A decision support system for automated guided vehicle system design Charles J. Malmhorg Department Institute,
of Decision Sciences
Troy, NY,
and Engineering
Systems,
Rensselaer
Polytechnic
USA
An interactive decision support system (DSS) f or automated guided vehicle (AGV) system design is described. The DSS allows the user to flexibly access an analytical model relating changes in the levels of design variables to performance measures and operating dynamics for control zone AGV systems. The underlying analytical model applies recently developed advances in modelling the impact of vehicle dispatching within an extended analytical model for AGV system design. Using the DSS, the system designer can interactively screen preliminary design solutions prior to the development of the simulation models used to develop and validate detail design speciJications. This makes it possible to explore a broader range of the design solution space in a process of intelligent enumeration, A sample problem is examined using the DSS. Keywords: decision
support systems, automated
alytical
Introduction Like design problems in other domains the design of automated guided vehicle systems (AGVS) forces the modeler to identify the minimum level of model detail that effectively supports design decision making. Models must provide a capability for perturbation of design solutions without imposing impractical computational requirements. Unfortunately, analytical models for AGVS design reported in most previous literature fail to capture more than one or two of the basic criteria influencing the effectiveness of a system design.lm4 Detailed models are generally simulation based,sx and although such models have been shown to be highly diagnostic,6*8,9 they are generally impractical for exploring a significant range of design variables.‘~“’ An analytical model reported in recent literaturelO has been designed to accommodate the full set of major decision variables involved in the design of zone control AGVS. Although this model lacks a simple closed form that is practical for optimization, it has been shown to perform well relative to simulation models in predicting the performance of a system as a function of its major design variables.9 The purpose of this paper is to apply an extended version of this model in a tool developed specifically to solve the AGVS design problem. The extended model incorporates recently developed an
Address Decision Institute,
reprint requests to Dr. Malmborg Sciences and Engineering Systems, Troy, NY 121803590, USA.
Received 2 January October 1991
170
guided vehicle systems
1991; revised
at the Department of Rensselaer Polytechnic
6 September
Appl. Math. Modelling,
1991; accepted
1992, Vol. 16, April
10
procedures
for characterizing
the impact
of
vehicle dispatching in AGVS.” The resultant design tool involves a decision support system (DSS) through which a designer can perturb an AGVS profile to selectively develop a set of feasible design solutions which warrant detailed investigation through simulation. This DSS allows the user to perform “intelligent” enumeration by effectively combining context specific knowledge with the computational efficiency and flexibility of the analytical model. The next section describes the major decision variables associated with the design of zone control AGVSs and provides background discussion of the problem. This section also presents the extended model based on the improved methods for predicting the impact of vehicle dispatching. ‘I The third section describes the structure of the DSS and its intended role in the AGVS design process. The fourth section illustrates the application of the DSS to a sample problem and discusses advantages associated with the combined analytical and simulation modeling approach to AGVS design. A summary and conclusions are offered in the final section. Background A key feature of an AGVS is the control technology used to manage movement of vehicles along a closed guidepath. Today the most common control technology for AGVS is zone control. With zone control the system guidepath is broken into discrete segments (“control zones”) where vehicle collisions are avoided by allowing only a single vehicle into a zone at any given time. Vehicles are routed through the control
0
1992 ButterworthHeinemann
DSS for AGV system design: C, J. Malmborg
zones of the guidepath as they serve the materials handling transactions between the workcenters of a manufacturing or service facility. Vehicles seeking passage through occupied zones are buffered outside the zone (often blocking the zone they are in), until cleared to enter. Although zone control is simple and economical from a hardware and software perspective, it creates obvious problems in system operation. For example, guidepath gridlock can arise as more vehicles are added in a system. This can increase the average travel times between pairwise combinations of workcenters and ultimately cause “shop locking.” Shop locking is a condition that requires manual intervention to restore system operation after vehicles become gridlocked in a loop on the guidepath or workcenters become idled due to insufficient input or output storage capacity (resulting from inadequate access to vehicles). The materials handling throughput capacity of an AGVS and risks associated with shop locking must be considered when designing an AGVS. Unfortunately, it is difficult to predict how the levels of design variables will influence these performance measures when designing a system. The major design variables associated with an AGVS include the following: Guidepath
layout:
Fleet size:
Load transfer point locations:
Workcenter capacity:
storage
Vehicle routings:
Vehicle dispatching rules:
the location and size of individual (linear) control segments over which a wire or strip guidance medium is provided for vehicles; vehicle movement is restricted to theguidepath; the number of vehicles used on the guidepath to service the materials handling workload between the workcenters of a facility; the locations (on the guidepath) where unit load transfers from/to vehicles to workcenter (input or output) storage queues take place; these locations usually correspond to the endpoints of control zones; the capacity (in unit loads) of the input and output workinprocess storage queues at the individual workcenters; the sequences of control zones followed by vehicles in transporting unit loads between workcenter pairs; and the realtime control strategy used for recirculation of empty vehicles. As described in a recent paper,” vehicle dispatching rules have a fundamental impact on system performance by influencing the volume of empty travel
required for vehicle recirculation and the distribution of service response times experienced by individual workcenters. Using recent results for predicting the effects of vehicle dispatching in an AGVS, it is possible to develop an improved version of the control zone model for AGVS design.” This model would have an enhanced capability for predicting AGVS operating dynamics and performance measures, which include the following: Vehicle interference levels:
Empty vehicle travel:
Vehicle minutes required:
Shop locking probabilities:
the average time lost by vehicles travelling through each control zone due to blocking, i.e., waiting for other vehicles to clear the zone before entering; the volume of empty travel (in vehicle trips per unit time) resulting from the recirculation of empty vehicles associated with vehicle dispatching; the total number of vehicle minutes required per unit time (including blocking) to meet the materials handling transactions demand imposed in a facility; and the probabilities influencing system shutdowns due to inadequate workcenter storage or guidepath gridlocking.
