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Conveyor Theory: A SurveyEginhard J. Muth

a & John A. White

b

a Department of Industrial and Systems Engineering , University of Florida , Gainesville,

Florida, 32611b School of Industrial and Systems Engineering, Georgia Institute of Technology , Atlanta

Georgia, 30332

Published online: 09 Jul 2007.

To cite this article: Eginhard J. Muth & John A. White (1979) Conveyor Theory: A Survey, A I I E Transactions, 11:4, 270-27DOI: 10.1080/05695557908974471

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Conveyor Theory:

A

Survey

EGINHARD

J

MUTH

Department o f Industrial and Systems Engineering

University of Florida

Gainesville Florida 3261 1

JOHN

A.

WHITE

SENIORMEMBER,AIIE

School of Industrial and Systems Engineering

Georgia Institute of Tech nology

Atlanta Georgia 30332

Abstract This paper surveys the research which has been published in the area of conveyor theory.

Deterministic and probabilistic approaches as well as descriptive and normative approaches to modeling

conveyor systems are discussed. Areas for further study are suggested.

The subject of m aterial handling is one of current interest

in both the public and the private sectors. Whether the

material to be handled is people, mail, solid waste, raw

materials, finished good s, in-process goods, or in forma tion,

some material handling equipment is normally used to

facilitate the material transfer. Conveyor systems are very

universally employed, perhaps more than any other type of

material handling equipment.

The mechanical design problems of conveyor systems

have been well studied by m echan ical and electrical engineers.

However, the operational problems of conveyor systems are

not as well understo od. Th e study of the operational charac-

teristics of conveyor systems has long been a concern of

industrial engineers. In an operational sense, the conveyor is

an element of a larger system, including loading and unload-

ing stations, material supply and demand, operating disci-

plines, and human components as well. Hence, system

to classify conveyors, to give an overview of the literature,.

to discuss several representative research contributions, and

to point ou t areas for further study.

onveyor lassification

There are m any criteria by which one can classify conveyors.

We wish t o classify m odels and m ethods used to describe

and t o analyze the opera tion of conveyor systems. With this

purpose in mind we list some common criteria for classifica-

tion.

1. Conveyor arrangement

a. Feedforward

b. Closed-loop recirculating)

2.

Conveyor use

a. Deliverv

parameters include no t only equipment parameters, but also

b. Storage

such considerations as waiting space allowances and t he

3. Loading and unloading stations

number, spacing, and sequencing of loading and unloading

a. Single

stations.

b. Multiple

This paper is directed at conveyor theory in terms of the

operational setting. I ts purpose

is

to provide a bibliography,

4

Material flow in and ou t of stations

a. Continuous in time

b. Discrete in time.

Received June 1977; revised July 1979. Paper was handled y

Scheduling Planning and Control Departm ent.

c. Deterministic

d. Stochastic

270

0569-5554/79/1200-0270/ 02.00/0

197 9 AIIE

AIIE

TRANSACTIONS

Volume

11

NO.

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5. Placement of material on conveyors

a. Continuous placement

b. Discrete placement, uniformly spaced

c. Discrete placement, randomly spaced

6. Nature of material flows

a. Bulk loads

b. Discrete parts

7. Method of modeling

a. Analytical models

b. Simulation models

c. Deterministic models

d. Queueing models

e. Markovian models

f. Other stochastic models.

Overview o th

iterature

It appears that the earliest published work seeking to

identify a body of knowledge called conveyor theory is

that of Kwo [34]. His appeal for analytical approaches in

the study of conveyors was followed by a surge of publica-

tions in the early 1960's. Among the earliest publications

were those of Kwo [34], [35], Mayer [37], Helgeson [29],

Reis and Schneider [56] Reis, Dunlap, and Schneider [57]

Reis and Hatcher [58], and Morris [39].

It is interesting to note that the authors of the first four

publications (Helgeson, Kwo, and Mayer) were employed as

engineers in industry. Thus, conveyor theory developed

from a concern within industry to develop analytical models

of a real world problem, the design of conveyor systems.

Also, it is worthwhile to observe that Helgeson and Kwo

employed a deterministic modeling approach, whereas Mayer

employed a probabilistic approach.

