# Scheduling and Routing Algorithms for AGVs: A Survey

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29 Οκτ 2013 (πριν από 4 χρόνια και 6 μήνες)

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Scheduling and Routing
Algorithms for AGVs: A Survey

Ling Qiu

Wen
-
Jing Hsu

Shell
-
Ying Huang

Han Wang

presented by O
ğ
uz Atan

OUTLINE

Introduction

Problem of Scheduling & Routing

Similar Problems

Classification of Algorithms

Future Directions of Research

Concluding Remarks

INTRODUCTION

AGVs are popular in

Automatic Materials Handling Systems

Flexible Manufacturing Systems

Container Handling Applications

AGVs are composed of

Hardware

: AGVs, paths, controllers, sensors, etc.

Software

: algorithms for managing the hardware

INTRODUCTION

Great number of tasks

Large Fleet

Many hazards, i.e., congestion, deadlocks

Non
-
trivial scheduling / routing

Cancellation of AGV system deployment

THE SCHEDULING PROBLEM

dispatches a set of AGVs

realizes a batch of pickup/drop
-
off jobs

considers a number of constraints

priority

tries to achieve certain goals

minimizing the number of AGVs

minimizing the total travel time

THE ROUTING PROBLEM

After Scheduling Decision is Made;

finds a suitable route for every AGV

from origin to destination

based on the traffic situation

considering a certain goal

shortest
-
distance path

shortest
-
time path

minimal energy path

THE ROUTING PROBLEM

Routing Decision involves two issues:

whether there exists a route

indirect transfer system

whether the selected route is feasible

congestion

conflicts

THE PROBLEM

A system with few vehicles & jobs

trivial scheduling algorithms are OK, i.e., FCFS

nearest idle vehicle

routing is main issue

A system with many jobs & limited number of vehicles

many hazards : collusion, congestion, livelock, deadlock

nontrivial scheduling & routing

SIMILAR PROBLEMS

A variation of
Vehicle Routing Problem (VRP)

Bodin and Golden, 1981 ; Bodin et al., 1983

significant distinctions:

length of a vehicle

load capacity of a path

shortest time path vs. shortest distance path

revision of existing layout

SIMILAR PROBLEMS

A variation of
Path Problems in Graph Theory

shortest path problem

Hamiltonian
-
type problem

main differences:

time
-
critical problem

existence of an optimal path

when & how an AGV gets to its destination

graph problem disregards:

system control mechanism

path layout

SIMILAR PROBLEMS

A variation of
Routing Electronic Data in a Network

some analogies:

AGVs / data packets

paths / data links

traffic control devices / routers

some distinctions:

time for transportation
: a function of distance or not?

in case of failure
: discard & re
-
send

CLASSIFICATION OF ALGORITHMS

1) Algorithms for General Path Topology

treats the problem as a graph theory problem

2) Path Optimization

considers optimization of path network

3) Algorithms for Specific Path Topologies

single
-
loop, multi
-
loops, meshes, etc.

4) Dedicated Scheduling Algorithms

without consideration of routing

1) Algorithms for General Path Topology

2) Path Optimization

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Algorithms for General Path Topology

Focus mainly on finding the feasible routes

do not consider the topological characteristics

offer universal routing solutions

aim is to give
conflict
-
free

and
shortest
-
time

routings

Methods used can be put in three categories:

static methods

time
-
window based methods

dynamic methods

1) Algorithms for General Path Topology

static methods

time
-
window based methods

dynamic methods

2) Path Optimization

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Algorithms for General Path Topology

Static Methods

routing procedure using Dijkstra’s shortest path algorithm

Broadbent et al., 1985

matrix of path occupation times of vehicles

potential conflicts are avoided a priori

-
on conflicts
: find another shortest path

-
to
-
tail & junction conflicts
: slowing down the latter

complexity of
O(n
2
), n
is # P/D stations or junctions

Algorithms for General Path Topology

Static Methods

bidirectional path AGV systems are advantageous

utilization of vehicles

potential throughput efficiency

improvement in productivity

reduction in # vehicles

Egbelu and Tanchoco, 1986; Egbelu, 1987

no algorithm is given to guarantee the optimal routes

Static Methods

bidirectional flow path network

partitioning shortest path (PSP)

algorithm

finds a route for new added AGV, without changing previous’

complexity O(n x a), a is # of arcs (path segments)

if a path is allocated to a vehicle, unusable for others until

destination is reached

may not find a path even if there exists one

suitable for small networks with less AGV’s

Daniels, 1988

Algorithms for General Path Topology

1) Algorithms for General Path Topology

static methods

time
-
window based methods

dynamic methods

2) Path Optimization

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Algorithms for General Path Topology

