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 o...
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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.
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 intege...
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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.
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...
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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.
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 h...
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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 linearprogramming 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.
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....
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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. You can easily create routes in real time using open data and integerprogramming.
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 opac...
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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.
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 f...
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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.
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 ...
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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.
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 wh...
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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.
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 pr...
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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.
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