To apply dispatching results reported in Ref. 11, we need to estimate the combined loaded and empty vehicle flow volumes between each pair of workcenters in a facility. To illustrate the formulation of estimators for these values, the following notation is used: the number of workcenters served by the AGVS mu the material flow volume between workcenters i and j per unit time (in loaded vehicles per hour) for i,j = 1,. . . , W m,$ the total vehicle flow volume (loaded and empty) between workcenters i and j per unit time (in vehicles per hour) for i, j = 1, . . . , W
W e,j
eij’
pi’
the number of empty trips per unit time between workcenters i and j resulting from vehicleinitiated dispatching for i, j = 1, . . . , W the number of empty trips per unit time between workcenters i and j resulting from workcenterinitiated dispatching for i, j = 1, .,w
. the. probability that workcenter j initiates a request for a vehicle forj = 1, . . . , W
Appl. Math. Modelling,
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DSS for AGV system
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C. J. Malmborg
the probability that a vehicle responding to a transaction request is located at workcenter i fori = 1,. . . , W
Pi
Assuming symmetric travel routings between workcenters, we can estimate flow volumes for empty travel based on a given dispatching rule. For the vehicleinitiated case the logical approach is to estimate the number of empty trips per unit time between workcenters i and j as the product of (a) the probability that a randomly selected transaction results in empty travel between i andj and (b) the total number of loaded trips in the system per unit time. Mathematically, this can be expressed as shown below for the random workcenter rule:
for estimating the expected number of empty trips per unit time between workcenters i and j is once again to use the product of the probability that a randomly selected transaction will result in an empty trip between workcenters i and j, and the total number of transactions per unit time. Mathematically, this can be expressed as shown below for the random vehicle rule:
x(j,/gmph) (@ where K, denotes the set of combinations of workcenters that include workcenter i and could have a transaction waiting for a vehicle. For the nearest vehicle (and farthest vehicle) dispatching rules in the workcenterinitiated case we use the formulations 4=P:{kz,[gPo]
where the index k defines individual combinations of workcenters within the set Kj, which represents the set of all combinations of one or more workcenters that include workcenter j and could have requests for transactions pending. The pi and pj’ values are estimated by
i=
1
5 rnij
i=
l,...,W
(2)
j=
l,...,W
(3)
i= Ij=,
x (j,
j=l
$Zj mu
i=lj=l
For shortest travel time (and longest travel time) dispatching rules in the vehicleinitiated case we use the formulations
where
f/j(x)
=
(5) In the vehicleinitiated case the pj’ values are interpreted as the probability that workcenter j initiates a request for a vehicle, and the pi values estimate the probability that the responding vehicle is located at workcenter i. In the workcenterinitiated case the pj values are interpreted as the probability that workcenter j makes the current vehicle selection, and the pi values are interpreted the same way as for the vehicleinitiated case. In the workcenterinitiated case the logic
172
Appl. Math. Modelling,
1992, Vol. 16, April
mph)
(‘1
if i is the minimum (maximum) distance workcenter toj in combination k otherwise (8)
The results above are an application of the results in Ref. 11. However, they include only expected trip frequencies instead of the product of trip frequencies and travel times. This is due to the fact that the extended control zone model for AGVS design used in the DSS requires empty trip frequencies between specific workcenter pairs to estimate the vehicle arrival rates to control zones. (The objective of the models presented in Ref. 11 was to estimate total empty vehicle travel time for a system.) Using the above results, the total vehicle flow volume per unit time (loaded and empty) is given by rn; = mti + max {eG,eb}
1 ifjis the minimum (maximum) distance workcenter from i in combination k [o otherwise
/g
f&)
r0 pj’ = 5 rn,ig
P+D))
where 1
pi = $J rn,/g
[p
i,j=
l,...,W
(9)
Given the representation of vehicledispatching effects, an extended version of the basic control zone modeli can be developed by augmenting the procedure to represent vehicle blocking and workcenter queuing dynamics. Estimates of vehicle blocking times are obtained by using the maximum arrival rates to individual zones given N, the number of vehicles in the system. The maximum arrival rates are estimated as the product of (a) the relative frequency with which a zone is accessed and (b) the ratio of the total vehicle minutes available per unit time and the sum of the unobstructed travel times through each control zone. Ignoring the time associated with load transfers, letting C denote the number of control zones in the guidepath, Z, denote
DSS for AGV system
5
5 yep&
5 p=l
izlj=1
5 yign;
i=]j=l
)
x
(6OeNli,
tb)
(10)
where 1 ifkEZ, 0 otherwise
Yijh =
0
(11)
1
N
1
2
.**
p(2)
...
p(N  1)
0
b(0)
1
~(0)
~(1)
~(2)
. ..
p(N  1)
2
0
Pm
P(l)
**.
PW2)
0
0
000
PUN
0
0
000
0
~(1)
N 1 0 LO N
... .. .. ..
N ~0’) ~0’)
p(N
1)
[(N  i)/N)TktklX
(l/x!)
P(O)
vMR=~&&vk
eXp
wk
=
fk +
5
[(j


(14)
0.5)tkpkjl
(15)
If this value exceeds 60eN, i.e., the total number of vehicle minutes available per hour, it implies that the current fleet size of N vehicles is not adequate to meet the materials handling workload. Insight into shoplocking risk factors associated with guidepath gridlock are obtainable from the steadystate probability distribution described above. To study shoplocking risk factors associated with the inability of workcenters to receive incoming unit loads, the probability distribution of the number of unit loads in the input queue at each workcenter j is computed. Denoting these probabilities as, p,$ for k = I, 2, . . . , Zj, (where Zj denotes the input storage queue capacity at workcenter j in unit loads), these probabilities represent the steadystate solution vector of a Markov chain with system states corresponding to the number of unit loads in the input queue at workcenter j. This Markov chain is of the form
I’YN)T,tJ (13) where i denotes the current system state, and transitions of the Markov process correspond to vehicle departures from the control zone. The time for a vehicle to travel through control zone k including blocking time is then approximated, using I(W
(12)
P(l) .
Assuming arrivals to zone k follow a Poisson distribution, transition probabilities p(x) for x = 0, 1, . . . , N are of the form P(X) =
C. J, Malmborg
In the equation above, e denotes the system efficiency factor, which is the proportion of each time period that vehicles are actually available for servicing transactions. This incorporates allowances for such factors as battery charging, maintenance, etc. It follows that 60eN yields the total vehicle minutes available each hour given a fleet size of N. Estimates of vehicle blocking times are obtained through expectation, using the probability distribution of the number of vehicles using (and waiting to use) each control zone k, i.e., pm,, pkl, . . . , pkN. These probabilities are given by the steadystate solution to the Markov chain:
the set of control zones in the routing between workcenters i and j, and t; denote the travel time through zone p (p = 1, . . . C), this yields Tk =
design:
j=l
(which arbitrarily assumes that the current vehicle in service is half completed when an arriving vehicle is blocked from using the zone). Given the travel times through each control zone including blocking, the total number of vehicle minutes required (VMR) per unit time to implement the material handling workload is given by subsequent state (k) 0
0 1 current state(i)
1
2
3
..*
Ij  1
P(l)
Pt2)
Pt3)
’. *
pCzj 
PC2)
PC31
” .
p(l;  l)
PCrZj)
p(Zj  2, p(Zj  3) :
p(?Zj  1)
P(O)
P(l)
2
O
P(O)
P(l)
PC21
’”
3
0
0
P(O)
P(l)
*.*
:
:
:
:
:
::: ,..
zj1
0
0
0
0
:::
Zj
0
0
0
0
I)
rj
P(O)
PtzZjl
(16)
p(?Zj  2)
P(l)
P(Z2)
P(O)
P(rl)
Appl.
