1. Scheduling and Routing Algorithms for AGVs: A Survey Ling Qiu · Wen-Jing Hsu · Shell-Ying Huang · Han Wang presented by Oğuz 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 Hardware : AGVs, paths, controllers, sensors, etc. Software 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 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 head-on conflicts: find another shortest path head-to-tail & junction conflicts head-to-tail & junction conflicts: slowing down the latter complexity of O(n 2 ), 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. 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

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(w 2 log w), w is # time-windows of all nodes Huang et al., 1988

21. Time-window-based Methods labelling algorithm 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(v 4 n 2 ), v # vehicles, n # nodes, suitable for small systems Kim and Tanchoco, 1991 conservative myopic 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 Algorithms for General Path Topology

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 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. 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

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 branch&bound 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 vehicle numberrouting control 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 can’t be a large system

38. 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 Algorithms for Specific Path Topologies

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. 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(n 2 ) and O(n 3 ) Algorithms for Specific Path Topologies

41. Mesh Topology Qiu and Hsu, 2000 n x n mesh-like topology can schedule & route simultaneously up to 4n 2 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 4n 2, 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 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 time constrained vehicle routing problem (TCVRP) 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. QUESTIONS & ANSWERS