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A new integer linear programming formulation for the problem of political districting

ANNALS OF OPERATIONS RESEARCH 2020年第1期288卷 247-263页

作者： Dugosija, Djordje Savic, Aleksandar Maksimovic, Zoran Univ Belgrade Fac Math Studentski Trg 16-4 Belgrade 11000 Serbia Univ Def Mil Acad Generala Pavla Jurisica Sturma 33 Belgrade 11000 Serbia

The problem of dividing political territories in electoral process is a very important factor which contributes to the development of democracy in modern political systems. The most significant criteria for fairness of electoral process are demographic, geographic and political. Demographic criterion in the first place refers to the population equality, while the geographic one is mostly represented by compactness, contiguity and integrity. In this paper we propose a new integer linear programming formulation for the problem of political districting. The model is based on the graph representation of political territory, where territorial units are vertices and direct links between them are edges. The correctness of integer linear programming formulation is mathematically proven. In contrast to the most of the previous formulations, all three major criteria, population equality, compactness and contiguity, are completely taken into consideration. There are two models, one which deals with afore mentioned criteria where compactness is taken as an objective function, and the other one which takes into account interests of the decision maker, i.e. the political ruling body which organizes elections. Several numerical examples for the presented models are given which illustrate general aspects of the problem. The experimental results are obtained using CPLEX solver.

关键词： Political districting integer linear programming Graph partitioning Combinatorial optimization

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integer linear programming models for the weighted total domination problem

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APPLIED MATHEMATICS AND COMPUTATION 2019年 358卷 146-150页

作者： Ma, Yuede Cai, Qingqiong Yao, Shunyu Xian Technol Univ Sch Sci Xian 710021 Shanxi Peoples R China Nankai Univ Coll Comp Sci Tianjin 300350 Peoples R China Nankai Univ Ctr Combinator Tianjin 300071 Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China

A total dominating set of a graph G = (V, E) is a subset D of V such that every vertex in V (including the vertices from D) has at least one neighbour in D. Suppose that every vertex v is an element of V has an integer weight w(v) >= 0 and every edge e is an element of E has an integer weight w(e) >= 0. Then the weighted total domination (WTD) problem is to find a total dominating set D which minimizes the cost f (D) := Sigma(u is an element of D )w(u) + Sigma(e is an element of E[D]) w(e) + Sigma(v is an element of V\D) min{w(uv) vertical bar u is an element of N(v) boolean AND D}. In this paper, we put forward three integer linear programming (ILP) models with a polynomial number of constraints, and present some numerical results implemented on random graphs for WTD problem. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Weighted total domination integer linear programming Combinatorial optimization Graph theory

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integer linear programming for Influence Maximization

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF ELECTRICAL ENGINEERING 2019年第3期43卷 627-634页

作者： Baghbani, Farzaneh Ghayour Asadpour, Masoud Faili, Heshaam Univ Tehran Dept Elect & Comp Engn Tehran Iran

Influence Maximization is one of the important research topics in social networks which has many applications, e.g., in marketing, politics and social science. The goal of Influence Maximization is to select a limited number of vertices (called seed set) in a social graph, so that upon their direct activation, the maximum number of vertices is activated through social interaction of the seed set with the other vertices. Social interaction is modeled by diffusion models among which linear Threshold Model is one of the most popular ones. In linear Threshold Model, influence of nodes on each other is quantized by edge weights and nodes have a threshold for activation. If sum of the influence of activated neighbors of a node reaches a certain threshold, the node is activated. When thresholds are fixed, Influence Maximization reduces to Target Set Selection Problem. Ackerman et al. solved Target Set Selection Problem by integer linear programming. In this paper, we analyze their work and show that their method cannot properly solve the problem in specific situations, e.g., when graph has cycle. We fix this problem and propose a new method based on integer linear programming and show in the results that our method can handle graphs with cycles as well.

