1. Scheduling and Routing Algorithms for AGVs: A Survey by Ling Qiu, Wen-Jing Hsu, Shell- Ying Huang and Han Wang Emrah Zarifoğlu 97021730

2. 2 AGVs AGVs becoming popular in AGVs becoming popular in –Automatic materials-handling systems –FMS –Container handling applications in seaports Scheduling and Routing has considerable attraction Scheduling and Routing has considerable attraction

3. 3 Agenda Description of problem Description of problem –Scheduling –Routing Common hazards in scheduling and routing of AGVs nad techniques to handle them Common hazards in scheduling and routing of AGVs nad techniques to handle them Comparison of several similarproblems Comparison of several similarproblems Survey of existing major works on AGV scheduling androuting Survey of existing major works on AGV scheduling androuting Classifications Classifications Recommendation of a few fertile areas for further study Recommendation of a few fertile areas for further study

4. 4 Problem Origin Hardware Hardware –AGVs –Paths –Controllers –Sensors –Guidance Devices Software Software –Approaches or algortihms to manage hardware resources (!) hardware exceeds software (!) (!) hardware exceeds software (!) Hazards due to software Hazards due to software –Congestion –Deadlocks

5. 5 Recent Problem Scheduling and Routing

6. 6 Problem Description Scheduling Scheduling –Aim  dispatch a set of AGVs to achieve goals for batch of P/D jobs under certain conditions –Goals  related to processing time or utilization of resources Routing Routing –Mission  find a suitable routefor AGVs from origin to destination based on current traffic situation –Two issues: existence of a route leading a vehicle from origin to destination existence of a route leading a vehicle from origin to destination feasibility feasibility

7. 7 Problem Description Relations between scheduling and routing Relations between scheduling and routing –A few vehicles and jobs  simpler scheduling algorithms –Many jobs  inadequacy of a simple scheduling algorithm to achieve a high system efficiency due to limitations of facility resources Issues in scheduling and routing Issues in scheduling and routing –Collisions –Congestion –Livelocks –Deadlocks

8. 8 AGV Scheduling & Routing vs VRP Path network  metropolitan scale Path network  metropolitan scale Load capacity of path not considered  assumption of nocollisions or congestion Load capacity of path not considered  assumption of nocollisions or congestion Shortest distance path ↔ shortest time path Shortest distance path ↔ shortest time path Path network predefined and unchangeable Path network predefined and unchangeable Not ignorable AGV path occupation Not ignorable AGV path occupation High possibility of collusion of congestion due to bad scheduling and routing High possibility of collusion of congestion due to bad scheduling and routing Not necessarily shortest time path ↔ shortest path Not necessarily shortest time path ↔ shortest path Path layout may be revised Path layout may be revised

9. 9 Other Differences from VRP AGVs inferior to human drivers AGVs inferior to human drivers –Sensory and decision making capabilities Algorithms handle collision-free property Algorithms handle collision-free property Appropriate and effective algorithms required Appropriate and effective algorithms required

10. 10 Distinction of AGV problems Different from conventional path problems in graph theory Different from conventional path problems in graph theory –Shortest path problem –Hamiltonian-type problem –Scheduling problem Graph theory Graph theory –Optimal path AGV problem AGV problem –Optimal path and when and how (time critical) –System control mechanism and path layout

11. 11 Similarity with Routing Electronic Data in a Network AGVs ↔ data packets AGVs ↔ data packets paths ↔ data links paths ↔ data links Traffic control devices ↔ routers Traffic control devices ↔ routers Also some distinctions Also some distinctions

12. 12 Taxonomy of Algorithms Algorithms for general path topology  treating problem as graph theory Algorithms for general path topology  treating problem as graph theory –Dijkstra’s shortest path algorithm –Partitioning shortest path algorithm Algorithms for path layout optimization  focus on optimization of path network Algorithms for path layout optimization  focus on optimization of path network –Integer programming Algorithms for specific path topology  developed to route and control AGVs in specific topologies Algorithms for specific path topology  developed to route and control AGVs in specific topologies –Single-loop –Multi-loops –Meshes Dİspatching or scheduling of AGVswithout consideration of routing Dİspatching or scheduling of AGVswithout consideration of routing

13. 13 Algorithms for General Path Topology Focus  finding feasible routes for AGVs w/o considering topological characteristic of path layout Focus  finding feasible routes for AGVs w/o considering topological characteristic of path layout –Universal routing solutions Basic  conflict-free and shortest-time routing solutions for AGVs Basic  conflict-free and shortest-time routing solutions for AGVs Method classification Method classification –Static methods –Time-window-based methods –Dynamic methods

