determining type and number of automated guided vehicles required in a system dr. david sinreich...
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Determining Type and Number of Automated Guided Vehicles
Required in a System Dr. David Sinreich
Faculty of Industrial Engineering and ManagementTechnion - Israel Institute of Technology
Courtesy of Frog Navigation Systems Inc.This presentation can’t be reproduced
without the author’s permission
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
IntroductionFactors 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
IntroductionFactors which impact the required number of vehicles
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
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Unit load SizeThe impact on the vehicles
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 Job orders arriving to the shop floor are divided into transferable unit loads, this division has a dual effecttransferable unit loads, this division has a dual effect
Based on the type and size (weight and volume) of the unit load transferred a vehicle type has to be chosen
The opposite is also true smaller unit loads means a more vehicles are needed
The larger the unit load is the more expensive each vehicle will be
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Unit load SizeThe impact on total cost of the system
Fle
et s
ize
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Flow Path NetworkThe 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 pathsintersections
The opposite is also true
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
P/D Station LocationThe 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationBasic formula
Number Vehicles =Required Transfer Capacity (Time)
Planning Horizon (Time)
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationThe 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationClassifying 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationFlow 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
1
2
:
i
f1jf12
f23f21
f13
f2j
fi1 fi2
-
-
-
..
..
fi3 ..
..
: :
fij
1 2 3 .. j
1
2
:
i
d1jd12
d23d21
d13
d2j
di1 di2
-
-
-
..
..
di3 ..
..
: :
dij
i j
ijf Total number of transfer operations Total number of load and unload operations
From pick-up station i to
delivery station j
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationLoaded travel time and load/unload time calculations
i j
ijL ft Total time spent loading at pick-up stations (TL)
Let us define the following system parameterstL - Loading operation time
tU - Unloading operation time
V - Vehicle speed
T - Time horizon
i j
ijU ft
i j
ijijdf
Total time spent unloading at delivery stations (TU)
Total loaded flow distance between workcenters
i j
ijij Vdf Total loaded flow time (TLT)
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationIdle, blocking, charging and empty travel time estimations
e - vehicle’s efficiency estimationb - percentage of time the vehicle is blockedc - percentage of time the vehicle is idletb - time estimation the vehicle spends charging
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
)( LTT - empty travel time estimation as a function of the loaded travel time
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationSimple 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)
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationSimple one dimensional methods (1)
Simple Method 1a constant as the empty travel function estimation (Egbelu 1987)
cbtTe
ttfTVdf
Nb
ULi j
ijLTi j
ijij
1
)(
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationSimple one dimensional methods (2)
Simple Method 2empty travel estimation based on workcenter Net Flow (Egbelu 1987)
i: :fji fik
j k
ikjii ffNF
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationSimple one dimensional methods (3)
Empty travel distance between workcenters
01
iNFii
i jij
i jijij NFfdfET
* assuming average loaded flow distance = average empty flow distance
Empty travel distance between stations of the same workcenter
ideliveryuppick
j kikji ii
dffET 2 ,min
cbtTe
ttfVETETdf
Nb
ULi j
iji j
ijij
1
21
: :fji fik
Di PiET2
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationSimple one dimensional methods (4)
Simple Method 3empty travel estimation using a transportation model
(Maxwell & Muckstadt 1982)
jix
NFiNFx
NFiNFx
dxET
st
ET
ij
iik
ki
iij
ij
iji j
ij
, 0
0
0
.
min
Number of empty vehicles moving from delivery
station i to pick-up station j
From delivery station i to pick-
up station j
NFi > 0 NFi < 0
This estimation serves as a lower bound to the actual empty travel
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationComplex 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)
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationComplex one dimensional methods (1)
Complex Method 1empty travel estimation using FCFS* allocation rule (Egbelu 1987)
1 2 3 .. j
1
2
:
i
f1jf12
f23f21
f13
f2j
fi1 fi2
-
-
-
..
..
fi3 ..
..
: :
fij
:
k i jijiki ffp
pi - the probability that the next empty vehicle will be needed at pick-up station i
pj - the probability that the next empty vehicle will be released at delivery station j
k i jijkjj ffp
*- First Come First Serve
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationComplex 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
i j
ijjiij fppg
jiij ppp
i j
jiijdgETFrom delivery
station j to pick-up station i
1 2 3 .. j
1
2
:
i
g1jg12
g23g21
g13
g2j
gi1 gi2
-
-
-
..
..
gi3 ..
..
: :
gij
:
1 2 3 .. j
1
2
:
i
f1jf12
f23f21
f13
f2j
fi1 fi2
-
-
-
..
..
fi3 ..
..