Math.
Modelling,
1992,
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16, April
173
DSS for AGV system
design:
C. J. Malmborg
In the above, transition probabilities, p(x) for x = 0, 1 correspond to the probability of a given number of arrivals to workcenter j (assumed to follow a Poisson distribution) during the processing time, i.e.,
(5
p(x) = (I/x!)
m,kl7j)“ev
p=I
workcenterj removes unit loads from the input queue (assumed to be a constant that is independent of the state of the output queue), and transitions of the process correspond to the removal of unit loads from the input queue. Shoplocking risks associated with inadequate output storage capacity at workcenterj are measured by using the analogous steadystate probabilities of the form p,!k for k = 1, 2, . . . , Oj, where ?j denotes the output storage capacity at workcenterj (m unit loads). In this case the Markov chain yielding the steadystate probability vector is of the form
( j, mpki,) (17)
with x = k  i for i = 1 and x = k  i + 1 for i = 2 > . . ’ , I.,’ In the above, 7 denotes the rate at which subsequent state (k) 1 P(O) P(l) P(O) P(l) O P(O) 0 0 0
0 1 2 3
current state(i)
Oj
3 P(3) P(3)
...
P(l)
Pt2)
‘.’
P(O)
p(1)
.**
0,  1
’’’
Oj
P(Oj  1)
PC20j)
* ’ * P(Oj  l)
PCrOj)
P(Oj  2) p(Oj  3) ;
P(?Oj p(?Oj
 1)  2)
:
:
:
:
;;;
0
0
0
0
“.
P(l)
PG2)
_ 0
0
0
0
**’
P(O)
P(~l)
: Oj
2 P(2) P(2)
1
during the time between entries. These transition probabilities, p(i  k + 1) for i  k + 1 = 0, 1, . . . , are of the form shown below for the case of Poisson departures (i.e., Poisson vehicle arrivals):
where transitions correspond to entries of unit loads into the output queue (assumed to occur at a constant rate) and transition probabilities correspond to the number of unit load departures from the output queue
W
p(i  k + 1) = l/(i  k + l)! [ 7Tj/j,
mjp]iiph+“eXp
(

lTjl
x
mj,
p=l
In the above, the Tj parameter represents the average rate of departures from the output queue at workcenter j. This value must be determined by estimating the travel time required for a free vehicle to reach workcenterj and the average time that workcenterj must wait for a free vehicle after making a material handling request. To obtain an estimate of the call waiting time, the control zone model represents the AGVS as a M/G/l system where the arrival rate (A’) and the service rate (p’) are approximated by
CT2=
I
i=Ij= 1 ww
p’=N
[
xx
2
kEZ,
tk
(
rn,$is p=l
$rnLk k=l
I )I
(20)
(19)
/
2 5 [kEZ,, c th 
(pflN)1]1
;=,j=,
x
(
rn;lE grnAk p=lk=l
(23)
The average vehicle travel time for a requested vehicle to reach workcenter j is estimated by the model as w
Rj =
rw
1
x L,z
m:k/c
k=l
h’=ggm; i1 j=*
(18)
z I=lp=l
dp]
x
1~
(24)
rEZA,
Thus 7rj = (W + Rj) l is used to approximate the rate at which unit loads are removed from the output queue at workcenter j. The decision support system for AGVS design
(21)
Using the M/G/I, the average call waiting time is W = (l/A’) [(A’)2& + (A’//_~‘)~]/[2(1 A'/p')] (22) where the variance of the service time is estimated as 174
Appl. Math. Modelling,
1992, Vol. 16, April
The shoplocking risk factors obtainable from the control zone model allow the system designer to screen potential design solutions that may be feasible from a throughput perspective but risky in terms of shoplocking frequency. If done early in the design process, this
DSS for AGV system design: C. J. Malmborg
type of analysis could be used to define a reduced set of candidate designs for which detailed simulation analyses could be justified. Apart from the use of simple rules of thumb for fleet size estimation, system suppliers sometimes rely on simulation as the preliminary analysis tool. Although this technique is excellent for performing diagnostic validation studies (effective for validating the feasibility of a system), it tends to lock the designer into premature specification of the design variables. This is due to the fact that detailed simulation models do not provide the flexibility to perform the type of extensive “what if” analyses needed to optimally specify the basic design variables that will ultimately determine the performance and cost of a system. The net result is that a system is apt to be overspecified initially, followed by a retroactive cost reduction step, for example, specifying a dense guidepath layout with an excessive allocation of storage space and then performing a series of simulation studies aimed at finding the minimum number of vehicles needed to meet the transactions demand. The time and effort involved in performing adequate simulation experimentation, data development, and model modification for the initially specified guidepath and queue sizes presents a barrier to evaluation of additional system configurations. To a varying extent the same problem exists with the perturbation of other design variables. The control zone model provides the potential to allow the system designer to creatively explore a wide range of basic design solutions by screening design profiles prior to performing the simulation step. However, this requires a computational shell for the model that facilitates the designer/model interface in a way that allows the designer to use his or her knowledge in an intelligent enumeration process. The system must allow the designer to generate the data base describing a design quickly and efficiently and to provide feedback of model results in a flexible and easily analyzed fashion. With these objectives in mind a DSS was developed specifically for the design of zone control AGVSs, but with potential for extending the basic concepts to other problems involving multiple, discrete vehicles sharing a closed network. The system provides modules that allow the designer to quickly adjust the basic system design variables, execute the model, analyze the resultant model outputs, and save the data base defining intermediate design profiles. The system is implemented on IBM PS2 level hardware. (Subsequent experimentation with some large problems has prompted work on the development of a workstationbased version of the system.) For small to moderatesized problems (up to seven workcenters and 40 control zones), response times have been found to be acceptable on an 80386 chip microcomputer. In interfacing with the user the system uses the main access menu shown in the first panel of Figure 1, which provides options to adjust the system design variables, run the model, or analyze the outputs. The features contained under the various user options included in Figure 1 are summarized below.
Options 1 and 2:
Option 3:
Option 4:
Option 5:
Option 6:
The user can change the number of vehicles, vehicle speed, load transfer time, system efficiency factor, and dispatching rule combination. The user can modify, add, delete, or display vehicle routings to relieve conjestion areas discovered in the system through examination of the state probabilities associated with individual control zones. The user can display and modify the guidepath layout of the system by adding or deleting linear segments and redefining control zones within the guidepath to reducing blocking delays. The user can change the material flow matrix defining the workload imposed on a system in order to study the ability of a design to adapt to uncertainty in future workloads. The user can adjust the workinprocess storage capacity of the system at individual workstations or adjust the processing rates at individual workcenters. This option allows the user to study the effects of alternative space allocations for buffering transactions within the system to reduce shoplocking risks.