14. 14 Static Methods Small scale AGV systems Small scale AGV systems –Advantage  simplicity –Disadvantage  its optimal solutions Introduction of conflict-free and shortest time AGV routing by Broadbent et al. (1985)  Dijkstra’s shortest path algorithm Introduction of conflict-free and shortest time AGV routing by Broadbent et al. (1985)  Dijkstra’s shortest path algorithm Bidirectional path is more advantageous than unidirectional path for utilization of vehicles and potential throughput efficiency by Egbelu and Tanchoco (1986) and Egbelu (1987)  improved productivity and reduced number of AGVs in bidirectional paths Bidirectional path is more advantageous than unidirectional path for utilization of vehicles and potential throughput efficiency by Egbelu and Tanchoco (1986) and Egbelu (1987)  improved productivity and reduced number of AGVs in bidirectional paths Routing vehicles in bidirectional flowpath ntwork when PSP is applied to find shortest path for an AGV by Daniels (188)  algoithm only suitable for a system with a small path netwprk and a small number of AGVs Routing vehicles in bidirectional flowpath ntwork when PSP is applied to find shortest path for an AGV by Daniels (188)  algoithm only suitable for a system with a small path netwprk and a small number of AGVs

15. 15 Time-Window-Based Methods Aim  to share path network more efficiently Aim  to share path network more efficiently Main contribution  enhancement of path utilization Main contribution  enhancement of path utilization Labelling algorithm to find shortest time path for routing a single vehicle in a bidirectional path network by Huang et al. (1989)  unacceptably large amount of computation Labelling algorithm to find shortest time path for routing a single vehicle in a bidirectional path network by Huang et al. (1989)  unacceptably large amount of computation Conflict-free and shortest timealgorithm for routing AGVs in a bidirectional pathnetwork based on Dijkstra’s algorithm by by Kim and Tanchoco (1991)  more suitable for a small system with few vehicles in the worst case Conflict-free and shortest timealgorithm for routing AGVs in a bidirectional pathnetwork based on Dijkstra’s algorithm by by Kim and Tanchoco (1991)  more suitable for a small system with few vehicles in the worst case Operational control of bidirectional path AGV systems for conflict- free and shortest time routing algorithm employing a conservative myopic strategy by Kim and Tanchoco (1993) Operational control of bidirectional path AGV systems for conflict- free and shortest time routing algorithm employing a conservative myopic strategy by Kim and Tanchoco (1993)

16. 16 Dynamic Methods Aim  to speed up the process of finding routes for AGVs Aim  to speed up the process of finding routes for AGVs Incremental route planning by Taghaboni and Tanchoco (1995)  quicker than static algorithm Incremental route planning by Taghaboni and Tanchoco (1995)  quicker than static algorithm Algorithm giving an optimal solution for planning dispatching, conflict-free routing and scheduling of AGVs in FMS based on dynamic programming by Langevin et al. (1996) Algorithm giving an optimal solution for planning dispatching, conflict-free routing and scheduling of AGVs in FMS based on dynamic programming by Langevin et al. (1996)

17. 17 Path Optimization Optimization of path layout or distribution of P/D stations  integer programming formulation Optimization of path layout or distribution of P/D stations  integer programming formulation

18. 18 0-1 Integer Programming Model Path layout problem as a 0-1 integer programming model with given facility layout and P/D stations byGAskins and Tanchoco (1987)  only considering unidirectional path network whichhas lower utilization than bidirectional ones do by Egbelu and Tanchoco (1986) Path layout problem as a 0-1 integer programming model with given facility layout and P/D stations byGAskins and Tanchoco (1987)  only considering unidirectional path network whichhas lower utilization than bidirectional ones do by Egbelu and Tanchoco (1986) 0-1integer programming model and branch-and- bound method by Gaskins and Tanchoco (1990)  reduce computationtime at cost of quality path design 0-1integer programming model and branch-and- bound method by Gaskins and Tanchoco (1990)  reduce computationtime at cost of quality path design

19. 19 Intersection Graph Method İntersection graph method based on branch-and-bound wherein only a reduced subset of nodes in path network is considered and only intersection nodes are used to find optimal for solving AGV flowpath optimization model by Sİnriech and Tanchoco (1991)  amount f computation greatly reduced İntersection graph method based on branch-and-bound wherein only a reduced subset of nodes in path network is considered and only intersection nodes are used to find optimal for solving AGV flowpath optimization model by Sİnriech and Tanchoco (1991)  amount f computation greatly reduced

20. 20 Integer Linear Programming Model İnteger linear programming problem of selecting the pathand location of P/D stations by Goetz and Egbelu (1990)  unidirectional path, low path utilization andsystem throughput İnteger linear programming problem of selecting the pathand location of P/D stations by Goetz and Egbelu (1990)  unidirectional path, low path utilization andsystem throughput

