Scheduling and Routing Scheduling and Routing Algorithms for AGVs: A Algorithms for AGVs: A

SurveySurveyby Ling Qiu, Wen-Jing Hsu, by Ling Qiu, Wen-Jing Hsu, Shell-Ying Huang and Han Shell-Ying Huang and Han

WangWang

Emrah ZarifoğluEmrah Zarifoğlu

9702173097021730

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AGVsAGVs

• AGVs becoming popular in AGVs becoming popular in – Automatic materials-handling systemsAutomatic materials-handling systems– FMSFMS– Container handling applications in Container handling applications in

seaportsseaports

• Scheduling and Routing has Scheduling and Routing has considerable attractionconsiderable attraction

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AgendaAgenda

• Description of problemDescription of problem– SchedulingScheduling– RoutingRouting

• Common hazards in scheduling and routing of Common hazards in scheduling and routing of AGVs nad techniques to handle themAGVs nad techniques to handle them

• Comparison of several similarproblemsComparison of several similarproblems• Survey of existing major works on AGV scheduling Survey of existing major works on AGV scheduling

androutingandrouting• ClassificationsClassifications• Recommendation of a few fertile areas for further Recommendation of a few fertile areas for further

studystudy

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Problem OriginProblem Origin

• HardwareHardware– AGVsAGVs– PathsPaths– ControllersControllers– SensorsSensors– Guidance DevicesGuidance Devices

• SoftwareSoftware– Approaches or algortihms to manage hardware Approaches or algortihms to manage hardware

resourcesresources• (!) hardware exceeds software (!)(!) hardware exceeds software (!)• Hazards due to softwareHazards due to software

– CongestionCongestion– DeadlocksDeadlocks

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Recent ProblemRecent Problem

Scheduling and Routing

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Problem DescriptionProblem Description

• SchedulingScheduling– Aim Aim dispatch a set of AGVs to achieve goals dispatch a set of AGVs to achieve goals

for batch of P/D jobs under certain conditionsfor batch of P/D jobs under certain conditions– Goals Goals related to processing time or utilization related to processing time or utilization

of resourcesof resources• RoutingRouting

– Mission Mission find a suitable routefor AGVs from find a suitable routefor AGVs from origin to destination based on current traffic origin to destination based on current traffic situationsituation

– Two issues: Two issues: • existence of a route leading a vehicle from origin to existence of a route leading a vehicle from origin to

destinationdestination• feasibilityfeasibility

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Problem DescriptionProblem Description

• Relations between scheduling and routingRelations between scheduling and routing– A few vehicles and jobs A few vehicles and jobs simpler scheduling simpler scheduling

algorithmsalgorithms– Many jobs Many jobs inadequacy of a simple inadequacy of a simple

scheduling algorithm to achieve a high system scheduling algorithm to achieve a high system efficiency due to limitations of facility efficiency due to limitations of facility resourcesresources

• Issues in scheduling and routingIssues in scheduling and routing– CollisionsCollisions– CongestionCongestion– LivelocksLivelocks– DeadlocksDeadlocks

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AGV Scheduling & Routing vs AGV Scheduling & Routing vs VRPVRP• Path network Path network

metropolitan scalemetropolitan scale• Load capacity of path Load capacity of path

not considered not considered assumption of assumption of nocollisions or nocollisions or congestioncongestion

• Shortest distance path Shortest distance path ↔ shortest time path↔ shortest time path

• Path network Path network predefined and predefined and unchangeableunchangeable

• Not ignorable AGV Not ignorable AGV path occupationpath occupation

• High possibility of High possibility of collusion of congestion collusion of congestion due to bad scheduling due to bad scheduling and routingand routing

• Not necessarily Not necessarily shortest time path shortest time path ↔ ↔ shortest pathshortest path

• Path layout may be Path layout may be revisedrevised

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Other Differences from VRPOther Differences from VRP

• AGVs inferior to human driversAGVs inferior to human drivers– Sensory and decision making Sensory and decision making

capabilitiescapabilities

• Algorithms handle collision-free Algorithms handle collision-free propertyproperty

• Appropriate and effective algorithms Appropriate and effective algorithms requiredrequired

