A decision support system for automated guided vehicle system design

A decision support system for automated guided vehicle system design

Charles J. Malmhorg

Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY, 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 guided vehicle systems

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 De- tailed 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 ex- ploring 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 reprint requests to Dr. Malmborg at the Department of Decision Sciences and Engineering Systems, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USA.

Received 2 January 1991; revised 6 September 1991; accepted 10 October 1991

170 Appl. Math. Modelling, 1992, Vol. 16, April

alytical 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 se- lectively 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

required for vehicle recirculation and the distribution of service response times expe- rienced 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 the average time lost by ve- levels: hicles travelling through

each control zone due to blocking, i.e., waiting for other vehicles to clear the zone before entering;

Empty vehicle travel: the volume of empty travel (in vehicle trips per unit time) resulting from the recirculation of empty vehicles associated with vehicle dispatching;

Vehicle minutes the total number of vehicle required: minutes required per unit

time (including blocking) to meet the materials handling transactions demand imposed in a facility; and

Shop locking the probabilities influencing probabilities: system shutdowns due to

inadequate workcenter storage or guidepath grid- locking.

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:

W 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

e,j the number of empty trips per unit time between workcenters i and j resulting from vehicle-initiated dispatching for i, j = 1, . . . , W

’ eij the number of empty trips per unit time between workcenters i and j resulting from workcenter-initiated dispatching for i, j = 1,

pi’ . . .,w

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

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 con- dition 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: the location and size of individual (linear) control segments over which a wire or strip guidance medium is provided for vehicles; vehicle movement is re- stricted to theguidepath;

Fleet size: the number of vehicles used on the guidepath to service the materials handling workload between the workcenters of a facility;

Load transfer the locations (on the guidepath) point locations: 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;

Workcenter storage the capacity (in unit loads) of capacity: the input and output work-

in-process storage queues at the individual workcenters;

Vehicle routings: the sequences of control zones followed by vehicles in transporting unit loads between workcenter pairs; and

Vehicle dispatching the real-time control strategy rules: used for recirculation of

empty vehicles. As described in a recent paper,” vehicle dispatching rules have a fun- damental impact on system performance by influencing the volume of empty travel

Appl. Math. Modelling, 1992, Vol. 16, April 171

DSS for AGV system design: C. J. Malmborg

Pi the probability that a vehicle responding to a transaction request is located at workcenter i fori = 1,. . . , W

Assuming symmetric travel routings between workcenters, we can estimate flow volumes for empty travel based on a given dispatching rule. For the vehicle- initiated 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:

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

pi = $J rn,/g 5 rnij i= l,...,W (2) i= 1 i= Ij=,

pj’ = 5 rn,ig $Zj mu j= l,...,W (3) j=l 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) 1 ifjis the minimum (maximum) distance

workcenter from i in combination k

[o otherwise

(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 vehicle- initiated case. In the workcenter-initiated case the logic

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, /g mph) (@ 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] [p -P+D))

x (j, /g mph) (‘1

where

f&)

r

1 if i is the minimum (maximum) distance = workcenter toj in combination k

0 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} 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


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 = 5 5 yep& 5 5 yign; izlj=1 p=l i=]j=l )

x (6OeNli, tb) (10)

where

Yijh = 1 ifkEZ,

0 otherwise (11)

DSS for AGV system design: 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:

0 b(0) ~(1) p(2) . . . p(N - 1) ~0’)

1 ~(0) ~(1) ~(2) . . . p(N - 1) ~0’)

2 0 Pm P(l) **. PW-2) p(N- 1)

N- 1

N

. . . . . . . . .

. 0 0 0 000 PUN P(l)

LO 0 0 000 0 P(O)

0 1 2 .** N- 1 N

(12)

Assuming arrivals to zone k follow a Poisson distribution, transition probabilities p(x) for x = 0, 1, . . . , N are of the form

vMR=~&&vk (15)

P(X) = (l/x!) [(N - i)/N)TktklX eXp

I-(W - 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

wk = fk + 5 [(j - 0.5)tkpkjl (14) j=l

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.