21. 21 Algorithms for Specific Path Topologies In realistic applications, path topologies  specific and regular In realistic applications, path topologies  specific and regular Path layouts  linear, loop or loops, mesh, etc... Path layouts  linear, loop or loops, mesh, etc... Algorithms for specific path topologies better effects than algorithms for general path topologies Algorithms for specific path topologies better effects than algorithms for general path topologies

22. 22 Linear Topology Linear path topology  basic type of path layouts Linear path topology  basic type of path layouts Introductionofascheme to schedule and route a batch of AGVs concurrently on a bidirectional linear path layout amploying the idea of concurrent processing by Qiu and Hsu (2001a) Introductionofascheme to schedule and route a batch of AGVs concurrently on a bidirectional linear path layout amploying the idea of concurrent processing by Qiu and Hsu (2001a)

23. 23 Loop Topology Loop topology including single-loops, multi-loops, segmented floor topology is commonfor path layout Loop topology including single-loops, multi-loops, segmented floor topology is commonfor path layout Few vehicles run in same direction within loop Few vehicles run in same direction within loop Simple routing control Simple routing control But not very high system throughput But not very high system throughput

24. 24 Loop Topology (Cont’d) Optimal closed single-loop path layout for AGV system based on integer programming to find optimal single- loop by Tanchoco and Sinriech (1992)  may not be very suitable for large material handling system with a great number of vehicles and stations Optimal closed single-loop path layout for AGV system based on integer programming to find optimal single- loop by Tanchoco and Sinriech (1992)  may not be very suitable for large material handling system with a great number of vehicles and stations Routing AGVs among non-overlapping closed loops within a tandem AGV system by Lin and Dgen  scale of such a system could not be very much Routing AGVs among non-overlapping closed loops within a tandem AGV system by Lin and Dgen  scale of such a system could not be very much SFT  can be used with oneof three network types (connected, partitioned and split-flow) SFT  can be used with oneof three network types (connected, partitioned and split-flow) –Advantage of SFT  lower value of flow x distance compared withother path topologies (single-loop, bidirectional and uni- directional conventional paths,etc..) –Disadvantage of SFT  transferring devices in the buffers are the additional cost of the overall system

25. 25 Mesh Topology Mesh-like path topology  arrangement into rectangular blocks in the container stacking yards of container shipping andtransportation at container terminals Mesh-like path topology  arrangement into rectangular blocks in the container stacking yards of container shipping andtransportation at container terminals Analysis of time and space complexities for some basic AGV routing operations in several specific bidirectional path topologies by Hsu and Huang (1994) and Huang and Hsu (1994) Analysis of time and space complexities for some basic AGV routing operations in several specific bidirectional path topologies by Hsu and Huang (1994) and Huang and Hsu (1994) –routing operations  single delivery distribution, scattering, accumulation, gathering, sorting, total exchange (shuffling) –Path topologies  linear array, ring, binary-tree, H-tree, star, 2D mesh, n-cube and cube-connected cycles, and complete graph Different methods to schedule and route AGVs in an n X n mesh-like path topology by Qiu and Hsu (2000a-c)  in all algorithms, freedom of conlictsamong AGVs is provably guaranteed Different methods to schedule and route AGVs in an n X n mesh-like path topology by Qiu and Hsu (2000a-c)  in all algorithms, freedom of conlictsamong AGVs is provably guaranteed

26. 26 Dedicated Scheduling Algorithms Scheduling without consideration of routing Scheduling without consideration of routing Schedule vehicles and jobs in a decision-making hierarchy based on mixed-integer programming by Akturk and Yilmaz (1996) Schedule vehicles and jobs in a decision-making hierarchy based on mixed-integer programming by Akturk and Yilmaz (1996) –Micro-opportunistic scheduling algorithm (MOSA) combines job- based and vehicle-based approaches  applicable for AGV systems with a small number of jobs and vehicles A model for scheduling of AGVs for multiple container- cranes to minimize the delay of carrying out all loading unloading operations without consideration of AGV routing by Kim and Bae (1999)  with increase of number of AGVs, congestions or collisions of AGVs might occur at the operating area of container cranes A model for scheduling of AGVs for multiple container- cranes to minimize the delay of carrying out all loading unloading operations without consideration of AGV routing by Kim and Bae (1999)  with increase of number of AGVs, congestions or collisions of AGVs might occur at the operating area of container cranes

27. 27 Future Research Directions Most fertile  development of new scheduling and routing algorithms for specific path topologies Most fertile  development of new scheduling and routing algorithms for specific path topologies –In many applications AGV path metworks areregular graphs (linear array, loop/loops, 2D mesh) –Relatively lower computational complexity compared algorithms for general path topology –More feasible and more efficient

28. 28 Important Notice AGV systems are parallel and distributed systems AGV systems are parallel and distributed systems