Scheduling and Routing Algorithms for AGVs: A Survey

1
Scheduling and Routing Algorithms for AGVs A
Survey
Ling Qiu Wen-Jing Hsu Shell-Ying Huang Han
Wang
presented by Oguz Atan
2
OUTLINE

• Introduction
• Problem of Scheduling Routing
• Similar Problems
• Classification of Algorithms
• Future Directions of Research
• Concluding Remarks

3
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

4
INTRODUCTION

• Great number of tasks
• Large Fleet
• Many hazards, i.e., congestion, deadlocks
• Non-trivial scheduling / routing
• Cancellation of AGV system deployment

5
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

6
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

7
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

8
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

9
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

10
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

11
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

12
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

13
1) Algorithms for General Path Topology 2) Path
Optimization 3) Algorithms for Specific Path
Topologies 4) Dedicated Scheduling Algorithms
14
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

15
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
16
Algorithms for General Path Topology

• Static Methods
• routing procedure using Dijkstras 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(n2), n is P/D stations or
  junctions

17
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

18
Algorithms for General Path Topology

• 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 AGVs
• Daniels, 1988

19
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
20
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

21
Algorithms for General Path Topology

• Time-window-based Methods
• labelling algorithm to find a shortest-time path
• conflict-free shortest time routing in
  bidirectional path network
• based on Dijkstras 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 myopic
  strategy
• one vehicle at a time, previous routes are
  strictly respected
• subsequent schedule made after the vehicle
  becomes idle

22
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
23
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

24
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

25
1) Algorithms for General Path Topology 2) Path
Optimization 3) Algorithms for Specific Path
Topologies 4) Dedicated Scheduling Algorithms
26
Path Optimization

• 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

27
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
28
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 branchbound to reduce the computation
• worse quality, since not all possibilities are
  enumerated

29
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
30
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

31
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
32
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

33
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
34
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

35
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
36
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

37
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 cant
  be a large system

38
Algorithms for Specific Path Topologies

• 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

39
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
40
Algorithms for Specific Path Topologies

• 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)

41
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
• AGVs 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

42
1) Algorithms for General Path Topology 2) Path
Optimization 3) Algorithms for Specific Path
Topologies 4) Dedicated Scheduling Algorithms
43
Dedicated Scheduling Algorithms

• considers the scheduling of AGVs 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

44
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

45
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

46
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

47
QUESTIONSANSWERS