|
Vehicle Rescheduling Problem
The vehicle rescheduling problem (VRSP) is a combinatorial optimization and integer programming problem seeking to service customers on a trip after change of schedule such as vehicle break down or major delay. Proposed by Li, Mirchandani and Borenstein in 2007, the VRSP is an important problem in the fields of transportation and logistics. Determining the optimal solution is an NP-complete problem in combinatorial optimization, so in practice heuristic and deterministic methods are used to find acceptably good solutions for the VRSP. Overview Several variations and specializations of the vehicle rescheduling problem exist: * Single Depot Vehicle Rescheduling Problem (SDVRSP): A number of trips need to be rescheduled due to delay, vehicle break down or for any other reason. The goal is to find optimal rescheduling of the existing fleet, using possibly extra vehicles from the depot, in order to minimise the delay and the operating costs. In the Single Depot variation, there is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vehicle Rescheduling
A vehicle (from la, vehiculum) is a machine that transports people or cargo. Vehicles include wagons, bicycles, motor vehicles (motorcycles, cars, trucks, buses, mobility scooters for disabled people), railed vehicles (trains, trams), watercraft (ships, boats, underwater vehicles), amphibious vehicles (screw-propelled vehicles, hovercraft), aircraft (airplanes, helicopters, aerostats) and spacecraft.Halsey, William D. (Editorial Director): ''MacMillan Contemporary Dictionary'', page 1106. MacMillan Publishing, 1979. Land vehicles are classified broadly by what is used to apply steering and drive forces against the ground: wheeled, tracked, railed or skied. ISO 3833-1977 is the standard, also internationally used in legislation, for road vehicles types, terms and definitions. History * The oldest boats found by archaeological excavation are logboats, with the oldest logboat found, the Pesse canoe found in a bog in the Netherlands, being carbon dated to 8040 - 751 ... [...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] |
Integer Programming
An integer programming problem is a mathematical optimization or Constraint satisfaction problem, feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are Linear function (calculus), linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. Canonical and standard form for ILPs In integer linear programming, the ''canonical form'' is distinct from the ''standard form''. An integer linear program in canonical form is expressed thus (note that it is the \mathbf vector which is to be decided): : \begin & \text && \math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-hard
In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem ''H'' is NP-hard when every problem ''L'' in NP can be reduced in polynomial time to ''H''; that is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve any NP-hard problem would give polynomial time algorithms for all the problems in NP. As it is suspected that P≠NP, it is unlikely that such an algorithm exists. It is suspected that there are no polynomial-time algorithms for NP-hard problems, but that has not been proven. Moreover, the class P, in which all problems can be solved in polynomial time, is contained in the NP class. Defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Single Depot Vehicle Scheduling Problem
Single may refer to: Arts, entertainment, and media * Single (music), a song release Songs * "Single" (Natasha Bedingfield song), 2004 * "Single" (New Kids on the Block and Ne-Yo song), 2008 * "Single" (William Wei song), 2016 * "Single", by Meghan Trainor from the album '' Only 17'' Sports * Single (baseball), the most common type of base hit * Single (cricket), point in cricket * Single (football), Canadian football point * Single-speed bicycle Transportation * Single-cylinder engine, an internal combustion engine design with one cylinder, or a motorcycle using such engine * Single (locomotive) In railway terminology, a single is a steam locomotive with a single pair of driving wheels. Some sources use 'Single' only for the 2-2-2 type, also known as a Jenny Lind locomotive, but more commonly singles could have any number of leading or t ..., a steam locomotive with a single pair of driving wheels * As a verb: to convert a double-track railway to a single-track railway O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multi Depot Vehicle Scheduling Problem
Multi is a shortened form of "multiple". It may refer to: * Alternate character, in online gaming * Multi two diamonds, a contract bridge convention * Multirhyme, a synonym for feminine rhyme used in hip hop music * Multi (''To Heart''), a character from the visual novel and anime series ''To Heart'' * Multi-touch display See also * Multiculturalism, a public policy approach for managing cultural diversity in a multiethnic society * Multitude, a term used by some philosophers to refer to the population of the world * ''Multitudes'' (journal), a French philosophical, political and artistic monthly review * Multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ..., an elementary arithmetic operation * Multitasking (other) {{disambiguation ... [...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] |
Vehicle Routing Problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which the first algorithmic approach was written and was applied to petrol deliveries. Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods. The objective of the VRP is to minimize the total route cost. In 1964, Clarke and Wright improved on Dantzig and Ramser's approach using an effective greedy algorithm called the savings algorithm. Determining the optimal solution to VRP is NP-hard, so the size of problems that can be optimally solved using mathematical programming or combinatorial optimization may be limited. Therefore, commercial solvers tend to use he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demand Responsive Transport
Demand-responsive transport (DRT), also known as demand-responsive transit, demand-responsive service, US National Transit Database Dial-a-Ride transit (sometimes DART), flexible transport services,CONNECT is a Coordination Action in the Sustainable Development Thematic Area of the European Union's 6th Framework Program, successfully ended on December 2005 MicrotransitWhat i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optimal Scheduling
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts 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 maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defined ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transportation Planning
Transportation planning is the process of defining future policies, goals, investments, and spatial planning designs to prepare for future needs to move people and goods to destinations. As practiced today, it is a collaborative process that incorporates the input of many stakeholders including various government agencies, the public and private businesses. Transportation planners apply a multi-modal and/or comprehensive approach to analyzing the wide range of alternatives and impacts on the transportation system to influence beneficial outcomes. Transportation planning is also commonly referred to as transport planning internationally, and is involved with the evaluation, assessment, design, and siting of transport facilities (generally streets, highways, bike lanes, and public transport lines). Models and sustainability Transportation planning, or transport planning, has historically followed the rational planning model of defining goals and objectives, identifying pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