Each of the major options is summarized in the three panels of Figure 1. The parameter values in the figure correspond to a sample problem for which a sketch of the guidepath is presented in Figure 2. Options 16 provide the designer with a method for instantaneously changing the hundreds of parameter values necessary to specify a basic AGVS design profile for moderatesized problems. By providing graphical and numerical feedback during this process the designer does not have to deal with many of the problems that deter the examination of alternative solutions. For example, the designer can easily check the reasonableness of a proposed design without having to deal with manual updating of dependent parameter values as changes are made. Rather, incremental or major changes can be made quickly, followed directly by their evaluation of the design profile using the control zone model. This type of rapid and direct feedback enables the designer to use the knowledge gained from each design modification to suggest the most plausible direction for improvements. Solutions found to be promising can be saved automatically in a computer file for later use. When a design solution is evaluated (option 7), the designer can invoke option 8 to analyze outputs from the model. Six primary modules are contained under
Appl.
Math.
Modelling,
1992,
Vol.
16, April
175
DSS for AGV system design: C. J. Malmborg A SLTMMRRY OF THE CURRENT MATCRIAL FLOW HATRIX IS GIVEN BELCW. IN THE DISPLAY, THE SO"RCE WORKSTATIONS ARE LISTED ALONG THE LEFT COLDMN AND THE DESTINATION STATIONS ARE LISTED ACROSS. THE VALUES IN EACH CELL REPRESENT TXE NUMBER OF "NIT LOADS PER HO"R TRANSFERRED BETWEEN TYE CORRESPONDING WORKSTATICN ?A;?..
TO "SE THIS DECISION SUPPORT SYSTEM FOR DESIGN OF ZONE CONTROL AUTOHRTED GUIDED VEHICLE SYSTEMS, JUST ENTER THE N"MBER OF THE OPTION THAT YOU WANT TO USE:
1. 2. 3. 4. 5. 6. 7. 8. 9. ENTER
ADJUST AG" FLEET SIZE/HARDWARE PAPJMETERS CHANGE THE VEHICLE DISPATCHING RULE CHANGE THE VE"ICLE ROUTINGS CHANGE THE SYSTEM GUIDEPATH LAYOUT CHANGE THE NATEXAL FLOW MATRIX CHANGE INPUT/OUTPUT QUEUE CAPACITIES/DELTA VALUES COMPUTE PERFORMANCE MEASURES FOR THE CtiRRENT DESIGN ANALYZE OUTPUTS FROM THE CONTROL ZONE NOOEL TERMINATE THE SESSION
THE N"MBiR
OF THE OPTION
YOU WISH
SOURCE
DESTINATION WORKSTATION 12 3 4 5 ______________~~~~~~
1
0
10
2 3 4 5
3 4 0 2
0 4 0
2 0 3 14
2
2
: 0
:
TO SELECT? 1. SNTER AN ENTIRELY NEW .YATRIX 2. C.HANGE A SINGLE CELL IN THE MATRIX 3. RETURN TO THE MAIN MEN"
A S"MMARY OF THE FLEE? CURRENT DESIGN PROFILE
SIZE AND K4P.DWAF.X PARRMETERS IS GIVEN BEXW:
SELECT
IN TYE
ONE
Figure 1. THE THE THE THE
THE NDXBER
1. 2. 3. 4. 5. ENTER
TEE T.HREE CPTIONS
MZVE
?
(continued)
AGV's FLEET SIZE IS 8 VEHICLE SPEED IS 1 FEET PER SECOND 10 SECONDS LOAD TRANSFER TIME IS EFFICI’CNCY FACTOR IS 0.75
CURRENT CURRENT CURRENT CURRENT
ENTER
OF
CHANGE CHANGE CHANGE CHANGE RETDRN
OF THE OPTION
THE THE THE THE TO
THE OPTION
SELLCTED
FROM
THOSE
SUMMRRIZED
BELOW
FLEET SIZE VEHICLE SPEED LOAD TRANSFER TIME EFFICIENCY FACTOR THE MAIN MEN"
YOU WIS"
TO SELECT
?
DO YOU WISH TO ESTIMATE TBE ?ROPORCION OF WOP.XSTAT:ON VERSUS VEHICLE INITIATED INVOCATIONS OF THE DISPATCSING X"Li (Y 28 N, ? ?I
THE CNT
VEHICLE RANDOM
DISPATCHING
RULE COMBINATION
VEHICLE/RANDOM
IS:
WORKSTATION
TO CHANGE THE "EHICLE DISPATCXING SUNKAHIZED IN THE LIST BEXW:
RULE,
SELECT
AMONG
THE 0P:ICNS
I
I I
/
1. NEAREST VEHICLE/SHORTEST TRAVEL TX% 2. NST ‘JEHICLE,RANi)OM WORKSTATION 3. NEAREST '0XICLE,LONGEST TXA'JEL TIME 4. RRNDOH "EHICLZ,SHOR?EST T?.AVEL T:KE 5. P..&VDOMVEHICLE/RANDOM XOPXSTATION 6. RANDOM "EHICLElLONGEST TRAVEL T:ME 7. FABTHEST VEHICLE/SHORTEST TRAVEL TIHE 8. FMTXEST "E"ICLE,?.A..DOM WORKSTATION 9. FARTI(EST VEHICLE/LONGEST T?.AvEL TIXE 10. PZT"P.N TO THZ XAA:N llENU ENTER
THE NUMBER
1. 2. 3. 4. S. 6.
ENTER
OE ONE OF THE ABOVE
OPTIONS
?
DISPLAY ALL VEHICLE ROUTINGS IN THE C3P.JJNT JESIGN DISPLAY A PARTiCULU ROUTING IN THE CCRXSNT DES:IW C.XANGE AN EXISTING RO"T:NG IN THE C"FZ.ENT DEJ::N ADD A NZW ROUTING TO TBE EXISTING DESIGN DEL&Z AN EXISTING ROL'TING IN THE CURI1ENT JESZGN RETURN TO THE VAIN MENU
THE N"MBER
OF ONE OF THE ABOVE
OPTIONS
?
THE OPTIONS AVAILABLE FOR C:HANGING AND VIEWING GUIDEPATH ARE SUMHARIZED BELOW: 1. 2. 3. 4. 5. 6. 7. 8. ENTER
DRAW THE CURRENT SYSTEM GUIDEPATH EXAMINE THE CWCTERICTICS OF A CONTROL ZONE DISPLAY THE ENDPOINTS AND ZONES OF THE LINEAR SEGXiNTS ADD A CONTROL ZONE TO THE SYSTEM GUIDEPATH CHANGE A CONTROL ZONE IN THE SYSTEM GUIDEPATH ADD A LINEAR SEGMENT TO THE SYSTEM GUIDEPATH CHANGE A LINEAR SEGKENT IN THE SYSTEM GVIDEPATB RET"P.N TO THE MAIN MENU
THE NLMBER 3.. 2.