(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

Insight into shop-locking risk factors associated with guidepath gridlock are obtainable from the steady-state probability distribution described above. To study shop- locking 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. De- noting 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

subsequent state (k)

0 1 2 3 ..* Ij - 1 rj 0 P(O) P(l) Pt2) Pt3) ’ . * pCzj - I) PtzZjl 1 P(O) P(l) PC2) PC31 ” . p(l; - l) PCrZj) 2 O P(O) P(l) PC21 ’ ” p(Zj - 2, p(?Zj - 1)

current 3 0 0 P(O) P(l) *.* p(Zj - 3) p(?Zj - 2) state(i) : : : : : : : : : , . .

zj-1 0 0 0 0 ::: P(l) P(Z2)

Zj 0 0 0 0 P(O) P(rl)

(16)



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.,

p(x) = (I/x!) ( 5 p=I

m,kl7j)“ev (- 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 > . . ’ , ,’

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

subsequent state (k)

0 1 2 3 ... 0, - 1 Oj 0 P(O) P(l) P(2) P(3) ’ ’ ’ P(Oj - 1) PC20j) 1 P(O) P(l) P(2) P(3) * ’ * P(Oj - l) PCrOj) 2 O P(O) P(l) Pt2) ‘.’ P(Oj - 2) P(?Oj - 1)

current 3 0 0 P(O) p(1) .** p(Oj - 3) p(?Oj - 2)

state(i) : : : : : ; ; ; ;

Oj- 1 0 0 0 0 “. P(l) PG-2)

Oj 0 0 0 0 **’ P(O) P(~l) _

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

p(i - k + 1) = l/(i - k + l)! [ 7Tj/j, mjp]iiph+“eXp (

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

h’=ggm; (20) i-1 j=*

[

ww -I p’=N xx 2 tk i= Ij= 1 kEZ, (

rn,$is $rnLk p=l k=l )I

(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

(18)

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):

W

- lTjl x mj, I (19) p=l /

CT2 = 2 5 [ c th - (pflN)-1]1

;=,j=, kEZ,,

x ( rn;lE grnAk (23) p=lk=l

The average vehicle travel time for a requested vehicle to reach workcenter j is estimated by the model as

w rw 1

Rj = x L,z m:k/c z dp] x 1~

k=l I=lp=l rEZA,

(24)

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

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



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 sup- pliers 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 experi- mentation, 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. How- ever, 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 imple- mented on IBM PS2 level hardware. (Subsequent ex- perimentation 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: The user can change the number of vehicles, vehicle speed, load transfer time, system efficiency factor, and dispatching rule combination.

Option 3: The user can modify, add, delete, or display vehicle routings to relieve conjestion areas discov- ered in the system through examination of the state probabilities associated with individual control zones.

Option 4: 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.

Option 5: 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.

Option 6: The user can adjust the work-in- process 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 graph- ical 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



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. ADJUST AG" FLEET SIZE/HARDWARE PAPJMETERS 2. CHANGE THE VEHICLE DISPATCHING RULE 3. CHANGE THE VE"ICLE ROUTINGS 4. CHANGE THE SYSTEM GUIDEPATH LAYOUT 5. CHANGE THE NATEXAL FLOW MATRIX 6. CHANGE INPUT/OUTPUT QUEUE CAPACITIES/DELTA VALUES 7. COMPUTE PERFORMANCE MEASURES FOR THE CtiRRENT DESIGN 8. ANALYZE OUTPUTS FROM THE CONTROL ZONE NOOEL 9. TERMINATE THE SESSION

ENTER THE N"MBiR OF THE OPTION YOU WISH TO SELECT?

