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VRP问题及技术回顾 103页

VRP

CVRP

路径优化

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路径优化问题带约束路径优化问题各种各样不同算法的总结回顾 VRP CVRP

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Vehicle Routing

Problems

Massimo Paolucci

(paolucci@dist.unige.it)

010-353 2996

DIST – Università di Genova

VRP – Massimo Paolucci

Vehicle Routing Problems

Vehicle Routing Problems (VRP) deal with the

management of pickup and/or delivery activities

Critical problems, in particular in short distance

transportation

Operational decisions: how the available fleet of vehicles

(resources) can be efficiently used to satisfy a given

service demand according to a set of operational

requirements?

Vehicle Routing: define the routes and possibly the

schedule for the available vehicles

VRP – Massimo Paolucci

Vehicle Routing Problems

VRPs include:

Static problems: the service demand is fixed and a priori known

Dynamic problems: all or part of the service demand may become

known when the vehicles have already started their service (the

vehicle routes may be defined or changed on-line)

Main assumptions for the problems considered in the

following:

The problems are static

The available vehicles are homogeneous (every vehicle provide

the same kind of service)

VRP – Massimo Paolucci

VRP – Characteristics and Components

Freight transportation provided by vehicles through a route

network

Main components:

Road network

Customers

Vehicles

Depots

Drivers

Operational constraints:

global

for single routes

Optimization objectives

VRP – Massimo Paolucci

VRP – Characteristics and Components

The road network:

A graph G=(V, A), G=(V, E) or G=(V, A∪ E)

Directed, undirected or mixed

Sparse vs Dense

Sparse ⇒ |A|=O(|V|)

Dense ⇒ |A|=O(|V|

)

Undirected graph:

large scale road network (countries, regions)

Directed graph:

small scale road network (cities)

VRP – Massimo Paolucci

The road network:

Vertices

depots, customers, road intersections

V={0, 1, …, n}

Arcs

roads

directed (i, j)∈A or undirected e∈E

length, or travel cost c

∀

(i, j)∈A

travel time t

∀

(i, j)∈A

VRP – Characteristics and Components

VRP – Massimo Paolucci

VRP – Characteristics and Components

The road network:

The triangle inequality

≤ c

+ c

∀i, j, k

VRP – Massimo Paolucci

VRP – Characteristics and Components

Customers:

The entities requiring service

Associated with vertices or arcs

Service demand ⇒ quantity of goods or materials to be

delivered or picked up

Characteristics:

Service time windows

Desired service start time (with penalties)

Service time (load/unload)

Vehicle compatibility

Possibility of splitting service

VRP – Massimo Paolucci

VRP – Characteristics and Components

Vehicles:

Fleet size (fixed or variable)

Company or outsourced fleet (fixed vehicle cost)

Depot of reference (single, multiple, possibility of change)

Vehicle capacity (maximum load allowed; weight, volume)

Freight compatibility (perishable goods, dangerous materials)

Compatibility with streets

Load/unload procedure

Costs (associated with mileage, time, fuel, journey, load)

VRP – Massimo Paolucci

VRP – Characteristics and Components

Drivers

Employee workers or vehicle owners

Union and contract conditions

Working periods, shifts and breaks

Availability and possibility of overtime

Depots

Single or multiple

Number and type of available vehicles

Set of a priori assigned customers

⇒ decomposable problems

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