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Determining Type and Number of Automated Guided Vehicles Required in a System Dr. David Sinreich Faculty of Industrial Engineering and Management Technion - Israel Institute of Technology Courtesy of Frog Navigation Systems Inc. This presentation can’t be reproduced without the author’s permission

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Introduction Factors which impact the system performance Number of AGVs Unit Load P/D Stations Flow Path Network Control System WIP level System’s Throughput and Lead Time

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Introduction Factors which impact the required number of vehicles n The number of vehicles required so the system can operate efficiently is influenced by the unit load size and the flow path network and the location of P/D stations n The number of required vehicles has to be evaluated considering both economic and operational aspects Number of AGVs Unit Load P/D Stations Flow Path Network One of the most important factors which determine the performance level of a material handling system is the number of material handling devices operating in the system

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Unit load Size The impact on the vehicles n The larger each unit load is the less transfers per time unit are required (reduced transfer capacity), hence less vehicles are needed to support these transfers Job orders arriving to the shop floor are divided into transferable unit loads, this division has a dual effect n Based on the type and size (weight and volume) of the unit load transferred a vehicle type has to be chosen n The opposite is also true smaller unit loads means a more vehicles are needed n The larger the unit load is the more expensive each vehicle will be

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Unit load Size The impact on total cost of the system Fleet size Unit load size Payload capacity cost Unit load size Total cost AGV cost inventory cost Container cost Cost/item moved The larger the unit loads the more expensive the vehicles are due to the larger payloads required Courtesy of Egbelu 1993

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Flow Path Network The impact on the vehicles The flow path network is made up of flow paths and intersections both of which have a direct impact on the time is takes a vehicle to complete its mission - delivering unit loads between pick-up and delivery stations Long flow paths Proportional increase in flow time Transfer capacity increase More vehicles More intersections en route Potential increase in time delays Transfer capacity increase More vehicles flow paths intersections The opposite is also true

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich P/D Station Location The impact on the vehicles The pick-up and delivery station location has a direct impact on the blocking, interference and time delays, vehicles encounter en route Locating P/D stations next to busy intersections and on track More blocking, interference and time delays Transfer capacity increase More vehicles Locating P/D stations away from busy intersections and off trackLess vehicles

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Basic formula Number Vehicles = Required Transfer Capacity (Time) Planning Horizon (Time)

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation The states the vehicle can be in Idle moving or waiting Empty Travel to pick-up station Loading a unit load Loaded Travel to delivery station Unloading the unit load While on assignment the vehicles may be: Blocked at any stage Charging Batteries Idle time + Empty Travel time + Loading time + Loaded Travel time + Unloading time + Blocked time + Charging time = Required Vehicle’s Transfer Capacity

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Classifying the different states The time duration the vehicle spends in any of the different states can be calculated in some cases and estimated in other cases States that their time duration can be calculated States that their time duration has to be estimated n Loading n Unloading n Loaded Travel n Idle n Empty Travel n Blocked n Charging

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Flow and distance matrices The time spent loading/unloading and traveling loaded can be calculated based on the From-To flow matrix and the Distance matrix between the pick-up and delivery stations of the different workcenters From-To matrixDistance matrix 123..j 1 2 : i f1jf1j f 12 f 23 f 21 f 13 f2jf2j fi1fi1 fi2fi fi3fi3 :: f ij 123..j 1 2 : i d1jd1j d 12 d 23 d 21 d 13 d2jd2j di1di1 di2di di3di3 :: d ij Total number of transfer operationsTotal number of load and unload operations From pick-up station i to delivery station j

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Loaded travel time and load/unload time calculations Total time spent loading at pick-up stations ( T L ) Let us define the following system parameters t L - Loading operation time t U - Unloading operation time V - Vehicle speed T - Time horizon Total time spent unloading at delivery stations ( T U ) Total loaded flow distance between workcenters Total loaded flow time ( T LT )

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Idle, blocking, charging and empty travel time estimations e - vehicle’s efficiency estimation b - percentage of time the vehicle is blocked c - percentage of time the vehicle is idle t b - time estimation the vehicle spends charging n Idle, blocking and empty travel time are dependent on the rules, control methods and the dynamics of the system n Charging time is dependent on the type of batteries used/charging methods and assignments the vehicles perform n In order to estimate these times using simple methods estimation factors have been suggested - empty travel time estimation as a function of the loaded travel time

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Simple one dimensional methods n Methods are denoted as simple in the case the empty vehicle flow estimations are naive n These methods are denoted as one dimensional since predefined fixed unit load size and the flow path network are used, without considering an overall optimization n studies that fall under this category are: Maxwell and Muckstadt (1982), Egbelu (1987)

