1. י"ד/ניסן/תשע"ז
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
This presentation can’t be reproduced without the author’s permission
Courtesy of Frog Navigation Systems Inc.

2. Introduction Factors which impact the system performance
י"ד/ניסן/תשע"ז
Introduction Factors which impact the system performance
Number of AGVs
Flow Path Network
Control System
P/D Stations
Unit Load
WIP level
System’s Throughput and Lead Time

3. Introduction Factors which impact the required number of vehicles
י"ד/ניסן/תשע"ז
Introduction Factors which impact the required number of vehicles
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
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
The number of required vehicles has to be evaluated considering both economic and operational aspects

4. Unit load Size The impact on the vehicles
י"ד/ניסן/תשע"ז
Unit load Size The impact on the vehicles
Job orders arriving to the shop floor are divided into transferable unit loads, this division has a dual effect
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
Based on the type and size (weight and volume) of the unit load transferred a vehicle type has to be chosen
The larger the unit load is the more expensive each vehicle will be
The opposite is also true smaller unit loads means a more vehicles are needed

5. Unit load Size The impact on total cost of the system
י"ד/ניסן/תשע"ז
Unit load Size The impact on total cost of the system
The larger the unit loads the more expensive the vehicles are due to the larger payloads required
Total cost
Fleet size
Unit load size
Payload capacity
cost
Unit load size
AGV cost
inventory cost
Container cost
Cost/item moved
Courtesy of Egbelu 1993

6. Flow Path Network The impact on the vehicles
י"ד/ניסן/תשע"ז
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
flow paths
intersections
Long flow paths
More intersections en route
Proportional increase in flow time
Potential increase in time delays
Transfer capacity increase
Transfer capacity increase
More vehicles
More vehicles
The opposite is also true

7. P/D Station Location The impact on the vehicles
י"ד/ניסן/תשע"ז
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 track
Less vehicles

8. Vehicle Calculation Basic formula
י"ד/ניסן/תשע"ז
Vehicle Calculation Basic formula
Required Transfer Capacity (Time)
Number Vehicles =
Planning Horizon (Time)

9. Vehicle Calculation The states the vehicle can be in
י"ד/ניסן/תשע"ז
Vehicle Calculation The states the vehicle can be in
Idle moving or waiting
While on assignment the vehicles may be:
Empty Travel to pick-up station
Blocked at any stage
Loading a unit load
Charging Batteries
Loaded Travel to delivery station
Unloading the unit load
Idle time + Empty Travel time + Loading time + Loaded Travel time + Unloading time + Blocked time + Charging time = Required Vehicle’s Transfer Capacity

10. Vehicle Calculation Classifying the different states
י"ד/ניסן/תשע"ז
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
Loading
Unloading
Loaded Travel
Idle
Empty Travel
Blocked
Charging

11. Vehicle Calculation Flow and distance matrices
י"ד/ניסן/תשע"ז
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 matrix
Distance matrix 1 2 3 .. j : i
f1j
f12
f23
f21
f13
f2j
fi1
fi2 -
fi3
fij 1 2 3 .. j : i
d1j
d12
d23
d21
d13
d2j
di1
di2 -
di3
dij
From pick-up station i to delivery station j
Total number of load and unload operations
Total number of transfer operations

12. י"ד/ניסן/תשע"ז
Vehicle Calculation Loaded travel time and load/unload time calculations
Let us define the following system parameters
tL - Loading operation time
tU - Unloading operation time
V - Vehicle speed
T - Time horizon
Total time spent loading at pick-up stations (TL)
Total time spent unloading at delivery stations (TU)
Total loaded flow distance between workcenters
Total loaded flow time (TLT)

13. י"ד/ניסן/תשע"ז
Vehicle Calculation Idle, blocking, charging and empty travel time estimations
Idle, blocking and empty travel time are dependent on the rules, control methods and the dynamics of the system
Charging time is dependent on the type of batteries used/charging methods and assignments the vehicles perform
In order to estimate these times using simple methods estimation factors have been suggested
e - vehicle’s efficiency estimation
b - percentage of time the vehicle is blocked
c - percentage of time the vehicle is idle
tb - time estimation the vehicle spends charging
- empty travel time estimation as a function of the loaded travel time

14. Vehicle Calculation Simple one dimensional methods
י"ד/ניסן/תשע"ז
Vehicle Calculation Simple one dimensional methods
Methods are denoted as simple in the case the empty vehicle flow estimations are naive
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
studies that fall under this category are: Maxwell and Muckstadt (1982), Egbelu (1987)