: :
fij
:
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle CalculationMulti 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)
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle Calculationmulti dimensional methods (1)
Multi Dimensional Method 1in conjunction with flow path design (Ashayeri 1989)
Notationm - 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
1
0ijn
no lane from node i to node j
one lane set up from node i to node j
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle Calculationmulti dimensional methods (2)
jin
kjix
jiWnn
jiCpxn
kiNFxx
ts
nLVdxC
ij
ijk
ijjiij
m
kijijkij
rikrik
jijk
iji j
ij
m
k i jijijk
, )1,0(
,, 0
,
, 0
,
..
min
1
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle Calculationmulti dimensional methods (3)
Multi Dimensional Method 2in 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Vehicle Calculationmulti dimensional methods (4)
jikNuf
N
iCpAu
iu
LVdffuWTNL
uWfTNVdf
jikuAf
jikuAf
ts
f
ikij
kiji
i
i j kijkij
i j kkiji
i j kkkij
i j kijkij
kkkijkij
kkkijkij
i j kkij
,, integer ,,
1
,maxmin
1
)(1
)(
,, 1
,,
..
max
minmax
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
What Is NextStatic and dynamic factors
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:
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
What Is NextDrawbacks 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Operational Versus Economic AspectsMutual vehicle interference
Thr
ough
put
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
Tim
e-in
-Sys
tem
The same analysis is true for the job’s time-in-system
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
SimulationEvaluating 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
SimulationEvaluating the number of vehicles (2)
NotationPk, 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
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
SimulationEvaluating the number of vehicles (3)
NotationMc - 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
a1,a2 - function coefficients describing the system’s throughput performance
kw - weight associated with the relative importance of the positive and negative deviation of goal k
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
SimulationEvaluating the number of vehicles (4)
integer
0,
..
min
max
222
21
11
2
1
2
1
N
kqp
NN
qpNaNaTh
qpCCMNCMNNCC
ts
pwqw
kk
fixbatbcontcveh
k kkkkk
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
SimulationDecision 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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Numerical Example6 department manufacturing facility (1)
2
4
5
6
31
P2
P1
D2
D6
D5
P3
D3
P6
P5
P4
D4
60
6080 80
14080
80
80
80
60
70
110
20
70
60
110
907070
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Numerical Example6 department manufacturing facility (2)
JobType
Job Mix ProcessPlan
LotQuantity
Job Weight(lb)
Job Volume(in3)
1 0.3 1-2-6-5 40 100 80
2 0.4 1-3-6-5 50 80 100
3 0.2 1-2-5-4 40 110 70
4 0.1 1-3-2-5-4 40 70 120
Vehicle carrying capacity - 500 lbTote weight - 10 lbTote volume - 500 in3
Vehicle traveling speed - 150 ft/minLoading and unloading time - 30 secondsAverage job’s interarrival rate - 24 minuetsPlanning horizon - 8 hoursBattery charging during planning horizon - 30 minuets
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Numerical Example6 department manufacturing facility (3)
JobType
Jobs inTote
(Weight)
Jobs inTote
(Volume)
Jobs inTote -
Unit Load
Numberof Unitloads
1 4 6 4 10
2 6 5 5 10
3 4 7 4 10
4 7 4 4 10
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
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Numerical Example6 department manufacturing facility (4)
1 2 3 4 5 6
1 - 100 100
2 - 20 40 60
3 - 100
4 -
5 40 -
6 20 140 -
From-To Flow matrix 1 2 3 4 5 6
1 - 20 310 370 80 790
2 - - 390 450 160 170
3 - 130 - 480 190 360
4 - 330 80 - 150 560
5 - 400 150 210 - 630
6 - 400 150 210 220 -
Distance matrix
33.945150800,141 i j
VijdijfLTT
i j
ijLULftTT 3106205.0
2)( LTT
e = 0.85
756.685.030480
62033.9452
N
Questions
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Small To Medium Unit Load AGVs
Courtesy of Rapistan Demag Corp. and Apogee
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Fork AGVs
Courtesy of BT Systems Inc. and Apogee
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Pallet AGVs
Courtesy of Rapistan Demag Corp.
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Heavy Load AGVs
Courtesy of Rapistan Demag Corp., Mentor AGVS Inc. and Frog Navigation Systems Inc.
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Towing AGVs
Courtesy of Rapistan Demag Corp., Apogee and Control Engineering Company
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Assignment Dedicated AGVs
Courtesy of Rapistan Demag Corp., Apogee, Control Engineering Company and Mentor AGVS Inc.
Technion - Israel Institute of TechnologyCopyright Dr. David Sinreich
Work Platform AGVs
Courtesy of BT Systems Inc.