A decision support system for automated guided vehicle system design

A decision support system for automated guided vehicle system design

A decision support system for automated guided vehicle system design Charles J. Malmhorg Department Institute, of Decision Sciences Troy, NY, and E...

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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,s-x 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 12180-3590, 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 Butterworth-Heinemann

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 workin-process storage queues at the individual workcenters; the sequences of control zones followed by vehicles in transporting unit loads between workcenter pairs; and the real-time 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 vehicle-initiated dispatching for i, j = 1, . . . , W the number of empty trips per unit time between workcenters i and j resulting from workcenter-initiated dispatching for i, j = 1, .,w

. the. probability that workcenter j initiates a request for a vehicle forj = 1, . . . , W

Appl. Math. Modelling,

1992, Vol. 16, April

171

DSS for AGV system

design:

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 workcenter-initiated 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 vehicle-initiated case we use the formulations

where

f/j(x)

=

(5) In the vehicle-initiated 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 workcenter-initiated 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 workcenter-initiated 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 vehicle-dispatching 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)

**.

PW-2)

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 shop-locking risk factors associated with guidepath gridlock are obtainable from the steady-state 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 steady-state 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 steady-state 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)

*.*

:

:

:

:

:

::: ,..

zj-1

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,

Vol.

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. Shop-locking risks associated with inadequate output storage capacity at workcenterj are measured by using the analogous steady-state 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 steady-state 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)

PG-2)

_ 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; i-1 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 shop-locking 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 shop-locking 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 workstation-based version of the system.) For small to moderate-sized 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 work-inprocess 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 shop-locking 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 1-6 provide the designer with a method for instantaneously changing the hundreds of parameter values necessary to specify a basic AGVS design profile for moderate-sized 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 C-NT

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. N-ST ‘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. C-GE 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

2-6

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. Steady-state 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 shop-locking 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 1-3 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 b-NIT 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

4-9-6 4-9-6-3-2 l-3-6-9 l-3-6-8-7 6-8-5 3-l-4 3-2-5-7 2-l-4 5-7 4-l-2-5-7

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

l-3 l-2 4 4-9-8-7 3-2 6-9 6-8-7 5-8-9 5-7 9-8-7

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 LAG-3 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 11-Y 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.5TSt-f

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

4-9-6 11-1-2 11-10 4-9-8-7 3-2 6-9 6-8-J 2-l-10 5-J 9-8-7

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 model-based 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, 17-32 Blair, E. L., Charnsethikul, P., and Vasques, A. Optimal routing of driverless vehicles in a flexible material handling system. Mat. Flow 1987, 4, 73-83 Gaskins, R. J., Tanchoco, J. M. A. Flow path design for automated guided vehicle systems. Int. J. Prod. Res. 1987, 25, 667-676 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 174-179 Egbelu, P. J. and Tanchoco, J. M. A. Potentials for bi-directional guidepath for automated guided vehicle based systems. Int. J. Prod. Res. 1986, 24, 1075-1097

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, 33-52 Wilhelm, M. R. and Evans, G. W. The state-of-the-art 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, 1353-1366

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, 1741-1758 Malmborg, C. J. Tightened analytical bounds on the impact of vehicle dispatching in automated guided vehicle systems. Appl. Math. ModeDing, 1991, 1.5,305-311