A S"MMARY OF THE FLEE? SIZE AND K4P.DWAF.X PARRMETERS IN TYE CURRENT DESIGN PROFILE IS GIVEN BEXW:

THE CURRENT FLEET SIZE IS 8 AGV's THE CURRENT VEHICLE SPEED IS 1 FEET PER SECOND THE CURRENT LOAD TRANSFER TIME IS 10 SECONDS THE CURRENT EFFICI’CNCY FACTOR IS 0.75

ENTER THE NDXBER OF THE OPTION SELLCTED FROM THOSE SUMMRRIZED BELOW

1. CHANGE THE FLEET SIZE 2. CHANGE THE VEHICLE SPEED 3. CHANGE THE LOAD TRANSFER TIME 4. CHANGE THE EFFICIENCY FACTOR 5. RETDRN TO THE MAIN MEN"

ENTER THE OPTION 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 DISPATCHING RULE COMBINATION IS:

RANDOM VEHICLE/RANDOM WORKSTATION

TO CHANGE THE "EHICLE DISPATCXING RULE, SELECT AMONG THE 0P:ICNS SUNKAHIZED IN THE LIST BEXW:

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;?..

SOURCE DESTINATION WORKSTATION 12 3 4 5

_----__-_--________-__~~~-~-~~---

1 0 10 2 2

2 3 3 0 2 : 4 0 0 : 4 0 4 3 0 5 2 0 14

1. SNTER AN ENTIRELY NEW .YATRIX 2. C.HANGE A SINGLE CELL IN THE MATRIX 3. RETURN TO THE MAIN MEN"

SELECT ONE OF TEE T.HREE CPTIONS MZVE ?

Figure 1. (continued)

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..&VDOM VEHICLE/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 OE ONE OF THE ABOVE OPTIONS ?

1. DISPLAY ALL VEHICLE ROUTINGS IN THE C3P.JJNT JESIGN 2. DISPLAY A PARTiCULU ROUTING IN THE CCRXSNT DES:IW 3. C.XANGE AN EXISTING RO"T:NG IN THE C"FZ.ENT DEJ::N 4. ADD A NZW ROUTING TO TBE EXISTING DESIGN S. DEL&Z AN EXISTING ROL'TING IN THE CURI1ENT JESZGN 6. RETURN TO THE VAIN MENU

ENTER THE N"MBER OF ONE OF THE ABOVE OPTIONS ?

THE OPTIONS AVAILABLE FOR C:HANGING AND VIEWING THE S'fSTEX GUIDEPATH ARE SUMHARIZED BELOW:

1. DRAW THE CURRENT SYSTEM GUIDEPATH 2. EXAMINE THE CWCTERICTICS OF A CONTROL ZONE 3. DISPLAY THE ENDPOINTS AND ZONES OF THE LINEAR SEGXiNTS 4. ADD A CONTROL ZONE TO THE SYSTEM GUIDEPATH 5. CHANGE A CONTROL ZONE IN THE SYSTEM GUIDEPATH 6. ADD A LINEAR SEGMENT TO THE SYSTEM GUIDEPATH 7. CHANGE A LINEAR SEGKENT IN THE SYSTEM GVIDEPATB 8. RET"P.N TO THE MAIN MENU

ENTER THE NLMBER OF YOUR SELECTED OPTION ?

3.. CHANGE WORKSTATION DELTA VALUES 2. CHANGE WORKSTATION MXIMVM WIP INPUT QUEUE CAPACITIES 3. C-GE WORKSTATION tQ_XIMJM WIP OUTPUT QUEUE CAPACCITIES 4. RETURN TO THE MAIN MEN”

SELECT ONE OF THE ABOVE THREE OPTIONS?

Figure 1. Main menu and DSS options 2-6 for a sample problem

I I I /

Figure 2. Guidepath sketch for the sample problem

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: 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.

Module 2: The travel times with and without vehicle blocking are provided to give the


user some insights for revising vehicle fleet size, routings, the guidepath layout, control zones, etc., in order to eliminate excessive guidepath contention.

Module 3: 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.

Module 4: 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.

Module 5: 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.

