|
1-center Problem
The 1-center problem, also known as minimax problem or minmax location problem, is a classical combinatorial optimization problem in operations research of facilities location type. In its most general case the problem is stated as follows: given a set of ''n'' demand points, a space of feasible locations of a facility and a function to calculate the transportation cost between a facility and any demand point, find a location of the facility which minimizes the maximum facility-demand point transportation cost. There are numerous particular cases of the problem, depending on the choice of the locations both of demand points and facilities, as well as the distance function. A simple special case is when the feasible locations and demand points are in the plane with Euclidean distance as transportation cost (planar minmax Euclidean facility location problem, Euclidean 1-center problem in the plane, etc.). It is also known as the smallest circle problem. Its generalization to ''n''-di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsack problem. In many such problems, such as the ones previously mentioned, exhaustive search is not tractable, and so specialized algorithms that quickly rule out large parts of the search space or approximation algorithms must be resorted to instead. Combinatorial optimization is related to operations research, algorithm theory, and computational complexity theory. It has important applications in several fields, including artificial intelligence, machine learning, auction theory, software engineering, VLSI, applied mathematics and theoretical computer science. Some research literature considers discrete o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path (graph Theory)
In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipathGraph Structure Theory: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, Held June 22 to July 5, 1991p.205/ref>) in a directed graph is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction. Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. Bondy and Murty (1976), Gibbons (1985), or Diestel (2005). Korte et al. (1990) cover more advanced algorithmic topics concerning paths in graphs. Definitions Walk, trail, and path * A walk is a finite or infinite sequence of edges which joins a sequence of vertices. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-center Problem is the problem of how to share the co ...
A facility location problem is the problem of deciding where a given public facility (e.g. a school or a power station) should be placed. This problem has been studied from various angles. * Optimal facility location is an optimization problem: deciding where to place the facility in order to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing. * Facility location (competitive game) is a problem in game theory: finding an equilbrium in a game in which the players are different producers, each of which looks for a location for placing a facility in order to attract as many consumers as possible. * Facility location (cooperative game) The cooperative facility location game is a cooperative game of cost sharing. The goal is to share the cost of opening new facilities between the clients enjoying these facilities.Kamal Jain and Mohammad Mahdian, "Cost Sharing". Chapter 15 in The g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Obnoxious Facility Location
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis. Minimum facility location A simple facility location problem is the Weber problem, in which a single facility is to be placed, with the only optimization criterion being the minimization of the weighted sum of distances from a given set of point sites. More complex problems considered in this discipline include the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. In a basic formulation, the facility location problem consists of a set of potential facility sites ''L'' where a facility can be opened, and a set of demand points ''D'' that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxmin Facility Location is the problem of how to share the co ...
A facility location problem is the problem of deciding where a given public facility (e.g. a school or a power station) should be placed. This problem has been studied from various angles. * Optimal facility location is an optimization problem: deciding where to place the facility in order to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing. * Facility location (competitive game) is a problem in game theory: finding an equilbrium in a game in which the players are different producers, each of which looks for a location for placing a facility in order to attract as many consumers as possible. * Facility location (cooperative game) The cooperative facility location game is a cooperative game of cost sharing. The goal is to share the cost of opening new facilities between the clients enjoying these facilities.Kamal Jain and Mohammad Mahdian, "Cost Sharing". Chapter 15 in The g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Median
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. It is also known as the 1-median, spatial median, Euclidean minisum point, or Torricelli point. The geometric median is an important estimator of location in statistics, where it is also known as the ''L''1 estimator. It is also a standard problem in facility location, where it models the problem of locating a facility to minimize the cost of transportation. The special case of the problem for three points in the plane (that is, = 3 and = 2 in the definition below) is sometimes also known as Fermat's problem; it arises in the construction of minimal Steiner trees, and was originally posed as a problem by Pierre de Fermat and solved by Evangelista Torricelli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1-median Problem
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis. Minimum facility location A simple facility location problem is the Weber problem, in which a single facility is to be placed, with the only optimization criterion being the minimization of the weighted sum of distances from a given set of point sites. More complex problems considered in this discipline include the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. In a basic formulation, the facility location problem consists of a set of potential facility sites ''L'' where a facility can be opened, and a set of demand points ''D'' that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minsum Facility Location
The study of facility location problems (FLP), also known as location analysis, is a branch of operations research and computational geometry concerned with the optimal placement of facilities to minimize transportation costs while considering factors like avoiding placing hazardous materials near housing, and competitors' facilities. The techniques also apply to cluster analysis. Minimum facility location A simple facility location problem is the Weber problem, in which a single facility is to be placed, with the only optimization criterion being the minimization of the weighted sum of distances from a given set of point sites. More complex problems considered in this discipline include the placement of multiple facilities, constraints on the locations of facilities, and more complex optimization criteria. In a basic formulation, the facility location problem consists of a set of potential facility sites ''L'' where a facility can be opened, and a set of demand points ''D'' that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of The Operational Research Society
The ''Journal of the Operational Research Society'' is a peer-reviewed academic journal covering operations research. It is an official journal of The Operational Research Society and has been in existence since 1950. It publishes full length case-oriented papers, full length theoretical papers, technical notes, discussions (viewpoints) and book reviews. History The journal began as ''Operational Research Quarterly'' in 1950. At that time it was published by the Operational Research Club (Great Britain). It was published four times a year until 1978 (from 1953–1969 under the title ''OR'') when it became a monthly publication and the name was changed to ''Journal of the Operational Research Society''. Abstracting and indexing The journal is abstracted and indexed by ABI/INFORM, Compendex, Current Contents/Engineering, Computing & Technology, Current Contents/Social & Behavioural Sciences, Inspec, Science Citation Index, Social Sciences Citation Index, Scopus, and Zentralblatt M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimax Path Problem
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight of the minimum-weight edge in the path. The widest path problem is also known as the maximum capacity path problem. It is possible to adapt most shortest path algorithms to compute widest paths, by modifying them to use the bottleneck distance instead of path length. However, in many cases even faster algorithms are possible. For instance, in a graph that represents connections between routers in the Internet, where the weight of an edge represents the bandwidth of a connection between two routers, the widest path problem is the problem of finding an end-to-end path between two Internet nodes that has the maximum possible bandwidth. The smallest edge weight on this path is known as the capacity or bandwidth of the path. As well as its applications in network routing, the widest path problem is also an important component of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Graph
In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction). Graph theory itself is typically dated as beginning with Leonhard Euler's 1736 work on the Seven Bridges of Königsberg. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, had already appeared in the 13th century, in the work of Ramon Llull. Such a drawing is sometimes referred to as a mystic rose. Properties The complete graph on vertices is denoted by . Some sources claim that the letter in this notation stands for the German word , but the German name for a complete graph, , does not contain the letter , and other sources state that the notation honors the contributions of Kazimierz Kuratowski to graph theory. has edges (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
