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| 車両巡回問題（VRP）× | 整数計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1959 | 1958 |
| 提唱者≠ | George Dantzig & John Ramser | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) |
| 種類≠ | Combinatorial optimization problem | Mathematical optimisation — exact combinatorial method |
| 原典≠ | Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91. DOI ↗ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 |
| 別名≠ | Capacitated Vehicle Routing Problem, Fleet Routing Problem, Multi-Vehicle Routing Problem, Araç Rotalama Problemi | IP, MIP, mixed-integer programming, mixed-integer linear programming |
| 関連≠ | 3 | 4 |
| 概要≠ | The Vehicle Routing Problem (VRP) seeks the minimum-cost set of routes for a fleet of vehicles to serve a collection of geographically dispersed customers, each with a known demand, departing from and returning to a central depot. Originally formulated as the Truck Dispatching Problem by Dantzig and Ramser in 1959, VRP is a foundational model in logistics, supply chain management, and operations research, applicable whenever goods or services must be delivered efficiently across multiple stops. | Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems. |
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