CHANGE CHANGE
OF YOUR
OPTION
?
DELTA VALUES MXIMVM WIP
WORKSTATION TO THE MAIN
MEN”
ONE OF THE ABOVE
Figure 1. problem
SELECTED
WORKSTATION WORKSTATION
3. CGE 4. RETURN SELECT
THE S'fSTEX
Main
THREE
menu
INPUT QUEUE CAPACITIES tQ_XIMJM WIP OUTPUT QUEUE CAPACCITIES
Figure 2.
Guidepath
option 8 which allow the designer to analyze different aspects of the performance of a design. The features of these modules are summarized below. Module 1:
OPTIONS?
and
DSS options
26
for a sample
Module 2:
176
Appl.
Math. Modelling,
1992, Vol. 16, April
sketch for the sample problem
The number of vehicle minutes available per hour in the current design, and the number of vehicle minutes per hour that are required (i.e., including empty vehicle travel, vehicle blocking, etc.) are displayed. This module provides a throughput feasibility check on the current design. The travel times with and without vehicle blocking are provided to give the
DSS for AGV system design: C. J. Malmborg
user some insights for revising vehicle fleet size, routings, the guidepath layout, control zones, etc., in order to eliminate excessive guidepath contention. Steadystate probability vectors and blocking times for individual control zones times are displayed which also provide insights into routing changes, control zone boundaries, and the guidepath layout. This information also identifies potential gridlock problems associated with the current design. Loaded and empty vehicle travel volumes are displayed to illustrate the effects of alternative vehicle recirculation strategies and measure limitations on the use of alternative dispatching rules for increasing system capacity when the fleet size, guidepath, and other design variables are fixed. State probabilities for the input and output queues at individual workstations are displayed to indicate shoplocking risks at individual workstations. This information can be used to make storage space reallocations within and between individual workcenters.
Module 3:
Module 4:
Module 5:
The screens associated with the modules of option 8 are summarized in the three panels of Figure 3 for the sample problem. Illustration of the decision support system To illustrate an application of the decision support system, the design problem summarized in Figures 13 was analyzed. The outputs shown in Figure 3 are based on the minimum (throughput feasible) fleet size and random workcenter/random vehicle dispatching. Finding the minimum number of vehicles for a given design is a quick and simple process of trial and error using
BASX AND
ON THE A VEHICLE
AFTER
CURRENT FLEET AVAILABILITY
ACCOU?JTING
SIZE Of 3 ‘JEHICLPS EFF?CIENCV FACTOR OF 0.75
FOR GUIDEPATH
360 335.714
AS THE RESULTS OF THE HOCEL SHOW, THE CUMENT FLEET SIZE IS ADEQUATE TO NEET THE KEQ"Ii(ED YATERIAL HANDLiNG WORKLOlw. ?.RESS
ANY
KEY TO PROCEED?
SCREEN DISILAYS TUVEL P:XES WITHOUT SLOCKING MINUTES, EOR TEE ROUTING5 BE:WEEN EACI( WORKSTATION TiiE SOURCE WOWSTATiON IS LISTED ALONG THE LEfT COLUMN THE. DESTINATiON STATiON i5 LISXD ACROSS THE TOP ROW: SOURCE DESTINATION 'WORKSTATION 1 2 3 4 5
THIS (IN
Figure 3.
0.0 5.0
5.0 0.0
6.a
5.0
5.4
4.3
6.8 5.0 5.4
4.3 5.3 5.1
0.5 5.7 3.3
5.3 i.7 0.0 8.6
5.1 3.3 8.6 0.0
System outputs for the sample problem
TIKES WITH aLOCKiNG AXE: DE5T:NXTISN WORKSTATION ? 2 3 4 5 __________________
CORRESPONDING
: 3 :
5.3 0.0 7.1 5.1 5.6
PRESS
THIS
ANY
KEY
SCREEN
NUMBER CTRL
0.0 5.3 4.5 5.7 5.2
4.5 7.1 0.0 6.0 3.4
5.7 5.1 6.0 0.0 9.0
TO CONTINUE?
DISPIAAYS
OF VEHICLES
TBE STEMY STATE PROBABILITY 3f THE USING OR WAITING TO US; EACH CONTROL ZONE.
ZN

0
5.6 5.2 3.4 9.0 0.0
1SYSq,
4
STAjTE
WW5E4 5
Of VEHICLES 6 7
: 3 4 5 6
0.95 0.91 0.9, o.a4 0.92 0.95
0.05 0.08 0.03 0.15 0.08 0.05
0.00 0.01 0.00 0.01 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.30 0.00 3.00 0.00 0.00 0.30 0.30 0.00 0.30 0.30 0.00 3.00 3.30 0.00 0.00 0.00 0.00
: 9
0.97 0.9, 0.98
0.03 0.02
0.00 0.00
0.30 0.00 0.30
0.oc 3.00 0.30
DO YOU INCLUDING
WANT TO VI574 THE AN0 EXCLUDiNG
TV.‘wTL ERfC:E
EACH
CONTROL ZONE
CONTROL
0.00 0.00 0.30 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.30
c.30 0.30 0.00 0.00 0.33 0.90 0.00
0.30 0.00 0.00
0.00 0.00
TIES TSROUGH EACH CONTROL 3LOCKiX (ESTER Y OR N)?
13NE
ti?l
TIME ARE
5ZCONDSl SWPARIZED
TI.UE
YIY.OUT
150.0 130.0 65.0 45.0
135.6 i64.5
6 7 : 10
65.0 45.0 105.0
66.0 45.6 105.0
ANY
u%:C:+ SLLOW
TW.“EL T:NE WITIi 'VEERICLE BLOCXING __________
'iEtiICLE BLOCKI)I‘ ________________
:
PRESS
23NE
ZONE.
TSAVEL
____
9
0.00 0.00 0.00 0.00 0.00 0.00
TfZ T?A"EL TIbflS T'HROUGH MC:i CtXZZL INCLUDE AND EXCLJDE VEHICLS BLOCXING
FOR
8
66.7 45.8
KEY TO CONTINUE?
THIS SCREEN SHOWS THE "OLUNE Of LOACED TRAVEL (UNIT LOADS,HR) BETWEEN EACH HOPXSTATION PAIR SERVE5 5P THE AGVS. THE SOURCE WORKSTATION IS LISTED ALONG THE LEfT COLLMN AND THE DESTINATION STATION I5 LISTED ACROSS THE TOP ROW: SOURCE DE5T:NATION WCRKSTATION 12 3 4 5 _____________________________ 1 0.0 2 3.0 3 4.0 4 0.0 5 2.0 THE BLOW VOLXES SOURCE 1
1.0 0.0 2.0 0.0 2.0 3.0 0.0 0.0 2.0 4.0 3.0 0.0 0.0 1.0 4.0 INCLLJDING LHPTY OESTINATION 2 3 4
2.0 1.3 0.0 1.0 0.0 VEHICLE TRAVEL WOMSTATION 5
: 3 4 5 PRESS
1.1 1.6 0.7 3.3 0.7 0.9 4.1 4.2 0.9 2.0 PROCEZD?