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Distinction of AGV problemsDistinction of AGV problems

• Different from conventional path problems Different from conventional path problems in graph theoryin graph theory– Shortest path problemShortest path problem– Hamiltonian-type problemHamiltonian-type problem– Scheduling problemScheduling problem

• Graph theoryGraph theory– Optimal pathOptimal path

• AGV problemAGV problem– Optimal path and when and how (time critical)Optimal path and when and how (time critical)– System control mechanism and path layoutSystem control mechanism and path layout

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Similarity with Routing Similarity with Routing Electronic Data in a NetworkElectronic Data in a Network

• AGVs AGVs ↔ data packets↔ data packets

• pathspaths ↔ data links↔ data links

• Traffic control devicesTraffic control devices ↔ routers↔ routers

• Also some distinctionsAlso some distinctions

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Taxonomy of AlgorithmsTaxonomy of Algorithms

• Algorithms for general path topology Algorithms for general path topology treating problem as treating problem as graph theorygraph theory– Dijkstra’s shortest path algorithmDijkstra’s shortest path algorithm– Partitioning shortest path algorithmPartitioning shortest path algorithm

• Algorithms for path layout optimization Algorithms for path layout optimization focus on focus on optimization of path networkoptimization of path network– Integer programmingInteger programming

• Algorithms for specific path topology Algorithms for specific path topology developed to route developed to route and control AGVs in specific topologiesand control AGVs in specific topologies– Single-loopSingle-loop– Multi-loopsMulti-loops– MeshesMeshes

• Dİspatching or scheduling of AGVswithout consideration of Dİspatching or scheduling of AGVswithout consideration of routingrouting

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Algorithms for General Path Algorithms for General Path TopologyTopology• Focus Focus finding feasible routes for AGVs finding feasible routes for AGVs

w/o considering topological characteristic w/o considering topological characteristic of path layoutof path layout– Universal routing solutionsUniversal routing solutions

• Basic Basic conflict-free and shortest-time conflict-free and shortest-time routing solutions for AGVsrouting solutions for AGVs

• Method classificationMethod classification– Static methodsStatic methods– Time-window-based methodsTime-window-based methods– Dynamic methodsDynamic methods

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Static MethodsStatic Methods

• Small scale AGV systemsSmall scale AGV systems– Advantage Advantage simplicity simplicity– Disadvantage Disadvantage its optimal solutions its optimal solutions

• Introduction of conflict-free and shortest time AGV routing Introduction of conflict-free and shortest time AGV routing by Broadbent et al. (1985) by Broadbent et al. (1985) Dijkstra’s shortest path Dijkstra’s shortest path algorithmalgorithm

• Bidirectional path is more advantageous than unidirectional Bidirectional path is more advantageous than unidirectional path for utilization of vehicles and potential throughput path for utilization of vehicles and potential throughput efficiency by Egbelu and Tanchoco (1986) and Egbelu efficiency by Egbelu and Tanchoco (1986) and Egbelu (1987) (1987) improved productivity and reduced number of improved productivity and reduced number of AGVs in bidirectional pathsAGVs in bidirectional paths

• Routing vehicles in bidirectional flowpath ntwork when PSP Routing vehicles in bidirectional flowpath ntwork when PSP is applied to find shortest path for an AGV by Daniels (188) is applied to find shortest path for an AGV by Daniels (188) algoithm only suitable for a system with a small path algoithm only suitable for a system with a small path netwprk and a small number of AGVsnetwprk and a small number of AGVs

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Time-Window-Based Time-Window-Based MethodsMethods• Aim Aim to share path network more efficiently to share path network more efficiently• Main contribution Main contribution enhancement of path utilization enhancement of path utilization• Labelling algorithm to find shortest time path for routing a Labelling algorithm to find shortest time path for routing a

single vehicle in a bidirectional path network by Huang et single vehicle in a bidirectional path network by Huang et al. (1989) al. (1989) unacceptably large amount of computation unacceptably large amount of computation

• Conflict-free and shortest timealgorithm for routing AGVs in Conflict-free and shortest timealgorithm for routing AGVs in a bidirectional pathnetwork based on Dijkstra’s algorithm a bidirectional pathnetwork based on Dijkstra’s algorithm by by Kim and Tanchoco (1991) by by Kim and Tanchoco (1991) more suitable for a small more suitable for a small system with few vehicles in the worst casesystem with few vehicles in the worst case