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. Find- ing the minimum number of vehicles for a given design is a quick and simple process of trial and error using

BASX ON THE CURRENT FLEET SIZE Of 3 ‘JEHICLPS AND A VEHICLE AVAILABILITY EFF?CIENCV FACTOR OF 0.75

AFTER ACCOU?JTING FOR GUIDEPATH CONTENTION

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

THE VEHICLE MINUTE5 AVAILABLE EACli HOUR TOTALS: 360 THIS CObPARES WITH VEHICLE MINUTES REQUIRED OF:

STATION SYSTEH STATE - NUMBER Of WIT LO.%05 IN THE QUEUE 335.714 0 1 * 3 4 5 6, a 9

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?

THIS SCREEN DISILAYS TUVEL P:XES WITHOUT SLOCKING (IN MINUTES, EOR TEE ROUTING5 BE:WEEN EACI( WORKSTATION PAIR. TiiE SOURCE WOWSTATiON IS LISTED ALONG THE LEfT COLUMN XVD THE. DESTINATiON STATiON i5 LISXD ACROSS THE TOP ROW: SOURCE DESTINATION 'WORKSTATION

1 2 3 4 5

0.0 5.0 6.a 5.0 5.4 5.0 0.0 4.3 5.3 5.1 6.8 4.3 0.5 i.7 3.3 5.0 5.3 5.7 0.0 8.6 5.4 5.1 3.3 8.6 0.0


TIlE CORRESPONDING TIKES WITH aLOCKiNG AXE: 5OUiKE DE5T:NXTISN WORKSTATION

? 2 3 4 5 _------_---_-_--__-___---___---_--__--_-__-

: 0.0 5.3 5.3 0.0 7.1 4.5 5.1 5.7 5.6 5.2 3 7.1 4.5 0.0 6.0 3.4 : 5.1 5.7 6.0 0.0 9.0

5.6 5.2 3.4 9.0 0.0

PRESS ANY KEY TO CONTINUE?

THIS SCREEN DISPIAAYS TBE STEMY STATE PROBABILITY 3f THE NUMBER OF VEHICLES USING OR WAITING TO US; EACH CONTROL ZONE.

CTRL ZN 1 SYSq, STAjTE

- WW5E4 Of VEHICLES 0 4 5 6 7 8 9

: 0.91 0.08 0.01 0.00 0.30 3.00 0.00 0.00 0.95 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 0.9, 0.03 0.00 0.00 0.30 0.30 0.00 0.00 0.30 0.00 4 o.a4 0.15 0.01 0.00 0.30 0.30 0.00 0.00 0.00 0.00 5 0.92 0.08 0.00 0.00 3.00 3.30 0.00 0.00 0.00 0.00 6 0.95 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.30

: 0.9, 0.97 0.03 0.03 0.00 0.00 0.00 0.30 3.00 0.oc 0.00 c.30 0.30 0.30 0.00 0.00 0.00 0.30 0.00 0.00 9 0.98 0.02 0.00 0.30 0.30 0.33 0.90 0.00 0.00 0.00

DO YOU WANT TO VI574 THE TV.‘wTL TIES TSROUGH EACH CONTROL 23NE INCLUDING AN0 EXCLUDiNG ERfC:E 3LOCKiX (ESTER Y OR N)?

TfZ T?A"EL TIbflS T'HROUGH MC:i CtXZZL 13NE ti?l 5ZCONDSl u%:C:+ INCLUDE AND EXCLJDE VEHICLS BLOCXING TIME ARE SWPARIZED SLLOW FOR EACH CONTROL ZONE.

CONTROL ZONE TSAVEL TI.UE YIY.OUT TW.“EL T:NE WITIi 'iEtiICLE BLOCKI)I‘ 'VEERICLE BLOCXING

_----_--_--_ ________________ __-_--_____---__

: 150.0 130.0 6 65.0 7 45.0

: 45.0 65.0 10 105.0


i64.5 135.6 66.7 45.8

45.6 66.0 105.0

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 1.0 0.0 2.0 2.0 2 3.0 0.0 2.0 3.0 1.3 3 4.0 0.0 0.0 2.0 0.0 4 0.0 4.0 3.0 0.0 1.0 5 2.0 0.0 1.0 4.0 0.0

THE BLOW VOLXES INCLLJDING LHPTY VEHICLE TRAVEL ARE SHOWN BELOW: SOURCE OESTINATION WOMSTATION

1 2 3 4 5

: 4.9 1.0 1.6 1.1 0.7 3.3 3.0 4 9 2.5 1.9 3 5.2 0.7 0.9 3.3 0.6 4 1.6 4.1 4.2 1.7 ?.a 5 3.4 0.9 2.0 5.5 0.7

PRESS ANY KEY TO PROCEZD?