2.5 1.9 0.6 ?.a 0.7
ANY
4.9 1.0 5.2 1.6 3.4 KEY TO
3.09 4 3.3 1.7 5.5
ARE
SHOWN
BELOW:
THIS SCREEN DISPLAYS THE STEADY STATE PROBABILITY 'iECTOP.5 DESCRIBING THE NUMBER OF bNIT LOADS IN THE INPVT OVEUES. THE DATA CAN BE USED TO DETXT POTENTIAL SHOP LOCKiNG PR05LEXS
CONTENTION
THE VEHICLE MINUTE5 AVAILABLE EACli HOUR TOTALS: THIS CObPARES WITH VEHICLE MINUTES REQUIRED OF:
TIlE
5OUiKE
PAIR. XVD
STATION
SYSTEH
STATE
 NUMBER
Of
LO.%05
WIT
IN
THE
QUEUE
0 1 * 3 4 5 6, a 9 ________________________________1
2 3 4 5 PRESS
0.00 0.00 0.00 0.00 0.00 ANY KEY
0.14 0.19 0.18 0.38 0.33 0.17 0.50 0.32 0.12 0.27 0.29 0.20 0.34 0.32 o.la TO PROCEED?
0.14 0.07 0.04 0.11 0.09
o.:i 0.03 0.01 0.06 0.04
0.0a 0.06 0.01 0.01 0.00 0.00 0.03 0.02 0.02 0.01
0.35 0.00 0.00 0.01 5.00
0.04 0.00 0.00 0.01 0.00
THIS SCREEN DISPLAYS THE STEADY STATE PROBABILITY VECTORS DESCRIBING THE NUMBER OF UNIT LOADS IN THE OUTPUT QUECES. THE DATA CAN BE USED TO DETECT POTENTIAL SHOP LOCKING PROBLLNS STATION 0
SYSTEM 1
0.00 0.00 0.00 0.00 0.00 ANY KEY
Figure 3.
STATE *
 NUMBER 3 4
0.01 0.03 0.05 0.00 0.00 0.01 0.00 0.01 0.02 0.00 0.00 0.01 0.00 0.00 0.01 TO PROCEED?
0.10 0.02 0.05 0.02 0.03
Of
5 0.11 0.05 0.08 0.05 0.05
ONIT
LOADS
6, 0.13 0.09 0.12 0.11 0.12
IN
THE
a 0.20 O.i, 0.19 0.19 0.20
0.20 0.28 0.26 0.29 0.28
Q”L”E
9 0.1, 0.38 0.26 0.34 0.31
(continued)
Appl. Math. Modelling,
1992, Vol. 16, April
177
DSS for AGV system design: C. J. Malmborg
the system. Selection of the random workcenter/random vehicle dispatching rule yielded the empty vehicle travel estimates summarized in Figure 3. The (symmetric) vehicle routings input for the sample problem are summarized below:
BASED
ON
THE
AFTER
SIZE
OC EFFICIENCY
CURRENT FLEET AVAILABILITY
AlJO A MHICLE
ACCOUWTING
FOR
GUIDZPATH
5
VEHICLES FACTOR OF 0.75
CONTZNTION
THE VEHICLE MINUTES AVAILABLE EACH THIS COMPARES WITH VEHICLE MINUTES
HOUR TOTALS: REQ"P.ED OF:
225 laa.6503
SIZE AS THE RESULTS OF THE MODEL SHOW, THE CURRENT FLEET IS ADEQUATE TO MEET THE ?.EQUIRE5 XATER:AL HANDLING WORKLOAD.
From workcenter
To workcenter
Control zone sequence PRESS
2 3 4 5 3 4 5 4 5 5
2 3 3 4
496 49632 l369 l3687 685 3l4 3257 2l4 57 4l257
As can be seen from Figure 2, these routings could easily be streamlined to conserve vehicle hours. When the above routings are combined with the guidepath design shown in Figure 2, the minimum fleet size and dispatching weights, the outputs of the system shown in Figure 3 suggest that they produce a significant likelihood of operating problems. For example, the model outputs suggest that the initial design will result in significant vehicle blocking in control zones 1 and 4. Since these zones could potentially isolate workcenter 1, it seems advisable to adjust the vehicle routings to reduce congestion in these zones. In addition, this initial design would be likely to result in shop locking due to overflow of the output queues at virtually every workcenter. There may be several means by which the above problems could be addressed in the initial design. For example, the guidepath could be modified, workcenter load transfer points could be relocated, the routings could be shortened, etc. The most obvious of these possibilities appears to involve streamlining of the vehicle routings. Therefore the first design modification is to input the following (symmetric) alternative routings : From workcenter 1 1 1 1 2 2 2 3 3 4
To workcenter 2 3 4 5 3 4 5 4 5 5
ANY
KXY
SCREEN 3ISPLAYS T?AVEi TIUES Y:TSOUT BLOCKiNG (IN MINUTES) FOR THE Y&OUTINGS SETUEEN EACii WORKSTAT:GN ?A:?.(. THE SOURCE WORKSTATION IS LIST50 AIc3NG THE LZFT COLL‘XX AX THE DESTINATION STATIC?, IS LISTS0 ACWSS TRE TOP ROW: DISTINA"ION 10XXSTATION SOURCE
THIi
1 2 3 4 5 _____________________________________ 1
0.0
2 3 4 5
2.8 3.2 2.8 5.4
Math. Modelling,
3.2 2.2 0.0 4.3 3.3
TI?ES
THE COP.P.ES?ONDING SOCTRCE 1
l3 l2 4 4987 32 69 687 589 57 987
1992, Vol. 16, April
2.9 2.5 4.3 0.0 2.9
5.4 2.9 3.3 2.9 0.0
SLOCRING MS:
WITY
DESTINATION SlOaK3TATiON
2
3
4
5
1
0.0
2.9
3.2
2.9
5.6
: :
2.9 3.2 5.6 2.9
c.0 2.2 3.0 2.6
2.2 0.0 3.3 4.5
2.6 4.5 3.0 0.0
3.0 3.3 0.0 3.0
PRESS
ANY
KEY TO CONTINUE?
