Scheduling and Routing Algorithms for AGVs: A Survey

boorishadamantAI and Robotics

Oct 29, 2013 (3 years and 7 months ago)

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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




deadlines



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



deadlocks


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



head
-
on conflicts
: find another shortest path



head
-
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



task
-
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



minimize the delay of loading/unloading operations



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



intelligent navigation mechanisms



robot vision



image processing



information fusion

Problems of scheduling & routing will not disappear


QUESTIONS

&

ANSWERS