-----________________________--_-_--_-----_---___--_--- 1 0.00 0.14 0.19 0.18 0.14 o.:i 0.0a 0.06 0.35 0.04 2 0.00 0.38 0.33 0.17 0.07 0.03 0.01 0.01 0.00 0.00 3 0.00 0.50 0.32 0.12 0.04 0.01 0.00 0.00 0.00 0.00 4 0.00 0.27 0.29 0.20 0.11 0.06 0.03 0.02 0.01 0.01 5 0.00 0.34 0.32 o.la 0.09 0.04 0.02 0.01 5.00 0.00

PRESS ANY KEY TO PROCEED?

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 SYSTEM STATE - NUMBER Of ONIT LOADS IN THE Q”L”E 0 1 * 3 4 5 6, a 9

0.00 0.01 0.03 0.05 0.10 0.11 0.13 0.20 0.20 0.1, 0.00 0.00 0.00 0.01 0.02 0.05 0.09 O.i, 0.28 0.38 0.00 0.00 0.01 0.02 0.05 0.08 0.12 0.19 0.26 0.26 0.00 0.00 0.00 0.01 0.02 0.05 0.11 0.19 0.29 0.34 0.00 0.00 0.00 0.01 0.03 0.05 0.12 0.20 0.28 0.31

ANY KEY TO PROCEED?

Figure 3. System outputs for the sample problem Figure 3. (continued)



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:

From workcenter To workcenter

2 3 3 4

2 3 4 5 3 4 5 4 5 5

Control zone sequence

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 To workcenter Control zone sequence

1 2 l-3 1 3 l-2 1 4 4 1 5 4-9-8-7 2 3 3-2 2 4 6-9 2 5 6-8-7 3 4 5-8-9 3 5 5-7 4 5 9-8-7

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 pres- sure 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.

BASED ON THE CURRENT FLEET SIZE OC 5 VEHICLES AlJO A MHICLE AVAILABILITY EFFICIENCY FACTOR OF 0.75

AFTER ACCOUWTING FOR GUIDZPATH CONTZNTION

THE VEHICLE MINUTES AVAILABLE EACH HOUR TOTALS: 225 THIS COMPARES WITH VEHICLE MINUTES REQ"P.ED OF: laa.6503

AS THE RESULTS OF THE MODEL SHOW, THE CURRENT FLEET SIZE IS ADEQUATE TO MEET THE ?.EQUIRE5 XATER:AL HANDLING WORKLOAD.

PRESS ANY KXY TO PROCEED?

THIi 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: SOURCE DISTINA"ION 10XXSTATION

1 2 3 4 5 __________________________--___-__--_-_____

1 0.0 *.a 3.2 2.9 5.4 2 2.8 0.0 2.2 2.5 2.9 3 3.2 2.2 0.0 4.3 3.3 4 2.8 2.5 4.3 0.0 2.9 5 5.4 2.9 3.3 2.9 0.0

THE COP.P.ES?ONDING TI?ES WITY SLOCRING MS: SOCTRCE DESTINATION SlOaK3TATiON

1 2 3 4 5

1 0.0 2.9 3.2 2.9 5.6

: 2.9 3.2 c.0 2.2 2.2 0.0 2.6 4.5 3.0 3.3 : 2.9 5.6 2.6 3.0 4.5 3.3 0.0 3.0 0.0 3.0