关键词： Influence Maximization linear Threshold Model Target Set Selection Problem integer linear programming

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Proposal of a novel mixed integer linear programming model for site selection of a wind power plant based on power maximization with use of mixed type wind turbines

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ENERGY & ENVIRONMENT 2020年第5期31卷 825-841页

作者： Ari, Emin Sertac Gencer, Cevriye Osmaniye Korkut Ata Univ Dept Management Informat Syst Karacaoglan CampusBlock FRoom 211 Osmaniye Turkey Gazi Univ Fac Engn Dept Ind Engn Ankara Turkey

Several methods that have been developed to obtain energy, which is indispensable for life and whose necessity has increased geometrically in the course of time, are no longer sustainable. Therefore, human being has headed towards sustainable alternative energy sources. Wind has been one of the most interested renewable energy sources for human as of the beginning of the 20th century. This study focuses on one of the most important work items at the establishment phase of this important energy source, power plant site selection. Within the scope of linear programming perspective, two models were presented based on mixed integer linear programming. The first model provides employment of single-type wind turbine on the selected site, whereas the second model, which was developed within the current study, aims additional increase in total power output by allowing employment of multiple-type wind turbine on the selected site. The same region showed up as the most appropriate site to establish wind power plant as a result of both models of the study.

关键词： Renewable energy wind energy site selection integer linear programming Turkey

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Application of open data and integer linear programming to real-time generation of one-stroke traveling route for collecting and distributing for food loss reduction

Application of open data and integer linear programming to r...

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International Symposium on Soft Computing and Intelligent Systems (SCIS)

作者： Itaru Kaneko Emi Yuda Hitoshi Okada Center for Data-driven Science and Artificial Intelligence Tohoku University Sendai Japan Information and Society Research Division National Institute of Informatics Chiyoda-ku Tokyo

We believe that alleviating poverty and reducing food loss can contribute to the SDGs [1], and we have designed PoC for real time generation of one-stroke routes for real-time collection and distribution of food loss.... 详细信息

关键词： Food waste integer programming integer linear programming Real-time systems Automobiles Open data

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Assessment of Initial-State-Opacity in Live Bounded and Reversible Discrete Event Systems via integer linear programming

Assessment of Initial-State-Opacity in Live Bounded and Reve...

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Mediterranean Conference on Control and Automation (MED)

作者： Francesco Basile Gianmaria De Tommasi Carlo Motta Alberto Petrillo Stefania Santini DIEM University of Salerno Fisciano Italy DIETI Universit&#x00E0 degli Studi di Napoli Federico II Napoli Italy

ISBN: (数字)9781665406734

ISBN: (纸本)9781665406741

Opacity is a property of discrete event systems (DES) that is related to the possibility of hiding a secret from external observers (the intruders). When the secret is the initial state of the system, the related opacity problem is referred to as Initial State Opacity (ISO). A sufficient condition to check ISO by solving integer linear programming problems is given in this paper. Such a condition exploits the algebraic representation of Petri nets and a structural one of its behavior in terms of minimal support T-invariants. The effectiveness of the proposed approach is shown by means of examples.

关键词： Sufficient conditions Automation ISO Petri nets integer linear programming Observers Discrete-event systems

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Deriving consensus tumor trees using integer linear programming

Deriving consensus tumor trees using integer linear programm...

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IEEE International Conference on Bioinformatics and Biomedicine (BIBM)

作者： Matthew Smith-Erb Ziyun Guang Layla Oesper Department of Computer Science Carleton College Northfield Minnesota

ISBN: (数字)9781665468190

ISBN: (纸本)9781665468206

The acquisition of somatic mutations by a tumor can be modeled by a type of evolutionary tree. Although many methods have been developed to infer a tumor’s evolutionary history, they can produce conflicting results for a single patient. A consensus tree that reconciles these possible trees is important for understanding the tumor’s evolutionary process. We use integer linear programming to find a consensus tree among multiple plausible tumor evolutionary histories.