Since the initial surge of interest in the 1960's, conveyor

theory has attracted a steady following, as indicated by the

following chronological listing of known research efforts:

Disney [15] and Mednis [38] in 1962; Disney [16] Parker

[50], and Schumacher [61] in 1963; Ghare, Ward, and

Perry [20], Howell [32] Perry [51], and Ward [64] in

1965; Gupta [26], Pritsker [54], and Vars [63] in 1966;

Crisp

[12] and Reis, Brennan, and Crisp [59] in 1967;

Beightler and Crisp [4] and Phillips [52] in 1968; Crisp,

Skeith, and Barnes [13] and Phillips and Skeith [53] in

1969; Brady [5] and Burbridge [7] in 1970; Bussey and

Terrell [8] and Heikes [28] in 1971 gee and Cullinane [I]

and Muth [40] in 1972; Brady [6] and Bussey and Terrell

[9] in 1973; Gourley and Terrell [21] [22] and Muth [43]

in 1974; Gregory and Litton [24] [25], Gourley, Terrell,

and Chen [23], Matsui and Fukuta [36] and Muth [44]

[45] in 1975; Chen and Terrell lo]

l

11 Duraiswamy and

Terrell [17], El Sayed, Proctor, and Elayat [18], Hedstrom

[27], White [66] and White and Woodbury [67] in 1976;

El Sayed and Proctor

[19], Muth [47], and Proctor, El

Sayed, and Elayat [55] in 1977.

December 1979, AIIE TRANSACTIONS

The majority of the conveyor research has concentrated

on conveyor systems consisting of equally spaced hooks (or

carriers) passing a number of work stations. Kwo [34] [35]

developed a deterministic model of material flow on a

conveyor having one loading station and one unloading

station, and time-varying patterns of material flow. His

concern was in developing feasibility conditions to insure

that the input and output rates of material were compatible

with the design of the conveyor. Muth [40] [43] provided

a thorough mathematical analysis of the problem studied by

Kwo and considered both continuous-time and discrete-

time material flow. He employed methods of systems

analysis and control theory to develop stability conditions

for the conveyor system. Subsequently, Muth [44] extended

his results to the case of multiple loading and unloading

stations.

Mayer [37] appears to have been the first to model a

conveyor system probabilistically. He considered a closed

loop conveyor having loading stations operating indepen-

dently. His analysis allowed each discretely spaced carrier to

have a capacity to handle multiple items. Morris [39] ex-

tended the probabilistic approach of Mayer to include

multiple loading and multiple unloading stations. conser-

vation of flow approach was employed to develop perfor-

mance measures for the system. White and Woodbury [67]

used a simulation approach to test the validity of Morris'

model. Their results indicate the conservation of flow ap-

proach yields good approximations as long as the probability

of

self-blocking is small. White [66] developed normative

models based on the descriptive models of Mayer [37] and

Morris [39].

number of researchers have studied an individual work

station.

Reis and Schneider [56], Reis, Dunlap, andschneider

[57], and Reis and Hatcher [58] developed probabilistic

models of an individual work station which performs load-

ing andlor unloading operations. It was assumed that

temporary storage areas or banks are available so that in

the event of an unsuccessful loading attempt or unloading

attempt the worker is not unnecessarily delayed. The re-

search focused on determining the effect of various banking

disciplines on the productivity of the work station. Reis,

Brennan, and Crisp [59] modeled the individual work

station as a Markov process. banking discipline referred to

as the Sequential Range Policy was defined by Beightler

and Crisp [4] , who also employed Markov processes in

analyzing the in-process storage requirements of the individ-

ual work station. stationary Bernoulli arrival distribution

was assumed for each work station. In a later study, Crisp,

Skeith, and Barnes [13] employed simulation to test the

assumption that arrivals were Bernoulli distributed. It was

found that such an assumption could not be supported.

Schumacher [61] Ward [ a ] , Perry [50], and Vars [63]

investigated conveyor systems involving variations of the

banking disciplines studied by Reis et al. Ghare, Ward, and

Perry [20] examined the effects of interaction for a number

of loading and unloading stations. Heikes [28] developed

approximations of the interaction effects and employed

them in an economic model of the conveyor system.


