scheduling and routing algorithms for agvs: a survey ling qiu · wen-jing hsu · shell-ying huang ·...

Scheduling and Routing Algorithms for AGVs: A Survey

Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang

presented by Opresented by Oğğuz Atanuz 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

• HardwareHardware : AGVs, paths, controllers, sensors, etc.

• SoftwareSoftware : 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: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: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:some analogies:

• AGVs / data packets

• paths / data links

• traffic control devices / routers

some distinctions: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

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


static methods

time-window based methods

dynamic methods





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 conflictshead-on conflicts: find another shortest path

• head-to-tail & junction conflictshead-to-tail & junction conflicts: slowing down the latter

• complexity of O(n2), n is # P/D stations or junctions


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



static methods


dynamic methods





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(w2log w), w is # time-windows of all nodes

Huang et al., 1988

Time-window-based Methods

• labelling algorithmlabelling 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(v4n2), v # vehicles, n # nodes, suitable for small systems

Kim and Tanchoco, 1991

• later in 1993, using conservative myopicconservative myopic strategy

• one vehicle at a time, previous routes are strictly respected

• subsequent schedule made after the vehicle becomes idle



static methods


dynamic methods





Dynamic Methods

• in order to speed up the process of finding routes

• utilization of path segments determined during routing

• incremental route planningincremental 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


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

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



0-1 integer-programming model

intersection graph method

integer linear programming model



Path Optimization0-1 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

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

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 numbervehicle number & routing controlrouting control not considered




Linear Topology

Loop Topology

Mesh Topology


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




Linear Topology

Loop Topology

Mesh Topology



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


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)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





Linear Topology

Loop Topology

Mesh Topology


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(n2) and O(n3)



Mesh Topology

Qiu and Hsu, 2000

• n x n mesh-like topology

• can schedule & route simultaneously up to 4n2 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 4n2, solution might not be optimal

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

Dedicated Scheduling Algorithms

considers the scheduling of AGV’s & jobs without considering the routing process

Akturk and Yilmaz, 1996

• micro-opportunistic scheduling algorithm (MOSA)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)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 RemarksLatest 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

scheduling and routing algorithms for agvs: a survey ling qiu · wen-jing hsu · shell-ying huang ·...

Documents

path shortest time path

routing algorithms

path optimization

scheduling problem

optimal path

consideration of routing

variation of path problems

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