Transcript No Slide Title

Scheduling and Routing
Algorithms for AGVs: A Survey
Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang
presented by Oğuz 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(n2), 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
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 AGV’s
Daniels, 1988
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(w2log w), w is # time-windows of all nodes
Huang et al., 1988
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 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 myopic strategy
• one vehicle at a time, previous routes are strictly respected
• subsequent schedule made after the vehicle becomes idle
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
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
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
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
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
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
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
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