4/9

Queueing theory has been employed by a number of

researchers in analyzing conveyor systems. In particular, a

power and free conveyor system having two unloading

stations was studied by Disney [16] . The problem was for-

mulated as a multichannel queueing problem with ordered

entry. Gupta [26] extended the results of Disney's research

to obtain the steady state distribution for material queued

at each of the two w ork stations. Pritsker [54] generalized

Disney's analysis to include m unloading stations with

storage allowed only at the last station. Whereas Disney

assumed an M/M/m queue, Pritsker considered the M/G/m

and DIM lm queueing situations. Additionally, Pritsker con-

sidered the effects of recirculation; this case was studied

using simulation. Gregory and Litton [24] modeled a

queueing system with m dissimilar service channels and

ordered entry, where the interarrival times are random

multiples of a fuced time interval. They showed tha t in order

to minimize the number of units which are lost, the

channels should be ordered by descending service rate, that

is, the fastest server should com e first. R ecirculation of units

is not allowed in their analysis. El Sayed, Procto r, and E layat

[18 ], El Sayed and Proctor [19 ], and Procto r, El Sayed,

and Elayat [55] used queueing models which include bulk

arrivals, dual inputs with different service characteristics,

and heterogeneous servers; they determined the steady-state

probabilities of the system. I t should be observed that all of

the work quoted in this paragraph addresses queueing sys-

tems rather than conveyor systems since there are no

conveyor parameters contained in the analyses. Also, the

assumption is made that items which find all servers busy

are lost to the system. This assumption is highly unrealistic.

Agee and Cullinane

[I ] studied a conveyor system which

connected a single loading point with a single unloading

point. Multiple loading (unloading) stations were allowed at

the loading (unloading) point. A nonstationary Poisson

process was assumed and blocking could occur when the

conve yor was fu ll. A transient analysis was performed using

numerical methods. n economic model was developed to

determine the optimum number of loading and unloading

stations and conveyor length.

Hedstrom [27] appears to be the first t o study the

problem of sequencing heterogeneous loading stations along

a continuous space conveyor. Workers are assumed to be

placing cartons of unequal length on a constant speed,

powered belt conveyor; workers operate independently at

different rates. n approximate analytical model and a

simulation model are developed to assist in the determina-

tion of the optimu m sequence of workers along the belt.

Muth [47] analyzed a closed loop conveyor with one

loading station, one unloading station, and random m aterial

flow. The flow is modeled as signal plus noise and recircula-

tion is taken into account. It is shown that with a suitable

decision rule for unloading the conve yor acts as a smoothing

device, that is, the variance of the output flow is smaller

than the variance of the input flow.

Phillips and S keith [53] performed a simulation analysis

of the m unloading station case involving homogenous and

heterogeneous service stations. Recirculation and storage at

each station are allowed. The simulation model was used to

validate the results obtained by Pritsker. Bussey and Terrell

[8] [9] employed a simulation model to account for the

discrete spacing of carriers on the conveyor, the storage of

units at each station, and the recirculation of units on the

conveyor. Their results indicate the importance of taking

into consideration the amount of spacing between carriers.

Gourley and

Terrell[21 ] [22] developed a modular general-

purpose simulation model to study performance aspects of

constant-speed, discretely loaded, recirculating conveyors.

The simulation model was extended by Gou rley, Terrell, and

Chen [23], Chen and Terrell [lo], and Duraiswamy and

Terrell [17] The mo dular general-purpose simulation model

was extended by Chen and Terrell [ l l ] to include multiple

loop co nveyor systems which service multiple floors.

Conveyors frequently serve as the link that transports

material to production lines. Therefore, a research area

closely related to conveyor th eory is that involving produc-

tion lines. Hillier and Boling [30] [3

1

Anderson and

Moodie [2] , Sadowski and Moodie [60], K nott [33], and

Muth 1411 [4 6], among others, have studied problems

related to the output rates of production lines. Another

productio n problem which relates to th e design of conveyor

systems is the assembly line balancing problem. Over one

hundred papers are available on this subject; Panwalker

[49] provides a recent survey of assembly line balancing

techniques.

Representative Research Contributions and Results

1. Deterministic Models

Kwo [34] [35] develops a deterministic model of material

flow o n a conveyor having one loading station, one unload-

ing station, equally spaced carriers, and periodically time-

varying patterns of m aterial flow. His objective is to deter-

mine conveyor design parameters that

will

assure the

compatibility of different input and output patterns. The

problem development makes use of three intuitively derived

principles. The principle of uniformity leads to some

feasible solutions under very restrictive inpu t outpu t condi-

tions, but it does not lead to a general solution procedure.

Muth 1401 [43] provides a thoroug h math ema tical

analysis of the problem studied by Kwo. He treats con-

veyors for continuous bulk loads [40], and for discretely

spaced loads [43] The material flow along the conveyor is

described by a difference equation whose solution yields

conditions under which stable conveyor operation is possible

for general periodic input and output flow patterns. It is

shown that a critical design parameter is the ratio SIP,

where S

=

T mod

P

T is the conveyor revolution time, and

P s the work-cycle period. In a good design SIP should be

in the range (0.25, 0.75). In the contin uou s load case SIP

should not be a rational number whose deno mina tor is a

small integer. In th e discrete load case

SIP

=r/p , where r =

k

mod p, k is the number of carriers on the conveyor and p =

kP/T

In that case r/p should be a proper fraction and for

AIIE

IRANSACTIONS,

Volume 1

1

No. 4


5/9

greatest operational flexibilityp should be a prime number.

