BE trucks. We develop a matched mixedintegerprogramming model to optimize the entire process, with the goal of minimizing the total potential economic and environmental costs. Notably, the model considers comprehensive cost components and employs a carbon trading policy to translate carbon emissions into carbon costs. We use robust optimization to generate optimal solutions that remain viable even under the worst -case scenario concerning uncertain parameters. We then test the feasibility of the proposed methodology in a real -world case. We conduct specific scenario analyses on capacity and mode of trucks to offer practical KW transportation strategies and recommendations. We found that the larger the capacity of a BE truck, the greater the economic and environmental benefits for the KW RLN. The self-sufficient KW RLN using BE trucks proved to be the least costly, followed by the ordinary KW RLN using BE trucks, while the KW RLN using diesel trucks was the most expensive and environmentally detrimental.
作者：
Ketkov, Sergey S.HSE Univ
Lab Algorithms & Technol Networks Anal Rodionova St 136 Nizhnii Novgorod 603093 Russia Univ Zurich
Dept Business Adm CH-8032 Zurich Switzerland
This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability dis...
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This study addresses a class of linear mixed-integer programming (MILP) problems that involve uncertainty in the objective function parameters. The parameters are assumed to form a random vector, whose probability distribution can only be observed through a finite training data set. Unlike most of the related studies in the literature, we also consider uncertainty in the underlying data set. The data uncertainty is described by a set of linear constraints for each random sample, and the uncertainty in the distribution (for a fixed realization of data) is defined using a type-1 Wasserstein ball centered at the empirical distribution of the data. The overall problem is formulated as a three-level distributionally robust optimization (DRO) problem. First, we prove that the three-level problem admits a single-level MILP reformulation, if the class of loss functions is restricted to biaffine functions. Secondly, it turns out that for several particular forms of data uncertainty, the outlined problem can be solved reasonably fast by leveraging the nominal MILP problem. Finally, we conduct a computational study, where the out-of-sample performance of our model and computational complexity of the proposed MILP reformulation are explored numerically for several application domains.
We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks Subject to multiple scenarios of externally caused damage. We present computation with netw...
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We consider optimization problems related to the prevention of large-scale cascading blackouts in power transmission networks Subject to multiple scenarios of externally caused damage. We present computation with networks with up to 600 nodes and 827 edges, and many thousands of damage scenarios. (c) 2006 Elsevier B.V. All rights reserved.
In the smart grid environment, optimal placement and sizing of microgrids have attracted a great deal of attention. Here, we propose a multi-scale optimization model for determining microgrid configuration, capacity, ...
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In the smart grid environment, optimal placement and sizing of microgrids have attracted a great deal of attention. Here, we propose a multi-scale optimization model for determining microgrid configuration, capacity, and geographical location, and we apply it to a municipality in Southwestern Ontario. The proposed approach accounts for the net present value of the project, power balance of the grid, maximum capacity of the current substations, and the geographic availability for the installation of a microgrid. The problem is tackled in two stages. First, a geographic information system/multicriteria decision analysis (GIS/MCDA) is performed to determine the suitable locations for the installation of distributed energy resources (DERs). Then, a mixedinteger optimization model is used to determine the capacities and final installation locations of the DERs based on the results obtained in the GIS/MCDA. Finally, three different scenarios are evaluated to elucidate the influence that retail price, microgrids' minimum contribution to the demand, and available land have over the final architecture, cost, and allocation of a renewable energy project.
Rapid population growth, industrialization, and lifestyle modernization all increase water demand. However, water supplies are dramatically decreasing due to declining and irregular precipitation and the excessive use...
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Rapid population growth, industrialization, and lifestyle modernization all increase water demand. However, water supplies are dramatically decreasing due to declining and irregular precipitation and the excessive use and deterioration of existing resources. This situation places tremendous pressure on decision-makers, who must implement plans to create new water supplies in regions likely to experience water shortages in the future. Deciding which projects to implement among various alternatives is challenging with a limited budget. This study aims to create a feasible strategic plan to select the most suitable alternative projects by proposing a multi-objective mixed-integer programming approach to the water supply problem. Considering several criteria, including chance of success, ease of application, nature-friendliness, and project prestige level, the proposed model is integrated using the analytical hierarchical process technique. Decision-makers' views of the project alternatives are reflected by weights in the model. Also, interval numbers represent the costs of alternatives to handle the problem more realistically. A real-life situation is simulated under various scenarios to test the proposed model. The results show that the proposed integrated model generates more applicable solutions than a classic multi-objective optimization model.
An exact algorithm is developed for the chance-constrained multi-area reserve sizing problem in the presence of transmission network constraints. The problem can be cast as a two-stage stochastic mixedinteger linear ...
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An exact algorithm is developed for the chance-constrained multi-area reserve sizing problem in the presence of transmission network constraints. The problem can be cast as a two-stage stochastic mixedinteger linear program using sample approximation. Due to the complicated structure of the problem, existing methods attempt to find a feasible solution based on heuristics. Existing mixed-integer algorithms that can be applied directly to a two-stage stochastic program can only address small-scale problems that are not practical. We have found a minimal description of the projection of our problem onto the space of the first-stage variables. This enables us to directly apply more general integerprogramming techniques for mixing sets, that arise in chance-constrained problems. Combining the advantages of the minimal projection and the strengthening reformulation from IP techniques, our method can tackle real-world problems. We specifically consider a case study of the 10-zone Nordic network with 100,000 scenarios where the optimal solution can be found in approximately 5 minutes.
As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction...
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As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.
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