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Simple one dimensional methods (1) Simple Method 1 a constant as the empty travel function estimation ( Egbelu 1987 )

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Simple one dimensional methods (2) Simple Method 2 empty travel estimation based on workcenter Net Flow ( Egbelu 1987 ) i : : f ji f ik NF i > 0 - workcenter has a surplus of empty vehicles to export elsewhere NF i < 0 - workcenter has a shortage of empty vehicle and needs to import NF i = 0 - workcenter is self sufficient

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Simple one dimensional methods (3) Empty travel distance between workcenters * assuming average loaded flow distance = average empty flow distance Empty travel distance between stations of the same workcenter :: f ji f ik DiDi PiPi ET 2

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Simple one dimensional methods (4) Simple Method 3 empty travel estimation using a transportation model ( Maxwell & Muckstadt 1982 ) Number of empty vehicles moving from delivery station i to pick-up station j From delivery station i to pick- up station j NF i > 0 NF i < 0 This estimation serves as a lower bound to the actual empty travel

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Complex one dimensional methods n Methods are denoted as complex in the case empty vehicle flow estimations are more precise and use actual dispatching rules that are used on the shop floor such as FCFS and STT n studies that fall under this category are: Egbelu (1987), Bakkalbasi (1990), Malmborg (1991)

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Complex one dimensional methods (1) Complex Method 1 empty travel estimation using FCFS* allocation rule ( Egbelu 1987 ) 123..j 1 2 : i f1jf1j f 12 f 23 f 21 f 13 f2jf2j fi1fi1 fi2fi fi3fi3 :: f ij : p i - the probability that the next empty vehicle will be needed at pick-up station i p j - the probability that the next empty vehicle will be released at delivery station j *- First Come First Serve

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Complex one dimensional methods (2) p ij - probability that the empty vehicle that was assigned to travel to pick-up station i came from delivery station j g ij - expected number of empty vehicle trips originating at delivery station j traveling to pick-up station i From delivery station j to pick- up station i 123..j 1 2 : i g1jg1j g 12 g 23 g 21 g 13 g2jg2j gi1gi1 gi2gi gi3gi3 :: g ij : 123..j 1 2 : i f1jf1j f 12 f 23 f 21 f 13 f2jf2j fi1fi1 fi2fi fi3fi3 :: f ij :

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation Multi dimensional methods n Methods are denoted as multi dimensional in the case the vehicle calculation problem is integrated with other directly related problems such as unit load size determination and flow path design n studies that integrate vehicle calculation with flow path design are: Ashayeri (1989), n studies that integrate vehicle calculation with unit load size determination are: Mahadevan and Narendran (1992), Egbelu (1993) and Beamon and Deshpande (1998)

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation multi dimensional methods (1) Multi Dimensional Method 1 in conjunction with flow path design ( Ashayeri 1989 ) Notation m - number of flow types f ijk - number of transfers required from node i to node j of flow type k NF ik - net flow at node i of flow type k per hour Cp ij - number of transfers allowed on a path from node i to n ode j per hour W ij - maximum number of flow path lanes allowed between nodes i and j L ij - lane installation cost from node i and j C - cost per vehicle including software and hardware no lane from node i to node j one lane set up from node i to node j

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation multi dimensional methods (2) Cost related to the number of vehicles required in the system Cost of the flow path network Maintaining the flow in the system Determining the number of flow path lanes required

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation multi dimensional methods (3) Multi Dimensional Method 2 in conjunction with the unit load size determination ( Beamon and Deshpande 1998 ) Notation A kij - number of parts of type k that need to be transferred from station i to j Cp - capacity of each vehicle (parts) L max, L min - maximal allowed and minimal desired vehicle utilization N - number of vehicles required to operate the system U kij - number of unit loads of part k need to be transferred from station i to j u k - size of unit load which contains parts of type k W(u k ) - load unload time of unit loads as a function of the unit load size

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Vehicle Calculation multi dimensional methods (4) Maximizing parts being transferred within a pre- specified amount of time Determining number of transfers based on unit load size Limiting Transfer capacity of vehicle Limiting vehicle utilization Limiting unit load size based on transfer lots and vehicle capacity

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich What Is Next Static and dynamic factors n Static predetermined factors such as the number of transfers (unit load size), transfer distances, load/unload time and type of battery charging methods all which can be calculated or estimated in a reasonable accurate manner (as shown by the previous models) The required number of vehicles is effected by: n Dynamic factors such as empty vehicle flow, dispatching rules, scheduling rules and mutual vehicle interference all which have a variable impact on the process The dynamic interference in general reduces the potential availability of vehicles and as a result reduces the vehicles fleet transfer capacity