In

[44]

Muth extends the results of

[43]

to th e case of

multiple loading and unloading stations, where each of the

stations can perform either pure loading, or pure unloading,

or alternating loading and unloading operations. Station

inputs

fi n)

units of material to carrier n on the conveyor;

the amou nt of material in carrier

n

after it leaves statio n is

Hi n).

The sequences

Cfi n))

re periodic with pe riod p. For

given values of

k

and p the required carrying capacity of the

carrier is the m aximum value in the sequence

{ H i @ ) )

or all

i and n . A recursive procedure for computing the sequence

of values is given in [44].

2. Stochastic Models

Mayer

[37]

analyzes a conveyor with discretely spaced

carriers which pass by

n

work stations. All carriers arrive

empty at the first work station. The conveyor transports

the unit produced from all work stations to the next stage

of the produ ction process. Each work station produces one

unit of product during one work cycle. The operator who

finishes work on a unit of product will place that unit on

the nearest carrier, or place it on the floor if the carrier is

already filed to capacity. A figure of demerit is

D ,

the

probability that a unit of production will be set aside on

the floor. With the assumption that a loading attempt will

be made with probability p as a carrier passes a sta t~ on ,he

total number of loading attempts per carrier as it passes n

work stations is binomially distributed. As a result Mayer

shows that when the carriers have capacity for one unit of

product, then

where

q

p , and

h l l p

is the expected number of

carriers passing a station during one work cycle. He further

shows that

for carriers with two-unit capacity.

White [661 considers the general case of a carrier with

capacity for

x

units. In that case

Based on this formulation White develops a normative

conveyor model. He notes that

D

is a function of two

equipment design parameters: h and x. D can be decreased

by either increasing th e conveyor speed, or decreasing the

spacing between carriers, or increasing the number of load-

ing positions per carrier. White's model for determining the

optim um value of

x ,

given a value of

h ,

is:

Minimize

TC x ) C1Rn D x ) D2Kx

Subject to

x =

1 . n

where

TC x) total expected cost per shift as a function of x

C 1

cost per unit set aside on the floor

z

cost per shift per loading position o n a carrier

D x)

fraction of loading attempts which are unsuccess-

ful as a function of

x

n

number of loading stations

R

expected num ber of work cycles per shift

K number of carriers on the conv eyor.

Employing difference calculus methods White shows that

the optim um value of is the smallest value satisfying the

relation

.-

where

F x t 1 )

s the complementary cumulative distribution

function of a binomial distribution with parameters n andp

evaluated at

x t l .

In

[66]

additional no rmative models arc

constructed for the case where h is the decision variable,

and for the case where both h and x are d ecision variables.

D

is shown to be a strictly convex function of

h .

Morris

[39]

extends the probabilistic model of Mayer

using a conservation of flow approach. His model includes

multiple unloading stations, and not all product placed on

the conveyor is guaranteed to be removed during one cycle.

The operating discipline is that assumed by Mayer, namely,

if a loading attem pt is unsuccessful, then the unit of product

is set aside on the floor. In addition, if an attempt to

unload a carrier is unsuccessful (due to an empty carrier

arriving next) then a unit of product is removed from the

reserve inventory located at the station. Each carrier is

assumed to have the capacity for carrying only one unit of

product. The following notation is used:

j

rate at which loading attempts are made by loading

station

j

pi

rate at which unloading attemp ts are made by unload-

ing station

rate at which carriers pass a station

fraction of carriers arriving at loading station which

are full

n

number of loading stations

--

December

1979

AIIE

TR NS CTIONS


6/9

pi

= fraction of carriers arriving at unloading station i

A n

which are fidl

C ; = m p - s

f i

m h

m

= number of unloading stations

1 - ( I - ( I - ; )

j = rate at which units are set aside on the floor at

loading station

wi

=

rate at which units are removed from the reserve at

unloading station i.