THIS SCREEN DISDLAAYS TSE STEAilV STATE PROSABILITY :E THE NUHBER OF VEHICLES USING OR WAITIYG TO USE LAG3 C:NTROL ZCNE ZN
CTRL
SYSTEH 12
0 0.91 0.95 0.97 0.94 0.95 0.97 0.97 0.9S 0.90
FOR
0.08 0.05 0.03 0.06 0.05 0.03 0.03 0.04 1.09
EACH CGNTROL
CONTROL
ZONF.
STATE 3 0.10 0.00 0.00
0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00
0.00
o.cc 0.00 0.00 0.00
$F VEiiICLiS 7 6 3
 YLXSER 4 5
3.00
0.50
PRESS
ANY
KEY
9
___.
0.00 0.00 0.00 0 co 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 3.30 0.00 3.20 0.00 0.00
0.00 0.00 0.50 0.00 0.00 0.30 0.00 3.:0 0.00
0 .oo 0 30 0 :30 0 3 0 9 .:o 0 .:c 3 .oo
.OO .CO .OO
ZONE ??AvEL TIXE 11Y b?HICLE SLsCxIx
T?AvzL TIME WITHCUT VEXICLS ILOCXI'IG
.___ _IO,. 1 63.5 45.4 L55.6 134.0 66.1 45.7 46.: 68.4 105.0
45.0 45.0 65.0 105.0 TO CONTINUE?
THIS SCREEN DISPLAYS TSE STEXDY STATS PROBABILITY VECTORS DESCRIBING THE NUHBER OF UNIT LOADS IN THE INPUT QUEUES. THE DATA CAN BE USED TO DETECT POTENTIAL SHOP LOCKING PROBLEMS STATION
: 3 :
SYSTEM STATE  NU"SER OF UNIT LORDS IN THE QUEUE 0 12 3 4 5 6 7 a 9 ___________________________________________________ 0.00 0.00 0.00
PRESS ANY
Appl.
*.a 0.0 2.2 2.5 2.9
Control zone sequence
Using these routings, the minimum (throughput feasible) fleet size is easily found by trial and error to be five vehicles. The resultant model outputs are shown in Figure 4. As the outputs for the modified design suggest, this change in routings would relieve the pressure on control zones 1 and 4 and produce a significant savings in vehicles required. In addition, probabilities associated with shop locking due to overflow of the output queues are substantially reduced following modification of the initial design.
178
TO PROCEED?
0.38 0.14 0.50 0.27 0.34
KEY
TO
0.33 0.19 0.32 0.29 0.32
0.17 0.1s 0.12 0.20 O.la
0.07 0.14 0.04 0.11 0.09
0.03 0.08 c.11 0.01 0.06 0.01 0.01 0.00 0.00 0.06 0.03 0.04 0.02 0.02 0.01
0.00 0.05 0.00 0.01 0.00
0.00 0.04 0.00 0.00 0.01
PROCEED?
SCREEN DISPLAYS THE STEADY STATE ?ROBRsILITY VECTORS DESCRIBING THE NUMBER OF UNIT LO&.05 IN TX OUTPUT Q”E”ES. THE CAN BE USED TO DETECT POTENTIAL SHOP LOCKING PROSLIMS
THIS
DATA
STATION
SY.5TStf
O
:
STATE

2
3
NUMBER
4
OF
UNLT
5
6
LOADS
7
IN
THE
a
OCEUE
9
_____ _________________________________________ :
0.00 0.00
0.22 0.75
0.19 0.19
0.16 0.05
0.13 0.0,
0.08 0.06 0.00 0.10 0.00 0.01
0.04 0.00
0.02 0.00
3
0.00
0.55
0.25
0.11
0.05 0.02 0.01 0.00
0.00
0.00
:
0.00
0.31 0.35
0.22 0.23
0.16
0.05 0.11 0.07 0.10 0.08 0.04
0.02 0.01
0.01
PRESS
ANY
Figure 4.
0.03
KEY TO PROCLED?
System outputs following
modification
of routings
DSS for AGV system design: C. J. Malmborg BASED ONTHECVRRENT FEET
To make further improvements in the design, a modification of the system guidepath and relocation of the load transfer points for workcenters 3 and 5 to the periphery of the guidepath is attempted. These modifications required less than 3 min to implement and are illustrated in Figure 5, in which a segment cutting back from workcenter 4 to control zone 1 has been added. As a result, control zone 1 has been subdivided into two zones numbered 1 and 11 in Figure 5. Relocation of the load transfer points for workcenters 3 and 5 effectively eliminates control zones 3 and 7 from the guidepath. The routings input for the revised control zone are as follows: From workcenter 1 1 1 1 2 2 2 3 3 4
To workcenter 2 3 4 5 3 4 5 4 5 5
AND A VEHICLE AFTER
SIZE
AVAILABILITY
ACCOUNTING
FOR
OF
5
EFFICIENCY
GUIDEPATH
“EHICXS
FACTOR
OF 0.75
CONTENTION
THE "EHICLE MINUTES AVAILABLE EACH HOUR TOTALS: THIS COMPARES WIT" VERICLZ MINUTES WCEC"IP.ED OF:
225 202.2107
AS THE P.ES"LTS OF THE MODEL SHOW, THE C"WNT FLEET SIZE IS ADEQUATE TO MEET THE XEQUIRED MATEilIAL HANDLING WDP.KLOM. PRESS
ANY
KEY
TO PROCEED?
THIS SCREEN DISPLAYS TRAVEL TIFFS WITYDUT BLOCKiNG (IN MINUTES) FOR THE ROUTiNGS BETWEEN EACH WORKSTATION THE SOURCE WORKSTATION IS LISTED ALONG THE LEFT CCLIXN THE DESTINATION STATION IS LISTED ACROSS THE TOP ROY: SOURCE DESTINATION WCRKSTATION 1 * 3 4 5
Control zone sequence
1
0.0
5.0
3.2
2.1
5.:
: 4 5
5.0 3.2 2.1 5.4
0.0 2.2 2.5 2.9
2.2 0.0 4.9 3.3
2.5 4.9 0.0 2.9
2.9 3.3 2.9 0.0
TYZ CORRESPONDING SCURCE 12
496 1112 1110 4987 32 69 68J 2l10 5J 987
TIbfES WITH BLOCKING ARE: DiSTINAiICN WRKSTATIDN 3 4 5
:
0.0 5.1 3.2
5.1 0.0 2.2
3.2 2.2 0.0
2.1 5.0 2.6
5.5 3.3 3.0
4 5
2.1 5.5
2.6 3.0
5.0 3.3
0.0 3.0
3.0 0.0
1
PRESS ANY
KEY
2.AI.I. .AK
TO CONTINUE?