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich What Is Next Drawbacks of analytical calculation methods n Since not all of the issues involved in the transport process can be modeled using analytical methods the dynamic factors are hard to predict and as a result vehicle calculations are not accurate enough n There is always a tradeoff between operational performance and economic aspects as a result determining the number of vehicles required in a system has to do with a sensitivity analysis and a decision making processes rather than a single calculated number

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Operational Versus Economic Aspects Mutual vehicle interference Throughput Number of vehicles Any addition of vehicles beyond this point reduces system performance due to mutual interference Max system throughput Max number of vehicles In the case the loss in throughput is marginal compared to the reduction in the number of vehicles it may be an economic gain Reduced number of vehicles Time-in-System The same analysis is true for the job’s time-in-system

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Simulation Evaluating the number of vehicles (1) n The conclusion of all of this is that all vehicle calculation and optimization methods discussed thus far only serve as a first estimator to a more comprehensive method to evaluate (not calculate) the required number of vehicles in a system n Simulation is the only method that can accurately predict the system’s performance when using a specific number of specific vehicles in the system n Tanchoco et al. (1987) compare CAN-Q a tool which is based on queuing theory with AGVSim a dedicated AGV simulation tool and reinforce the above conclusions

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Simulation Evaluating the number of vehicles (2) Notation P k, q k - negative and positive deviation from goal k respectively C veh - cost of automated vehicle C cont - controller cost which includes hardware and software C bat - cost of battery charging station C fix - fixed cost of related to the design and installation of the guide path N max - maximum number of vehicles which can operate in the system Sinreich and Tanchoco (1992) quantify the system’s throughput performance as function of the number of vehicles in the system using an extensive simulation study. This function is used in conjunction with a multi-goal optimization formulation to evaluate the required number of vehicles based on a tradeoff between cost and throughput

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Simulation Evaluating the number of vehicles (3) Notation M c - maximum number of vehicles a single controller can accommodate M b - maximum number of vehicles a single charger can accommodate Th - management’s target throughput C - management’s target system cost a 1, a 2 - function coefficients describing the system’s throughput performance - weight associated with the relative importance of the positive and negative deviation of goal k

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Simulation Evaluating the number of vehicles (4) Minimizing the positive and negative deviations from desired management’s goals Management’s cost goal Management’s throughput goal A concave function which represents the system’s throughput behavior

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Simulation Decision tables for evaluating the number of vehicles Based on this formulation and for a predetermined range of management goals, decision tables can be developed to be used to evaluate the required number of vehicles Management’s throughput goal Management’s cost goal Trade-off ratio (% to $) Suggested number of vehicles

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Numerical Example 6 department manufacturing facility (1) P2P2 P1P1 D2D2 D6D6 D5D5 P3P3 D3D3 P6P6 P5P5 P4P4 D4D

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Numerical Example 6 department manufacturing facility (2) Vehicle carrying capacity lb Tote weight - 10 lb Tote volume in 3 Vehicle traveling speed ft/min Loading and unloading time - 30 seconds Average job’s interarrival rate - 24 minuets Planning horizon - 8 hours Battery charging during planning horizon - 30 minuets

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Numerical Example 6 department manufacturing facility (3) During the the planning horizon 8/0.4 = 20 will arrive with the following job mix: Job1 - 20x0.3=6, Job2 - 8, Job3 - 4 and Job4 - 2 Based on this information the From-To flow matrix can be calculated based on the physical facility the distance matrix can be determined

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Numerical Example 6 department manufacturing facility (4) From-To Flow matrixDistance matrix e = 0.85

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Questions

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Small To Medium Unit Load AGVs Courtesy of Rapistan Demag Corp. and Apogee

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Fork AGVs Courtesy of BT Systems Inc. and Apogee

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Pallet AGVs Courtesy of Rapistan Demag Corp.

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Heavy Load AGVs Courtesy of Rapistan Demag Corp., Mentor AGVS Inc. and Frog Navigation Systems Inc.

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Towing AGVs Courtesy of Rapistan Demag Corp., Apogee and Control Engineering Company

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Assignment Dedicated AGVs Courtesy of Rapistan Demag Corp., Apogee, Control Engineering Company and Mentor AGVS Inc.

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Technion - Israel Institute of Technology Copyright Dr. David Sinreich Work Platform AGVs Courtesy of BT Systems Inc.

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