15. Vehicle Calculation Simple one dimensional methods (1)
י"ד/ניסן/תשע"ז
Vehicle Calculation Simple one dimensional methods (1)
Simple Method 1
a constant as the empty travel function estimation (Egbelu 1987)

16. Vehicle Calculation Simple one dimensional methods (2)
י"ד/ניסן/תשע"ז
Vehicle Calculation Simple one dimensional methods (2)
Simple Method 2
empty travel estimation based on workcenter Net Flow (Egbelu 1987)
fji i
fik : :
NFi > 0 - workcenter has a surplus of empty vehicles to export elsewhere
NFi < 0 - workcenter has a shortage of empty vehicle and needs to import
NFi = 0 - workcenter is self sufficient

17. Vehicle Calculation Simple one dimensional methods (3)
י"ד/ניסן/תשע"ז
Vehicle Calculation Simple one dimensional methods (3)
Empty travel distance between workcenters :
fji
fik Di Pi
ET2
Empty travel distance between stations of the same workcenter
* assuming average loaded flow distance = average empty flow distance

18. Vehicle Calculation Simple one dimensional methods (4)
י"ד/ניסן/תשע"ז
Vehicle Calculation Simple one dimensional methods (4)
Simple Method 3
empty travel estimation using a transportation model
(Maxwell & Muckstadt 1982)
NFi > 0
NFi < 0
From delivery station i to pick-up station j
This estimation serves as a lower bound to the actual empty travel
Number of empty vehicles moving from delivery station i to pick-up station j

19. Vehicle Calculation Complex one dimensional methods
י"ד/ניסן/תשע"ז
Vehicle Calculation Complex one dimensional methods
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
studies that fall under this category are: Egbelu (1987), Bakkalbasi (1990), Malmborg (1991)

20. Vehicle Calculation Complex one dimensional methods (1)
י"ד/ניסן/תשע"ז
Vehicle Calculation Complex one dimensional methods (1)
Complex Method 1
empty travel estimation using FCFS* allocation rule (Egbelu 1987)
pi - the probability that the next empty vehicle will be needed at pick-up station i 1 2 3 .. j : i
f1j
f12
f23
f21
f13
f2j
fi1
fi2 -
fi3
fij
pj - the probability that the next empty vehicle will be released at delivery station j
*- First Come First Serve

21. Vehicle Calculation Complex one dimensional methods (2)
י"ד/ניסן/תשע"ז
Vehicle Calculation Complex one dimensional methods (2)
pij - probability that the empty vehicle that was assigned to travel to pick-up station i came from delivery station j
gij - expected number of empty vehicle trips originating at delivery station j traveling to pick-up station i 1 2 3 .. j : i
f1j
f12
f23
f21
f13
f2j
fi1
fi2 -
fi3
fij 1 2 3 .. j : i
g1j
g12
g23
g21
g13
g2j
gi1
gi2 -
gi3
gij
From delivery station j to pick-up station i

22. Vehicle Calculation Multi dimensional methods
י"ד/ניסן/תשע"ז
Vehicle Calculation Multi dimensional methods
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
studies that integrate vehicle calculation with flow path design are: Ashayeri (1989),
studies that integrate vehicle calculation with unit load size determination are: Mahadevan and Narendran (1992), Egbelu (1993) and Beamon and Deshpande (1998)

23. Vehicle Calculation multi dimensional methods (1)
י"ד/ניסן/תשע"ז
Vehicle Calculation multi dimensional methods (1)
Multi Dimensional Method 1
in conjunction with flow path design (Ashayeri 1989)
Notation
m - number of flow types
fijk - number of transfers required from node i to node j of flow type k
NFik - net flow at node i of flow type k per hour
Cpij - number of transfers allowed on a path from node i to n ode j per hour
Wij - maximum number of flow path lanes allowed between nodes i and j
Lij - 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

24. Vehicle Calculation multi dimensional methods (2)
י"ד/ניסן/תשע"ז
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

25. Vehicle Calculation multi dimensional methods (3)
י"ד/ניסן/תשע"ז
Vehicle Calculation multi dimensional methods (3)
Multi Dimensional Method 2
in conjunction with the unit load size determination
(Beamon and Deshpande 1998)
Notation
Akij - number of parts of type k that need to be transferred from station i to j
Cp - capacity of each vehicle (parts)
Lmax, Lmin - maximal allowed and minimal desired vehicle utilization
N - number of vehicles required to operate the system
Ukij - number of unit loads of part k need to be transferred from station i to j
uk - size of unit load which contains parts of type k
W(uk) - load unload time of unit loads as a function of the unit load size