THIS SCREEN DISPLAYS THE STEADY STATE PROBABILITY OF THE N[IHBER OF VEHICLES USING OR WAITING TO "SF, EACH CONTROL ZONE. ZN
 NUKBER OF VEHICLES 0 .lSYST;N ST:,, 4 5 6 7 a 9 ______________________________________________ 0.96 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.97 0.03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.30 0.00 0.00 0.00 0.00 0.94 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3.00 0.96 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.98 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.98 0.02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.94 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.96 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.00
CTRL
Trial and error with the system quickly determined that the minimum fleet size needed to complete the materials handling workload is also five vehicles. Despite the intuitive appeal of the guidepath revision, the outputs shown in Figure 6 suggest that this modification
: 3 4 2 7
10

DO YOU WANT TO VI?%' THE TaX"EL TIHES THROUGX EACH CONTRCL INCLUDING AND EXCLUDING VEHIC:E SLOWING (ENTER Y DR. ?I)?
ZONE
THE
TRAVEL TIMES TXROUGH EACH C3NiROL ZONE (IN SECCNDS, WICB INCLUDE AND EXCLUDE VEHICLE aLCCKiNG TIME ARE SUMNIMIZED SELZW FOR EACH CONTROL ZONE. CONTROL
ZONE
T?AvEL PIXE YITXO"T VESICLE BLDCKING _
1 2 3
lC5.0 65.0 45.0 150.0 130.0 65.0 45.0 45.0 65.0 105.0
z 6 7
I
a 9 10
PRESS
ANY
TRAVEL TIME WITX '.%HICLE BLOCKING ______107.3 66.0 45.: 154.8 130.2 66.3 45.5 45.5 67.2 107.4
KEY TO CONTINUE?
THIS SCREEN DISPLAYS THE STEADY STATE PROBABILITY VECTORS DESCRIBING THE MJHBER OF UNIT LOADS IN THE INPUT QUEUES. THE DATA CAN BE USED TO DETECT POTENTIAL SHOP LOCKING P.SOBLEMS STATION
SYSTEM 12
0
STATE
 NUHBER 3 4
OF UNIT
5
6
LOADS 7
1 :
0.00 0.00
0.14 0.38 0.50
0.19 0.32 0.33
0.18 0.17 0.12
3.14 0.11 0.08 0.07 0.01 0.04 0.03 0.00 0.01
0.06 0.00 0.01
:
0.00
0.34 0.27
0.32 0.29
3.18 0.20
0.39 0.11
0.01 0.02
PRESS
ANY
0.04 0.06
0.02 0.03
IN THE QUEUE 8 9 0.05 0.04 0.00 0.00 0.00 0.00 0.01 0.01 0.00 3.00
KEY T3 PROCEED?
THIS SCREEN DISPLAYS THE STXADV STAT E PROBABIL;TY "ECXRS DESCRIBING THE NUMBER OF UNIT LOADS IN THE OUTPUT QUEUEJ. THE DATA CXN BE USED T3 DETECT POTENTIAL SXOP LOCKiN‘ PRCSLEMS STATION
1 2 3 4 5 PRESS
Figure 5.
Revision to system guidepath for the sample problem
SYSTEX STATS  NUHSEX OF "NIT LOADS IN TBE C'jEx 0 12 3 7 a 9 _______________________________________________ 0.00 0.41 0.25 0.15 0.09 0.05 0.03 0.02 0.01 O.CO 0.00 0.02 0.04 0.06 0.09 0.12 0.15 0.18 o.la C.15 0.00 0.17 0.16 0.15 0.14 0.12 0.10 0.08 0.06 0.03 0.00 0.07 0.09 0.11 0.12 0.14 0.14 0.14 0.12 o.oa 0.00 0.07 0.09 0.11 0.12 0.19 0.16 0.10 0.09 O.Oa
ANY
Figure 6.
Appl.
4
KEY
5
5
TO PRDCEE3?
System outputs following
Math.
Modelling,
1992,
guidepath
Vol.
modification
16, April
179
DSS for AGV system design: C. J. Malmborg
does not tion. This additional ifications 5 min.
add to the effectiveness of the current soluquestion could be investigated further through routing modifications. In total, the two modto the initial design required approximately
reviewers for their insightful comments, been incorporated. References 1
Summary
and conclusions
2
A prototype DSS that makes detailed analytical modelling accessible to AGVS designers has been presented. Although the prototype system uses a relatively crude interface, it provides a means by which designers can specify the approximate levels of basic AGVS design variables before creating the detailed simulation models needed to validate a design. The DSS makes it possible for designers to modify designs without difficulty and obtain instantaneous feedback. This provides a basis for performing intelligent enumeration of the design solution space in the preliminary phases of the design process. The use of an analytical modelbased DSS as opposed to an optimization model also allows the decision maker to implicitly incorporate detailed, context specific knowledge about a facility while developing a system design. The net effect of these capabilities is to enhance the designer’s effectiveness in using simulation models later in the design process to develop and validate design specifications. Acknowledgment This work was supported in part from a grant from the New York State Center for Advanced Technology in Automation and Robotics. The author is grateful to the
180
Appl. Math. Modelling,
1992, Vol. 16, April
which have
3 4
5
Egbelu, P. J. The use of nonsimulation approaches in estimating vehicle requirements in an automatic guided vehicle based transport system. Mat. Flow 1987, 4, 1732 Blair, E. L., Charnsethikul, P., and Vasques, A. Optimal routing of driverless vehicles in a flexible material handling system. Mat. Flow 1987, 4, 7383 Gaskins, R. J., Tanchoco, J. M. A. Flow path design for automated guided vehicle systems. Int. J. Prod. Res. 1987, 25, 667676 Usher, J. S., Evans, G. W., and Wilhelm, M. R. AGV flow path design and load transfer point location. Proceedings of the International Industrial Engineering Conference, Orlando, FL, 1988, pp 174179 Egbelu, P. J. and Tanchoco, J. M. A. Potentials for bidirectional guidepath for automated guided vehicle based systems. Int. J. Prod. Res. 1986, 24, 10751097
6 7 8
Tanchoco, J. M. A., Egbelu, P. J., and Taghaboni, F. Determination of the total number of vehicles in an AGV based material transport system. Mat. Flow, 1987, 4, 3352 Wilhelm, M. R. and Evans, G. W. The stateoftheart in AGV systems analysis and planning. Proceedings of the AGVS ‘87, Pittsburgh, PA, Oct. 1987 Ozden, M. A simulation study of multiple load carrying automatic guided vehicles in a flexible manufacturing system. Int. J. Prod. Res. 1988, 26, 13531366
Malmborg, C. J. Simulation based evaluation of the control zone model for AGVS design. Proceedings of the International Industrial Engineering Conference, San Francisco, CA, May 1990 Malmborg, C. J. A model for the design of zone control automated guided vehicle systems. Int. J. Prod. Res. 1990, 28, 17411758 Malmborg, C. J. Tightened analytical bounds on the impact of vehicle dispatching in automated guided vehicle systems. Appl. Math. ModeDing, 1991, 1.5,305311