determining type and number of automated guided vehicles required in a system

Determining Type and Number of Automated Guided Vehicles Required in a System

Dr. David SinreichFaculty 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

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


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


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


Unit load SizeThe impact on total cost of the system

Flee

t siz

e

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


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


More vehicles

flow pathsintersections

The opposite is also true


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


More vehicles

Locating P/D stations away from busy intersections and off track Less vehicles


Vehicle CalculationBasic formula

Number Vehicles =Required Transfer Capacity (Time)

Planning Horizon (Time)


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


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


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


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 timetU - Unloading operation timeV - Vehicle speedT - 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)


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


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)


Vehicle CalculationSimple one dimensional methods (1)

Simple Method 1a constant as the empty travel function estimation (Egbelu 1987)

cbtTe

ttfTVdfN

b

ULi j

ijLTi j

ijij

1

)(



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 elsewhereNFi < 0 - workcenter has a shortage of empty vehicle and needs to import NFi = 0 - workcenter is self sufficient



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

ttfVETETdfN

b

ULi j

iji j

ijij

1

21

: :fji fik

Di PiET2



Simple Method 3empty travel estimation using a transportation model

(Maxwell & Muckstadt 1982)

jix

NFiNFx

NFiNFx

dxETst

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


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)


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


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

:


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)


Vehicle Calculationmulti dimensional methods (1)

Multi Dimensional Method 1in conjunction with flow path design (Ashayeri 1989)

Notationm - number of flow typesfijk - number of transfers required from node i to node j of flow type kNFik - net flow at node i of flow type k per hourCpij - number of transfers allowed on a path from node i to n ode j per hourWij - maximum number of flow path lanes allowed between nodes i and jLij - lane installation cost from node i and jC - cost per vehicle including software and hardware

1 0

ijnno lane from node i to node j

one lane set up from node i to node j



jin

kjix

jiWnn

jiCpxn

kiNFxxts

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



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 utilizationN - number of vehicles required to operate the systemUkij - 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 kW(uk) - load unload time of unit loads as a function of the unit load size



jikNufN

iCpAuiu

LVdffuWTNL

uWfTNVdf

jikuAf

jikuAfts

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


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


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


Operational Versus Economic AspectsMutual vehicle interference

Thro

ughp

ut

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


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


SimulationEvaluating the number of vehicles (2)

NotationPk, qk - negative and positive deviation from goal k respectivelyCveh - cost of automated vehicleCcont - controller cost which includes hardware and softwareCbat - cost of battery charging stationCfix - 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



NotationMc - maximum number of vehicles a single controller can accommodateMb - maximum number of vehicles a single charger can accommodateTh - 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



integer 0,

..

min

max

222

21

11

2

1

2

1

Nkqp

NNqpNaNaTh

qpCCMNCMNNCCts

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


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


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



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



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



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


Small To Medium Unit Load AGVs

Courtesy of Rapistan Demag Corp. and Apogee


Fork AGVs

Courtesy of BT Systems Inc. and Apogee


Pallet AGVs

Courtesy of Rapistan Demag Corp.


Heavy Load AGVs

Courtesy of Rapistan Demag Corp., Mentor AGVS Inc. and Frog Navigation Systems Inc.


Towing AGVs

Courtesy of Rapistan Demag Corp., Apogee and Control Engineering Company


Assignment Dedicated AGVs

Courtesy of Rapistan Demag Corp., Apogee, Control Engineering Company and Mentor AGVS Inc.


Work Platform AGVs

Courtesy of BT Systems Inc.

determining type and number of automated guided vehicles required in a system

Documents

required number of vehicles

time unit

direct impact

transferable unit loads

true smaller unit loads

vehiclesthe flow path

reduced transfer capacity

busy intersections