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Transit Route Network Design Problem
The transit route network design problem is a mathematical optimization problem in the context of Transportation network (graph theory), transportation networks with well-defined stops, routes and timetables such as bus and railway networks. The problem can be broken down into five subproblems: transportation network design, frequency setting, timetable development, vehicle scheduling, and crew scheduling. See also * Liner shipping network design and scheduling problem * Highway network optimization References Mathematical optimization Operations research Mathematical optimization in business Road transport Rail transport {{bus-transport-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transportation Network (graph Theory)
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in operations research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow. A flow network can be used to model traffic in a computer network, circulation with demands, fluids in pipes, currents in an electrical circuit, or anything similar in which something travels through a network of nodes. As such, efficient algorithms for solving network flows can also be applied to solve problems that can be reduced to a flow network, including survey design, airline scheduling, image segmentation, and the matching probl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Railway
Rail transport (also known as train transport) is a means of transport using wheeled vehicles running in railway track, tracks, which usually consist of two parallel steel railway track, rails. Rail transport is one of the two primary means of land transport, next to road transport. It is used for about 8% of passenger and rail freight transport, freight transport globally, thanks to its Energy efficiency in transport, energy efficiency and potentially high-speed rail, high speed.Rolling stock on rails generally encounters lower friction, frictional resistance than rubber-tyred road vehicles, allowing rail cars to be coupled into longer trains. Power is usually provided by Diesel locomotive, diesel or Electric locomotive, electric locomotives. While railway transport is capital intensity, capital-intensive and less flexible than road transport, it can carry heavy loads of passengers and cargo with greater energy efficiency and safety. Precursors of railways driven by human or an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transportation Network Design
Transport (in British English) or transportation (in American English) is the intentional Motion, movement of humans, animals, and cargo, goods from one location to another. Mode of transport, Modes of transport include aviation, air, land transport, land (rail transport, rail and road transport, road), ship transport, water, cable transport, cable, pipeline transport, pipelines, and space transport, space. The field can be divided into infrastructure, vehicles, and operations. Transport enables human trade, which is essential for the development of civilizations. Transport infrastructure consists of both fixed installations, including roads, railways, airway (aviation), airways, waterways, canals, and pipeline transport, pipelines, and terminals such as airports, train station, railway stations, bus stations, warehouses, trucking terminals, refueling depots (including fuel docks and fuel stations), and seaports. Terminals may be used both for the interchange of passengers and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Setting
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second. Special definitions of frequency are used in certain contexts, such as the angular frequency in rotational or cyclical properties, when the rate of angular progress is measured. Spatial frequency is defined for properties that vary or cccur repeatedly in geometry or space. The unit of measurement of frequency in the International System of Units (SI) is the hertz, having the symbol Hz. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Timetable Development
A schedule (, ) or a timetable, as a basic time-management tool, consists of a list of times at which possible tasks, events, or actions are intended to take place, or of a sequence of events in the chronological order in which such things are intended to take place. The process of creating a schedule — deciding how to order these tasks and how to commit resources between the variety of possible tasks — is called scheduling,Ofer Zwikael, John Smyrk, ''Project Management for the Creation of Organisational Value'' (2011), p. 196: "The process is called scheduling, the output from which is a timetable of some form". and a person responsible for making a particular schedule may be called a scheduler. Making and following schedules is an ancient human activity. Some scenarios associate this kind of planning with learning life skills. Schedules are necessary, or at least useful, in situations where individuals need to know what time they must be at a specific location to rece ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vehicle Scheduling
A vehicle () is a machine designed for self-propulsion, usually to transport people, cargo, or both. The term "vehicle" typically refers to land vehicles such as human-powered vehicles (e.g. bicycles, tricycles, velomobiles), animal-powered transports (e.g. horse-drawn carriages/wagons, ox carts, dog sleds), motor vehicles (e.g. motorcycles, cars, trucks, buses, mobility scooters) and railed vehicles (trains, trams and monorails), but more broadly also includes cable transport ( cable cars and elevators), watercraft (ships, boats and underwater vehicles), amphibious vehicles (e.g. screw-propelled vehicles, hovercraft, seaplanes), aircraft (airplanes, helicopters, gliders and aerostats) and space vehicles (spacecraft, spaceplanes and launch vehicles). This article primarily concerns the more ubiquitous land vehicles, which can be broadly classified by the type of contact interface with the ground: wheels, tracks, rails or skis, as well as the non-contact technologies such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crew Scheduling
Crew scheduling is the process of assigning crews to operate transportation systems, such as rail lines or airlines. Complex Most transportation systems use software to manage the crew scheduling process. Crew scheduling becomes more and more complex as you add variables to the problem. These variables can be as simple as 1 location, 1 skill requirement, 1 shift of work and 1 set roster of people. In the Transportation industries, such as Rail or mainly Air Travel, these variables become very complex. In Air Travel for instance, there are numerous rules or "constraints" that are introduced. These mainly deal with legalities relating to work shifts and time, and a crew member's qualifications for working on a particular aircraft. Add numerous locations to the equation and Collective Bargaining and Federal labor laws and these become new considerations for the problem solving method. Fuel is also a major consideration as aircraft and other vehicles require a lot of costly fuel t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liner Shipping Network Design And Scheduling Problem
The liner shipping network design and scheduling problem (LSNDSP) is a mathematical optimization problem in operations research that models maritime transport logistic problems. It is of practical interest in the shipping industry, as improvements in mathematical technoques can be directly applied to real-world problems. The problem consists of the simultaneous resolution of three sub-problems: fleet design, ship scheduling and cargo routing, while minimizing overall cost. An industry-standard benchmark dataset, LINERLIB, is used to measure the effectiveness of mathematical approaches to the LSNDSP. In 2024, resarchers from Google's Operations Research group announced that they had produced a new optimization technique which outperformed all previous solutions to the problem, and offered substantial increases in both profit and throughput for shipping companies. References See also * Transshipment * Transit route network design problem The transit route network design p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Highway Network Optimization
Highway network optimization is the problem of configuring highway networks to maximize economic and social utility. Numerous mathematical optimization techniques have been brought to bear on the problem, including linear programming and deep learning. Recent research has included work on treating the highway optimization problem as a dynamic system. References See also * Traffic engineering * Transit route network design problem * Liner shipping network design and scheduling problem The liner shipping network design and scheduling problem (LSNDSP) is a mathematical optimization problem in operations research that models maritime transport logistic problems. It is of practical interest in the shipping industry, as improvements ... Mathematical optimization Operations research Mathematical optimization in business Road transport {{compsci-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maxima and minima, maximizing or minimizing a Function of a real variable, real function by systematically choosing Argument of a function, input values from within an allowed set and computing the Value (mathematics), value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. Optimization problems Opti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research
Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and decision-making. Although the term management science is sometimes used similarly, the two fields differ in their scope and emphasis. Employing techniques from other mathematical sciences, such as mathematical model, modeling, statistics, and mathematical optimization, optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlapped with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the Maxima and minima, maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