THIS SCREEN DISDLAAYS TSE STEAilV STATE PROSABILITY :E THE NUHBER OF VEHICLES USING OR WAITIYG TO USE LAG-3 C:NTROL ZCNE

CTRL ZN SYSTEH STATE - YLXSER $F VEiiICLiS

0 12 3 4 5 6 7 3 9

0.91 0.08 0.95 0.05 0.97 0.03 0.94 0.06 0.95 0.05 0.97 0.03 0.97 0.03 0.9S 0.04 0.90 1.09

0.01 0.10 0.00 0.00 0.00 0.00 0 0.00 0.00 0.00 0.00 0.00 0.00 0 0.00 0.00 0.00 0.50 0.00 0.00 0 0.00 0.00 0.00 0.00 0.00 0 co 0 0.00 0.00 0.00 0.00 3.30 0.00 3 0.00 o.cc 0.00 0.30 0.00 0.00 0 0.00 0.00 0.00 0.00 3.20 0.00 9 0.00 0.00 3.00 3.:0 0.00 0.00 0 0.00 0.00 0.50 0.00 0.00 0.00 3

___. .oo 30

:30 .OO .CO .OO .:o .:c .oo

FOR EACH CGNTROL ZONE

CONTROL ZONF. T?AvzL TIME WITHCUT ??AvEL TIXE 11-Y

VEXICLS ILOCXI'IG b?HICLE SLsCxIx

45.0 45.0 65.0

105.0

.___ -- _----- IO,. 1

63.5 45.4

L55.6 134.0 66.1 45.7 46.: 68.4

105.0


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 SYSTEM STATE - NU"SER OF UNIT LORDS IN THE QUEUE 0 12 3 4 5 6 7 a 9

________________________--_-_________-_________________

: 0.00 0.00 0.14 0.38 0.19 0.33 0.1s 0.17 0.14 0.07 c.11 0.03 0.08 0.01 0.06 0.01 0.05 0.00 0.04 0.00 3 0.00 0.50 0.32 0.12 0.04 0.01 0.00 0.00 0.00 0.00 : 0.00 0.00 0.27 0.34 0.29 0.32 0.20 O.la 0.11 0.09 0.06 0.04 0.03 0.02 0.02 0.01 0.01 0.00 0.00 0.01


THIS SCREEN DISPLAYS THE STEADY STATE ?ROBRsILITY VECTORS DESCRIBING THE NUMBER OF UNIT LO&.05 IN TX OUTPUT Q”E”ES. THE DATA CAN BE USED TO DETECT POTENTIAL SHOP LOCKING PROSLIMS

STATION SY.5TSt-f STATE - NUMBER OF UNLT LOADS IN THE OCEUE O : 2 3 4 5 6 7 a 9

________________________________--_________ -_----_--___ : 0.00 0.00 0.75 0.22 0.19 0.19 0.05 0.16 0.0, 0.13 0.01 0.10 0.00 0.08 0.06 0.00 0.00 0.04 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 0.00 0.35 0.31 0.23 0.22 0.16 0.16 0.10 0.11 0.07 0.08 0.04 0.05 0.03 0.03 0.01 0.02 0.01 0.01

PRESS ANY KEY TO PROCLED?

Figure 4. System outputs following modification of routings



BASED ON THE CVRRENT FEET SIZE OF 5 “EHICXS AND A VEHICLE AVAILABILITY EFFICIENCY FACTOR OF 0.75

AFTER ACCOUNTING FOR GUIDEPATH CONTENTION

THE "EHICLE MINUTES AVAILABLE EACH HOUR TOTALS: 225 THIS COMPARES WIT" VERICLZ MINUTES WCEC"IP.ED OF: 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.


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 To workcenter Control zone sequence

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

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

-

I Figure 5. Revision to system guidepath for the sample problem

THIS SCREEN DISPLAYS TRAVEL TIFFS WITYDUT BLOCKiNG (IN MINUTES) FOR THE ROUTiNGS BETWEEN EACH WORKSTATION 2.AI.I.