Time
-
window
-
based Methods

in order to share the path network efficiently

better path utilization

labelling algorithm to find a shortest
-
time path

single vehicle, bidirectional path network

path segments as nodes, arcs between adjacent segments

complexity of O(w
2
log w), w is # time
-
windows of all nodes

Huang et al., 1988

Time
-
window
-
based Methods

labelling algorithm

to find a shortest
-
time path

conflict
-
free & shortest time routing in bidirectional path network

based on Dijkstra’s shortest path algorithm

free time
-
windows as nodes, arcs as reachability among them

O(v
4
n
2
), v # vehicles, n # nodes, suitable for small systems

Kim and Tanchoco, 1991

later in 1993, using
conservative myopic

strategy

one vehicle at a time, previous routes are strictly respected

subsequent schedule made after the vehicle becomes idle

Algorithms for General Path Topology

1) Algorithms for General Path Topology

static methods

time
-
window based methods

dynamic methods

2) Path Optimization

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Algorithms for General Path Topology

Dynamic Methods

in order to speed up the process of finding routes

utilization of path segments determined during routing

incremental route planning

selects the next node for vehicle to visit until destination

selected among adjacent nodes for shortest travel time

optimal route not guaranteed, better for small systems

Taghaboni and Tanchoco, 1995

Algorithms for General Path Topology

Dynamic Methods

algorithm for an optimal integrated solution

dispatching, conflict
-
free routing, scheduling of AGVs

defines a partial transportation plan as a schedule and a

route for each vehicle

states are defined corresponding to partial transportation plans

dynamic programming tries to find the best final state

# states is very large, some are eliminated, vehicle limit is 2

optimality of the solution is not guaranteed

Langevin et al., 1995

1) Algorithms for General Path Topology

2) Path Optimization

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Since computation of finding optimal routes is difficult;

Optimize the path layout

Optimize the distribution of P/D stations

Three methods to formulate the problem:

0
-
1 integer
-
programming model

intersection graph method

integer linear programming model

Path Optimization

1) Algorithms for General Path Topology

2) Path Optimization

0
-
1 integer
-
programming model

intersection graph method

integer linear programming model

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Path Optimization

0
-
1 Integer Programming Model

Gaskins and Tanchoco, 1987

find the optimal unidirectional path network

facility layout and P/D stations are given

minimize the total travelling distance of loaded vehicles

unloaded vehicles not considered

a fleet of AGVs with same origin & destination every time

# 0
-
1 variables may be very large, inefficient computation

Kaspi and Tanchoco, 1990

use branch&bound to reduce the computation

worse quality, since not all possibilities are enumerated

1) Algorithms for General Path Topology

2) Path Optimization

0
-
1 integer
-
programming model

intersection graph method

integer linear programming model

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Path Optimization

Intersection Graph Method

Sinriech and Tanchoco, 1991

only a reduced subset of all nodes in path network is considered

only the intersection nodes are used to find the optimal solution

# branches is only half of the main problem

can be used in large systems

since only intersection nodes are considered, some optimal

solutions might be missed

1) Algorithms for General Path Topology

2) Path Optimization

0
-
1 integer
-
programming model

intersection graph method

integer linear programming model

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Path Optimization

Integer Linear Programming Model

Goetz and Egbelu, 1990

select the path and location of P/D stations together

minimize the total distance traveled by loaded & unloaded AGVs

a heuristic algorithm is used to reduce the size of the problem

can be used in large systems

can be used in design of large path layouts

issues of
vehicle number

&
routing control

not considered

1) Algorithms for General Path Topology

2) Path Optimization

3) Algorithms for Specific Path Topologies

Linear Topology

Loop Topology

Mesh Topology

4) Dedicated Scheduling Algorithms

Algorithms for Specific Path Topologies

Linear Topology

Qui and Hsu, 2001

schedule & route a batch of AGVs concurrently

bidirectional linear path layout

freedom of conflicts is guaranteed

size of the system does not effect the efficiency of the algorithm

unrealistic synchronization requirements of vehicles

1) Algorithms for General Path Topology

2) Path Optimization

3) Algorithms for Specific Path Topologies

Linear Topology

Loop Topology

Mesh Topology

4) Dedicated Scheduling Algorithms

Algorithms for Specific Path Topologies

Loop Topology

only few vehicles run in the same direction within a loop

simpler routing control, but lower system throughput

Tanchoco and Sinriech, 1992

finds the optimal closed single
-
loop path layout

algorithm based on integer programming

simple routing control:

vehicles running in same direction with uniform speed

no intersections in the optimal single
-
loop

vehicle limit is 10 / single
-
loop , not suitable for large systems

Algorithms for Specific Path Topologies

Loop Topology

Lin and Dgen, 1994

algorithm for routing AGVs on non
-
overlapping closed loops

P/D stations in each loop are served by a single vehicle

transit areas located between adjacent loops

-
list time
-
window algorithm used for shortest travel time path

computation for routing is small

system throughput is low, since single vehicle in a loop

transfer devices are expensive, therefore can’t be a large system

Loop Topology

Barad and Sinriech, 1998

segmented floor topology (SFT)

consisting of one or more zones

each zone is separated into non
-
overlapping segments

each segment served by a single vehicle moving bidirectional

transfer buffers located at both ends of every segment

transfer devices may be costly or time consuming

Algorithms for Specific Path Topologies

1) Algorithms for General Path Topology

2) Path Optimization

3) Algorithms for Specific Path Topologies

Linear Topology

Loop Topology

Mesh Topology

4) Dedicated Scheduling Algorithms

Mesh Topology

container handling

stacking yards arranged into rectangular blocks

Hsu and Huang, 1994

gave analysis of time complexities for some routing operations

delivery, distribution, scattering, accumulation, gathering, sorting

linear array, ring, binary tree, star, 2D mesh, n
-
cube, etc.

upper bounds of time and space complexities are O(n
2
) and O(n
3
)

Algorithms for Specific Path Topologies

Algorithms for Specific Path Topologies

Mesh Topology

Qiu and Hsu, 2000

n x n mesh
-
like topology

can schedule & route simultaneously up to 4n
2

AGVs at one time

schedules AGVs batch by batch based on job arrivals

AGV’s get to destination in 3n steps of well
-
defined physical moves

freedom of conflicts is guaranteed

when # AGVs less than 4n
2
, solution might not be optimal

since AGVs are sparse, shortest path will also be conflict free

1) Algorithms for General Path Topology

2) Path Optimization

3) Algorithms for Specific Path Topologies

4) Dedicated Scheduling Algorithms

Dedicated Scheduling Algorithms

considers the scheduling of AGV’s & jobs without

considering the routing process

Akturk and Yilmaz, 1996

micro
-
opportunistic scheduling algorithm (MOSA)

schedule vehicles & jobs in a decision
-
making hierarchy

based on mixed
-
integer programming

critical jobs & travel time of unloaded vehicles are considered

simultaneously

similar to
time constrained vehicle routing problem (TCVRP)

min. the deviation of the time windows, polynomially solvable

applicable for systems with small number of jobs & vehicles

Dedicated Scheduling Algorithms

Kim and Bae, 1999

scheduling of AGVs for multiple container
-
cranes

AGV routing not taken into consideration

congestion or collusions are possible

Future Directions

Development of new scheduling and routing algorithms

for specific path topologies

have lower computational complexity

more efficient algorithms can be developed by investigating

specific characteristics of topologies

most of the applications have path networks that can be put in

a specific path topology

Algorithms with provable qualities: “freedom of conflicts”

Concluding Remarks

Latest issues of research:

automated driving of vehicles

intelligentization of vehicles

robot vision

image processing

information fusion

Problems of scheduling & routing will not disappear

QUESTIONS

&