scheduling and routing algorithms for agvs: a survey ling qiu · wen-jing hsu · shell-ying huang ·...
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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
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OUTLINE
• Introduction
• Problem of Scheduling & Routing
• Similar Problems
• Classification of Algorithms
• Future Directions of Research
• Concluding Remarks
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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
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INTRODUCTION
• Great number of tasks
• Large Fleet
• Many hazards, i.e., congestion, deadlocks
• Non-trivial scheduling / routing
• Cancellation of AGV system deployment
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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
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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
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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
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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
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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
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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
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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
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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
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1) Algorithms for General Path Topology
2) Path Optimization
3) Algorithms for Specific Path Topologies
4) Dedicated Scheduling Algorithms
![Page 14: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/14.jpg)
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
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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
![Page 16: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/16.jpg)
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 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
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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
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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
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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
![Page 20: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/20.jpg)
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(w2log w), w is # time-windows of all nodes
Huang et al., 1988
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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
Algorithms for General Path Topology
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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
![Page 23: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/23.jpg)
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 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
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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
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1) Algorithms for General Path Topology
2) Path Optimization
3) Algorithms for Specific Path Topologies
4) Dedicated Scheduling Algorithms
![Page 26: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/26.jpg)
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
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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
![Page 28: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/28.jpg)
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
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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
![Page 30: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/30.jpg)
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
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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
![Page 32: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/32.jpg)
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
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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
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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
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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
![Page 36: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/36.jpg)
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
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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
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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
Algorithms for Specific Path Topologies
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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
![Page 40: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/40.jpg)
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)
Algorithms for Specific Path Topologies
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Algorithms for Specific Path Topologies
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
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1) Algorithms for General Path Topology
2) Path Optimization
3) Algorithms for Specific Path Topologies
4) Dedicated Scheduling Algorithms
![Page 43: Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz Atan](https://reader030.vdocument.in/reader030/viewer/2022032800/56649d4d5503460f94a2c611/html5/thumbnails/43.jpg)
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
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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
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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”
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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
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QUESTIONS&
ANSWERS