26. Vehicle Calculation multi dimensional methods (4)
י"ד/ניסן/תשע"ז
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

27. What Is Next Static and dynamic factors
י"ד/ניסן/תשע"ז
What Is Next Static and dynamic factors
The required number of vehicles is effected by:
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)
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

28. What Is Next Drawbacks of analytical calculation methods
י"ד/ניסן/תשע"ז
What Is Next Drawbacks of analytical calculation methods
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
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

29. Operational Versus Economic Aspects Mutual vehicle interference
י"ד/ניסן/תשע"ז
Operational Versus Economic Aspects Mutual vehicle interference
Any addition of vehicles beyond this point reduces system performance due to mutual interference
Throughput
Number of vehicles
Max system throughput
In the case the loss in throughput is marginal compared to the reduction in the number of vehicles it may be an economic gain
Time-in-System
Reduced number of vehicles
The same analysis is true for the job’s time-in-system
Max number of vehicles

30. Simulation Evaluating the number of vehicles (1)
י"ד/ניסן/תשע"ז
Simulation Evaluating the number of vehicles (1)
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
Simulation is the only method that can accurately predict the system’s performance when using a specific number of specific vehicles in the system
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

31. Simulation Evaluating the number of vehicles (2)
י"ד/ניסן/תשע"ז
Simulation Evaluating the number of vehicles (2)
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
Notation
Pk, qk - negative and positive deviation from goal k respectively
Cveh - cost of automated vehicle
Ccont - controller cost which includes hardware and software
Cbat - cost of battery charging station
Cfix - fixed cost of related to the design and installation of the guide path
Nmax - maximum number of vehicles which can operate in the system

32. Simulation Evaluating the number of vehicles (3)
י"ד/ניסן/תשע"ז
Simulation Evaluating the number of vehicles (3)
Notation
Mc - maximum number of vehicles a single controller can accommodate
Mb - maximum number of vehicles a single charger can accommodate
Th - management’s target throughput
C - management’s target system cost
- weight associated with the relative importance of the positive and negative deviation of goal k
a1,a2 - function coefficients describing the system’s throughput performance

33. Simulation Evaluating the number of vehicles (4)
י"ד/ניסן/תשע"ז
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

34. Simulation Decision tables for evaluating the number of vehicles
י"ד/ניסן/תשע"ז
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

35. Numerical Example 6 department manufacturing facility (1)
י"ד/ניסן/תשע"ז
Numerical Example 6 department manufacturing facility (1) 2 4 5 6 3 1 P2 P1 D2 D6 D5 P3 D3 P6 P5 P4 D4 60 80
140 70
110 20 90

36. Numerical Example 6 department manufacturing facility (2)
י"ד/ניסן/תשע"ז
Numerical Example 6 department manufacturing facility (2)
Vehicle carrying capacity lb
Tote weight lb
Tote volume in3
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

37. Numerical Example 6 department manufacturing facility (3)
י"ד/ניסן/תשע"ז
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

38. Numerical Example 6 department manufacturing facility (4)
י"ד/ניסן/תשע"ז
Numerical Example 6 department manufacturing facility (4)
From-To Flow matrix
Distance matrix
e = 0.85

39. י"ד/ניסן/תשע"ז
Questions

40. Small To Medium Unit Load AGVs
י"ד/ניסן/תשע"ז
Small To Medium Unit Load AGVs
Courtesy of Rapistan Demag Corp. and Apogee

41. י"ד/ניסן/תשע"ז
Fork AGVs
Courtesy of BT Systems Inc. and Apogee

42. י"ד/ניסן/תשע"ז
Pallet AGVs
Courtesy of Rapistan Demag Corp.

43. Heavy Load AGVs י"ד/ניסן/תשע"ז
Courtesy of Rapistan Demag Corp., Mentor AGVS Inc. and Frog Navigation Systems Inc.

44. Towing AGVs י"ד/ניסן/תשע"ז
Courtesy of Rapistan Demag Corp., Apogee and Control Engineering Company

45. Assignment Dedicated AGVs
י"ד/ניסן/תשע"ז
Assignment Dedicated AGVs
Courtesy of Rapistan Demag Corp., Apogee, Control Engineering Company and Mentor AGVS Inc.

46. י"ד/ניסן/תשע"ז
Work Platform AGVs
Courtesy of BT Systems Inc.