• Operational control of bidirectional path AGV systems for Operational control of bidirectional path AGV systems for conflict-free and shortest time routing algorithm employing conflict-free and shortest time routing algorithm employing a conservative myopic strategy by Kim and Tanchoco a conservative myopic strategy by Kim and Tanchoco (1993)(1993)

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Dynamic MethodsDynamic Methods

• Aim Aim to speed up the process of finding to speed up the process of finding routes for AGVsroutes for AGVs

• Incremental route planning by Taghaboni and Incremental route planning by Taghaboni and Tanchoco (1995) Tanchoco (1995) quicker than static quicker than static algorithmalgorithm

• Algorithm giving an optimal solution for Algorithm giving an optimal solution for planning dispatching, conflict-free routing and planning dispatching, conflict-free routing and scheduling of AGVs in FMS based on dynamic scheduling of AGVs in FMS based on dynamic programming by Langevin et al. (1996)programming by Langevin et al. (1996)

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Path OptimizationPath Optimization

• Optimization of path layout or Optimization of path layout or distribution of P/D stations distribution of P/D stations integer integer programming formulationprogramming formulation

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0-1 Integer Programming 0-1 Integer Programming ModelModel• Path layout problem as a 0-1 integer Path layout problem as a 0-1 integer

programming model with given facility programming model with given facility layout and P/D stations byGAskins and layout and P/D stations byGAskins and Tanchoco (1987) Tanchoco (1987) only considering only considering unidirectional path network whichhas unidirectional path network whichhas lower utilization than bidirectional ones do lower utilization than bidirectional ones do by Egbelu and Tanchoco (1986)by Egbelu and Tanchoco (1986)

• 0-1integer programming model and 0-1integer programming model and branch-and-bound method by Gaskins and branch-and-bound method by Gaskins and Tanchoco (1990) Tanchoco (1990) reduce reduce computationtime at cost of quality path computationtime at cost of quality path designdesign

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Intersection Graph MethodIntersection Graph Method

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

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Integer Linear Programming Integer Linear Programming ModelModel

• İnteger linear programming problem İnteger linear programming problem of selecting the pathand location of of selecting the pathand location of P/D stations by Goetz and Egbelu P/D stations by Goetz and Egbelu (1990) (1990) unidirectional path, low unidirectional path, low path utilization andsystem path utilization andsystem throughputthroughput

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Algorithms for Specific Path Algorithms for Specific Path TopologiesTopologies

• In realistic applications, path In realistic applications, path topologies topologies specific and regular specific and regular

• Path layouts Path layouts linear, loop or loops, linear, loop or loops, mesh, etc...mesh, etc...

• Algorithms for specific path Algorithms for specific path topologies better effects than topologies better effects than algorithms for general path algorithms for general path topologiestopologies

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Linear TopologyLinear Topology

• Linear path topology Linear path topology basic type of basic type of path layoutspath layouts

• Introductionofascheme to schedule Introductionofascheme to schedule and route a batch of AGVs and route a batch of AGVs concurrently on a bidirectional linear concurrently on a bidirectional linear path layout amploying the idea of path layout amploying the idea of concurrent processing by Qiu and concurrent processing by Qiu and Hsu (2001a)Hsu (2001a)

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Loop TopologyLoop Topology

• Loop topology including single-loops, Loop topology including single-loops, multi-loops, segmented floor multi-loops, segmented floor topology is commonfor path layouttopology is commonfor path layout

• Few vehicles run in same direction Few vehicles run in same direction within loopwithin loop

• Simple routing controlSimple routing control

• But not very high system throughputBut not very high system throughput

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Loop Topology (Cont’d)Loop Topology (Cont’d)

• Optimal closed single-loop path layout for AGV system Optimal closed single-loop path layout for AGV system based on integer programming to find optimal single-based on integer programming to find optimal single-loop by Tanchoco and Sinriech (1992) loop by Tanchoco and Sinriech (1992) may not be may not be very suitable for large material handling system with a very suitable for large material handling system with a great number of vehicles and stationsgreat number of vehicles and stations