关键词： Biological system modeling integer linear programming linear programming Data models History Bioinformatics Tumors

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Ingredient Inventory and Revenue Optimization of Restaurant Food Sales using integer linear programming

Ingredient Inventory and Revenue Optimization of Restaurant ...

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International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management (HNICEM)

作者： Jerahmeel K. Coching Adrian Jenssen L. Pe Seth Gabriel D. Yeung Wynnezel Wayne Naoto Akeboshi Robert Kerwin C. Billones Elmer P. Dadios Department of Manufacturing Engineering and Management Intelligent Systems Laboratory Center for Engineering and Sustainable Development Research De La Salle University Manila Philippines

Restaurant businesses require significant revenue generation to finance their operational costs. Without revenue, restaurants will operate under deficits, thus making operations unsustainable. This leads to increased risks of business closure and the inability to service any form of customer demand sustainably. Factors that affect revenue generation for restaurants include but are not limited to the following: capital, the availability and limit of stored ingredients, ingredient costs, customer demand, and food sales. This study used integer linear programming (ILP) to model a simulated restaurant’s monthly revenue sales. Optimal maximization of revenue served as the objective function of the ILP model. On the other hand, considerations in formulating the model’s constraint equations include ingredient usage for each menu item, budget for ingredient purchase, and the monthly sales demand distribution of menu items. The MATLAB software was used to simulate the ILP model. The simulation results provided the optimal ingredient inventory configuration and the required number of sales for each menu item.

关键词： Costs Simulation integer linear programming linear programming Mathematical models Software Optimization

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Multi-Period Inventory Management Optimization Using integer linear programming: A Case Study on Plywood Distribution

Multi-Period Inventory Management Optimization Using Integer...

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International Conference on Humanoid, Nanotechnology, Information Technology, Communication and Control, Environment and Management (HNICEM)

作者： Christalline Jhine L. Shi Nilo T. Bugtai Robert Kerwin C. Billones Department of Manufacturing Engineering and Management De La Salle University Manila Philippines

In the Philippines, plywood distributors heavily rely on inventory to maintain their relevance in the saturated market. Specifically, this paper focuses on the inventory management of a secondary plywood wholesaler who sources from a local supplier and whose clients are primarily small-time construction material retailers. To this end, an integer linear programming (ILP) approach is proposed with the aim to maximize net profit by determining the optimal monthly reorder quantities of each product. First, seasonal demand forecasts are made based on the wholesaler’s 3-year monthly sales volume data. Next, the ILP model is developed wherein the objective of the study is realized by the total gross profit less the total overhead costs. Subsequently, the model takes into account several constraints namely, monthly forecasted demands, crate capacities, storage capacity, trucking service capacity, and customer delivery truck. Finally, the ILP model is implemented using MATLAB to find the optimal monthly inventory and reorder quantity.

关键词： Schedules Costs Inventory management integer linear programming Predictive models Mathematical models Information technology

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Some binary products and integer linear programming for k -metric dimension of graphs

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APPLIED MATHEMATICS AND COMPUTATION 2021年 409卷 126420-126420页

作者： Klavzar, Sandi Rahbarnia, Freydoon Tavakoli, Mostafa Univ Ljubljana Fac Math & Phys Ljubljana Slovenia Univ Maribor Fac Nat Sci & Math Maribor Slovenia Inst Math Phys & Mech Ljubljana Slovenia Ferdowsi Univ Mashhad Fac Math Sci Dept Appl Math POB 1159 Mashhad 91775 Razavi Khorasan Iran

A sharp upper bound and a closed formula for the k-metric dimension of the hierarchical product of graphs is proved. Also, sharp lower bounds for the k-metric dimension of the splice and link products of graphs are presented. An integer linear programming model for computing the k-metric dimension as well as a k-metric basis of a given graph is proposed. These results are applied to bound or to compute the k-metric dimension of some classes of graphs that are of interest in mathematical chemistry. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Metric dimension k-metric dimension Binary product integer linear programming Chemical graph theory

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