Assuming that loading stations are followed by unloading

stations, and that flow rate in equals flow rate out, Morris

provides the following relations

Assuming further that loading attempts and unloading

attempts are completely random, such that

j

=

ajAj

and

wi

=

pi(l

-

Pi), the following balance equations app ly

Pi+1s = Pi(s - Pi) i = l , . . . , m

S i n ~ e a ~ ~ s = ~ , s a n d P ~ ~ s = a ~ s , i f h ~ = h V jn d p i = P

Vi , the following solution to the balance equations is obtained

The rate at which unsuccessful loading attempts occur

for the system is given by

@ A ' Y j

j=

Normative models are constructed by White [66] for the

multiple loading and unloading station conveyor system

studied by Mom s. White treats th e speed of the conveyor,

as a decision variable and determines the value of s which

yields an economic balance between the cost of unsuccess-

ful loading or unloading attem pts and the.cost of increasing

the speed of th e conveyor. It is noted for th e case of m = n =

1 that J and t are strictly increasing functions of s; hence

in that case s should be decreased rather than increased. For

other values of m and

n it appears that

@

and re strictly

convex functions of s and achieve a minimum value for

s > max (A, p).

An alternative to the models of Mayer [37] and Morris

[ 9]

for a conveyor system consisting only of unloading

stations is proposed by Gregory and Litton [24]. They

assume that the time betw een successive unloading attempts

is

expon entially distributed and that all carriers approaching

the first unloading station are loaded. If an unloading at-

tempt is unsuccessful due to a carrier being empty, the

operator waits for the next loaded carrier to arrive. Hence,

reserve accumulation is not provided at any station. Any

carriers which pass

a l l

m unloading stations are autom atically

diverted to an accumulation line and processed at a later

time. The conveyor speed is such that the equally spaced

carriers pass a given point at intervals o f t time units and

the operator's service time is exponentially distributed with

(@)-I Hence, given that an operator is busy when carrier

i

passes, the probability that he

will

still be busy when

carrier

i

1) passes is

e Pt.

Consequently, if an operator

unloads carrier k then the probability that the next carrier

he

will

unload is carrier k y is given by

Gregory and Litton employ Palm's recurrence formula for

overflows in queue s [4 8] in comb ination with a result given

by

T a k h

[62] to obtain a recurrence relation which is

used to analyze the individual work stations. Let A(')(z,

@

denote the probability generating function of the input to

the ith work s tation. The following result is used:

where

and

Likewise, the rate at which unsuccessful unloading attemp ts

occur fo r the system is given bv

hk(z, @ = A ( ~ ) ( @ ~ z ) ] 1

t = P

(1 - Pi)

or i=1

with D(')(z, @ = 1. Given the A(')(z, @) it is noted that

the input to the ith station is the output from the (i-1)st

74

AIIE

lkANSACTIONS

Volume 1 , No.

4


7/9

station. Gregory and Litton show that the proportion of

parts which are not unloaded by any of the unloading

stations is minimized by sequencing the servers using a

fastest-first rule.

Muth [47] introduces a model of a closed-loop conveyor

with a single loading station and a single unloading station

and with random material flow. The amount of material to

be loaded into bucket n as it passes the loading statio n isX, .

The sequence { X , is assumed t o be a wide sense stationary

process.This implies that th e m ean value fu nction is constant

and that the covariance of

Xn

and

,f,,+i

is a function of the

difference j only. The amount of material unloaded from

bucket n at the unloading station is Y , . Not

ll

of the

material in the bucket will be un loaded. T he idea is to use

the storage feature of the return loop to cause { Y , t o

have less random fluctuation than { X ,

1 .

In particular,it

is assumed that the fraction

a

of the amount G , arriving is

unloaded, leaving the amo unt

H ,

= (1 a)G, in the bucke t.

The sequence

Y ,

is thus governed by th e difference equation

where k is the number of buckets on the conveyor. Based

on this difference equation the stsady-state probability

properties of

{ Y ,

are derived.

A

measure of the reduction

in random fluctuation is the ratio of the variance of Y , to

the variance of

X, .

This variance reduction factor is found

to be equal to 4 ( 2 - a).It can be made arbitrarily small by

making

u

small. However, the conveyor bucket capacity

required to accommodate the greatest possible load G , on

the forward leg grows in proportion to l/ a. Thus the price

for decreased output variance has to be paid by providing

increased conveyor capacity.

reas for Further

Study

Further work in conveyo r modeling is likely to con tinue in

two directions. On one han d, there

is

a place for large-scale,

general-purpose simulation models th at can cope with the

complexity of actual conveyor systems and that allow

tradeoff studies in the design stage as well as the analysis of

operational problems of existing conveyors. Analytical

models, on the o ther hand, are inherently limited to a low

level of complexity but are designed to shed light on the

fundamental relationships among im portant conveyor para-

meters such as conveyor speed, length of forward and return

paths, spacing of carriers, number and spacing of work

stations, amounts of in process storage, service disciplines,

and material flow rates. Existing analytical models should

evolve towards greater complexity by including a greater

number of these parameters. In addition, considerable re-

search opportunities exist fo r the formulation and solution

of o ptimization problems. Several examples of specific areas

for fu rther work follow.