THE SOURCE WORKSTATION IS LISTED ALONG THE LEFT CCLIXN .AK

THE DESTINATION STATION IS LISTED ACROSS THE TOP ROY:

SOURCE DESTINATION WCRKSTATION 1 * 3 4 5

1 0.0 5.0 3.2 2.1 5.:

: 5.0 3.2 0.0 2.2 2.2 0.0 2.5 4.9 2.9 3.3 4 2.1 2.5 4.9 0.0 2.9 5 5.4 2.9 3.3 2.9 0.0

TYZ CORRESPONDING TIbfES WITH BLOCKING ARE: SCURCE DiSTINAiICN WRKSTATIDN

12 3 4 5

1 0.0 5.1 3.2 2.1 5.5 : 5.1 3.2 0.0 2.2 2.2 0.0 5.0 2.6 3.3 3.0

4 2.1 2.6 5.0 0.0 3.0 5 5.5 3.0 3.3 3.0 0.0


THIS SCREEN DISPLAYS THE STEADY STATE PROBABILITY OF THE N[IHBER OF VEHICLES USING OR WAITING TO "SF, EACH CONTROL ZONE.

CTRL ZN SYST;N ST:,,

- NUKBER OF VEHICLES 0 .l 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

3 1.00 0.00 0.00 0.00 0.00 0.30 0.00 0.00 0.00 0.00 4 0.94 0.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 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

7 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

10 0.96 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.33 0.00

DO YOU WANT TO VI?%' THE TaX"EL TIHES THROUGX EACH CONTRCL ZONE INCLUDING AND EXCLUDING VEHIC:E SLOWING (ENTER Y DR. ?I)?

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 TRAVEL TIME WITX VESICLE BLDCKING '.%HICLE BLOCKING

------------ ----------_----- _------__-_-_-_-

1 lC5.0 107.3 2 65.0 66.0 3 45.0 45.:

z 150.0 154.8 130.0 130.2

6 65.0 66.3 7 45.0 45.5 a 45.0 45.5 9 65.0 67.2

10 105.0 107.4


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 STATE - NUHBER OF UNIT LOADS IN THE QUEUE 0 12 3 4 5 6 7 8 9

1 0.00 0.14 0.19 0.18 3.14 0.11 0.08 0.06 0.05 0.04 : 0.00 0.00 0.38 0.50 0.32 0.33 0.17 0.12 0.07 0.04 0.01 0.03 0.00 0.01 0.00 0.01 0.00 0.00

0.00 0.00 : 0.00 0.00 0.27 0.34 0.29 0.32 0.20 3.18 0.11 0.39 0.06 0.04 0.03 0.02 0.01 0.02 0.01 0.01

0.00 3.00

PRESS ANY 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 0

SYSTEX STATS - NUHSEX OF "NIT LOADS IN TBE C'jEx 12 3 4 5 5 7 a 9

--_____--_____-_________________________-__________--__

1 0.00 0.41 0.25 0.15 0.09 0.05 0.03 0.02 0.01 O.CO 2 0.00 0.02 0.04 0.06 0.09 0.12 0.15 0.18 o.la C.15 3 0.00 0.17 0.16 0.15 0.14 0.12 0.10 0.08 0.06 0.03 4 0.00 0.07 0.09 0.11 0.12 0.14 0.14 0.14 0.12 o.oa 5 0.00 0.07 0.09 0.11 0.12 0.19 0.16 0.10 0.09 O.Oa

PRESS ANY KEY TO PRDCEE3?

Figure 6. System outputs following guidepath modification



does not add to the effectiveness of the current solution. This question could be investigated further through additional routing modifications. In total, the two modifications to the initial design required approximately 5 min.

Summary and conclusions

A prototype DSS that makes detailed analytical modelling accessible to AGVS designers has been presented. Although the prototype system uses a rela- tively 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

reviewers for their insightful comments, which have been incorporated.

References 1

2

3

4

5

6

7

8

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-direc- tional guidepath for automated guided vehicle based systems. Int. J. Prod. Res. 1986, 24, 1075-1097 Tanchoco, J. M. A., Egbelu, P. J., and Taghaboni, F. Deter- mination 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


Documents

A decision support system for automated guided vehicle system design