• Routing AGVs among non-overlapping closed loops Routing AGVs among non-overlapping closed loops within a tandem AGV system by Lin and Dgen within a tandem AGV system by Lin and Dgen scale scale of such a system could not be very muchof such a system could not be very much

• SFT SFT can be used with oneof three network types can be used with oneof three network types (connected, partitioned and split-flow)(connected, partitioned and split-flow)– Advantage of SFT Advantage of SFT lower value of flow x distance compared lower value of flow x distance compared

withother path topologies (single-loop, bidirectional and uni-withother path topologies (single-loop, bidirectional and uni-directional conventional paths,etc..)directional conventional paths,etc..)

– Disadvantage of SFT Disadvantage of SFT transferring devices in the buffers are transferring devices in the buffers are the additional cost of the overall systemthe additional cost of the overall system

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Mesh TopologyMesh Topology

• Mesh-like path topology Mesh-like path topology arrangement into rectangular arrangement into rectangular blocks in the container stacking yards of container shipping blocks in the container stacking yards of container shipping andtransportation at container terminalsandtransportation at container terminals

• Analysis of time and space complexities for some basic AGV Analysis of time and space complexities for some basic AGV routing operations in several specific bidirectional path routing operations in several specific bidirectional path topologies by Hsu and Huang (1994) and Huang and Hsu topologies by Hsu and Huang (1994) and Huang and Hsu (1994)(1994)– routing operations routing operations single delivery distribution, scattering, single delivery distribution, scattering,

accumulation, gathering, sorting, total exchange (shuffling)accumulation, gathering, sorting, total exchange (shuffling)– Path topologies Path topologies linear array, ring, binary-tree, H-tree, star, linear array, ring, binary-tree, H-tree, star,

2D mesh, n-cube and cube-connected cycles, and complete 2D mesh, n-cube and cube-connected cycles, and complete graphgraph

• Different methods to schedule and route AGVs in an n X n Different methods to schedule and route AGVs in an n X n mesh-like path topology by Qiu and Hsu (2000a-c) mesh-like path topology by Qiu and Hsu (2000a-c) in all in all algorithms, freedom of conlictsamong AGVs is provably algorithms, freedom of conlictsamong AGVs is provably guaranteedguaranteed

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Dedicated Scheduling Dedicated Scheduling AlgorithmsAlgorithms• Scheduling without consideration of routingScheduling without consideration of routing• Schedule vehicles and jobs in a decision-making Schedule vehicles and jobs in a decision-making

hierarchy based on mixed-integer programming by hierarchy based on mixed-integer programming by Akturk and Yilmaz (1996)Akturk and Yilmaz (1996)– Micro-opportunistic scheduling algorithm (MOSA) combines Micro-opportunistic scheduling algorithm (MOSA) combines

job-based and vehicle-based approaches job-based and vehicle-based approaches applicable for applicable for AGV systems with a small number of jobs and vehiclesAGV systems with a small number of jobs and vehicles

• A model for scheduling of AGVs for multiple A model for scheduling of AGVs for multiple container-cranes to minimize the delay of carrying container-cranes to minimize the delay of carrying out all loading unloading operations without out all loading unloading operations without consideration of AGV routing by Kim and Bae consideration of AGV routing by Kim and Bae (1999) (1999) with increase of number of AGVs, with increase of number of AGVs, congestions or collisions of AGVs might occur at the congestions or collisions of AGVs might occur at the operating area of container cranesoperating area of container cranes

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Future Research DirectionsFuture Research Directions

• Most fertile Most fertile development of new development of new scheduling and routing algorithms for scheduling and routing algorithms for specific path topologiesspecific path topologies– In many applications AGV path metworks In many applications AGV path metworks

areregular graphs (linear array, loop/loops, 2D areregular graphs (linear array, loop/loops, 2D mesh)mesh)

– Relatively lower computational complexity Relatively lower computational complexity compared algorithms for general path topologycompared algorithms for general path topology

– More feasible and more efficient More feasible and more efficient

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Important NoticeImportant Notice

• AGV systems are parallel and AGV systems are parallel and distributed systemsdistributed systems