The descriptive model of Gregory and Litton [ 5] may

be extended to provide performance measures leading to

determination of the optimum number of servers, the opti-

mum combination of the conveyor speed and carrier spa.

ing, and the optimum carrier capacity.

The deterministic model of Muth [44]

suggests several

optimization problems. 1) Given the seq uences Cfi(n)) of

material flow, how many carriers of what capacity

will

minimize the cost of the conveyor system? 2 Given the

total loading and unloading requirements, what sequences

&(n) will minimize the cost of the conveyo r system? Here

it is assum ed th at in process storage is available at th e load-

ing points and that delayed loading is permitted. This case

can be formulated as an integer programming problem.

3 Consider a single loading station having input sequence

X

=

{xi: = 1, . and a single unloading station having

output sequence

Y

=

bj

=

1

. where

xi

and

y

are

nonnegative integers. The following optimization problem

is posed:

Minimize

Ak

X,

Y

P

Subject to

C

xi = yj =K

j = l

j=l

k m o d p O

k x i, y j

nonnegative integers.

The objective function will be a nonlinear function of k and

the sequences X and Y . Differences in the actual loading

and unloading sequences

X

and

Y

and the natural loading

and unloading sequences fi@ and

Cf 69)

will resu lt in

added costs, perhaps of the form

[xi

-

fI j)l2

and lyj

f26]I2

The value of

k

selected yields an associated value o f

r

from the relation

r =

k mod

p,

and the relative convey or

loading can be d etermined fro m th e recursive relation

where Hi 0.

Letting

c

=

minHi*

then th e actual conveyor

i

loading is given by Hi = Hi* - c . The maximum carrying

capacity of carriers on the conve yor is given by

Knowing

B

and

k

the equipment cost component of the

objective function can be computed.

The stochastic model of M uth [47] offers the following

extensions. 1) Given the conve yor cost as a function of

conveyor capacity, and given the penalty one has to p ay fo r

the randomness in the conveyor outpu t flow, determine the

conveyor capacity that minimizes cost. 2) For a fmed

probability distribution of the inp ut sequence { Xn } and for

fmed conveyor capacity, determine if there are nonlinear

decision rules for unloading that achieve a greater variance

reduction tha n th e linear decision rule.

3

Extend this model

to the case of multiple loading and unloading stations, and

December 1979, AlIE

TRANSACTIONS


8/9

seek to reduce this to an equivalent two-station conveyor

model. One of the interesting aspects of this problem will

be the allocation of decision rules to the various unloading

stations, depending upon some predetermined expected

output rate at each station.

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AIIE

TRANSACTIONS,

Volume 1 1, No.

4


9/9

[37] Mayer, H. Introduction to Conveyor Theory,

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Analysis for Materials Handling Manag~ment

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4

2,134-143 1972).

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J.

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Eginhard J. Muth is a Professor

in

the Department of Industrial and

Systems Engineering at the University of Florida. He received his

Diplom-Ingenieur degree in electrical engineering from the University

of Karlsruhe, Germany, and

his

MS and PhD in systems sciencefrom

the Polytechnic Institute of Brooklyn. He joined the University *of

Florida in 1969 and prior to that spent 18 years in industry in a

variety of engineering assignments. His research interests include reli-

ability theory and modeling of materials handling processes. His

publications have appeared in various professional ournals. He is the

author of a book on transform methods. Dr. Muth is a member of

IEEE and ORSA.

John A. White is a Professor in the School of Industrial

and

Systems

Engineering at Georgia Institute of Technology. He holds a BSIE

from the University of Arkansas, an MSIE from Virginia Polytechnic

Institute and State University, and a PhD from The Ohio State

University. He is currently performing research in the areas of

material handling and warehousing. He has published papers in

several professional journals and has coauthored 3 texts, with 2

others forthcoming in 1980. He is a member of ASEE, IMMS,

NCPDM, ORSA, TIMS, SME, and WERC, and serves as a Department

Editor for

AIIE Dansactions

December

1979

AIIE

TRANSACTIONS

277

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