Dangerfield, B. C., "A System Dynamics Model of the U.K. Consumer Durables Manufacturing Industry: Some Preliminary Results", 1976

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A SYSTEM DYNAMICS MODEL
OF THE U.K. CONSUMER DURABLES

MANUFACTURING INDUSTRY : SOME
PRELIMINARY RESULTS

lL
ba ay
BC DANGERFIELD
DEPARTMENT OF BUSINESS AND ADMINISTRATION - UNIVERSITY OP SALFORD
SALFORD M5 4WT, ENGLAND .
ut
ABSTRACT
Ww

The paper describes a system dynamics model of the consumer
durables manufacturing industry in the United Kingdom. The model
purpose is to analyse the causes and effects of cyclical fluctuations
in the industry with a view to encouraging government or operational
policies that might improve industry stability. The paper extensively r
examines the consumer durables industry and explaing the model in detail, .
each equation being accompanied by an account of its construction. The
results of simulation experiments conducted on the model using various
test inputs are described. The paper appraises the technique of
spectral analysis, which has served as one means of assessing model
validity, The model, once validated, should form part of a larger
model which will also represent the steel stockholding and stee!
manufacturing industries. Work on the larger model is in progress.

CONTENTS

THE FRAMEWORK OF THE STUDY a

DESCRIPTION OF THE MODEL

‘The marketing and production planning sectors

The materials management sector

‘SIMULATION

EXPERIMENTS AND MODEL VALIDATION

Standard test inputs

Historical time-series inputs
CONCLUSION

REFERENCES:

APPENDIX 1 Two-sector DYNAMO flow diagram of the model
APPENDIX II Spectra} Analysis

APPENDIX III Documentor listing of the model

APPENDIX IV

On-Line Listing of the modet

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ACKNOWLEDGEMENTS

I would like to express my thanks to Mr E Stephenson of the School
of Business Studies, University of Liverpool, who provided guidance and
offered criticiom at various stages in the project, particularly during
the fieldwork and in preparation of an initial account of the development

of the model.

1 am also indebted to Dr R J Bhansali of the Department of Computation
and Statistical Science, University of Liverpool, who so kindly allowed

me to use his spectral analysis program.

Appreciation of the financial support provided by H.M. Treasury and
(in part) by the Institute of Purchasing and Supply is warranted because
without these funds no fieldwork would have been possible, no initial
descriptive report on the industry would have been prepared, and no
spark would have been ignited to enflame my curiosity toward the
system dynamics methodology.

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I, THE FRAMEWORK OF THE STUDY

The work described here evolved from research commissioned by
\ Her Majesty's Treasury into the reasons for and the effects of inventory
fluctuations in manufacturing industry in the United Kingdom, Some
earlier studies, mostly employing econometric techniques, were conducted
at precisely that level of aggregation : the whole of the U.K.
manufacturing industry. Our study is different in four major respectes

(a) Restricting the work to an examination of inventory fluctuations
alone seemed undesirable. An approach which isolated inventory

fluctuations from fluctuations in production, sales, and other

factors could not be justified.

(b) A single, coherently defined industry was investigated. Models of
the total industrial sector mask the common phenomenon that one
industry may experience a cyclical reversal of its demand trend
as much a8 9-12 months or more before another separate industry.

(c) Our study relied upon system dynamics, System dynamics is better
suited to modelling a complex closed-loop feedback system and to

ing the effects of alternative policy decisions by government,
the industry, or both. .

(4) Working at the industry level permitted extensive fieldwork, in the
form of interviews with involved executives. These discussions helped
provide a descriptive knowledge of the industry's structure and

operational policie

The consumer durables industry becomes more important as a developed

economy expands. (The volume of total retail sales increased by 36.3
percentage points from 1958 to 1973, while the volume of durable goods
shop sales and new car registrations increased by 74 and 90.8 percentage
points, respectively, over the same period) Therefore, to achieve *
greater stability in the economy generally, the government should move

toward effectively stabilizing the apparent fluctuations in the consumer

durables industry. Demand for many non-consumer products has its source
in demand originating in the consumer durables industry (the well-known
“accelerator effect" described by economists}> A reduction in fluctuations
apparent in that industry would go far towards reducing fluctuations in
other, interconnected industrial sectors,

_ SAU ~P RRERES ESLNTENEL TENETE NOTE TE PONE LEE OL NEI ALLTEL TELE LEED ELE I AER NTE EN ISO RO ie
-a-

Published applicationsof system dynamics to problems of instability
at this level of aggregation are relatively few. Forrester's early work
was largely concentrated at the level of the individual firm, and more
recently at the level of the national economy. However, attempts to
reduce instability at the national level might be best carried out by
a detailed examination of government policies toward the major constituent
industries of the econony and toward the consumer durables industry in

particular.

The consumer durables manufacturing industry in the U.K. consiste
of firms producing a variety of productsranging from expensive motor
cara to omall electric toasters, However, the nature of the particular
fir
industry as a whole is among the first to feel the effects of such

8 product is rather less important here than the fact that the

government reactions to demand as changes in tax and/or credit controls.

Successive governments in the U.K., as part of their overall efforts
to regulate the economy, have isolated the consumer durables industry for

a succession of policy changes. (The increase in Valuel Added Tax to 25%

for domestic electrical goods in the April 1975 Budget is typical)*, Mlowever,
people familiar with the industry have persistently complained that this
“treatment in the long run does individual firms (and the economy) a great
deal of hard. Prices and income elasticity of demand for dirables ‘is
significantly higher than for conaumables, and consequently the frequent
tax/credit changes generate fluctuations of considerable amplitude in

, the demand for durables,

H Ingha® provides asi apt general description of the type of firm
studied and visited during our research. Ingham refers to firms in the
Type 1 category as follows:

“offering a small range of standard products of the firm's om
choice, specification and design. The products are made for
stock in anticipation of orders because a considerable current
and probably continuing demand for them is assumed to exist".

*To further illustrate thie point, the same rate was halved to 124Z
in the April 1976 Budget.

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In terms of the Standard Industrial Classification (S.1..) index,
the firms visited during the fieldwork can be described as follows:

Table 1. Table of numbers of firms visited in relevant Minimum List
, Heading categories
Number of firms 8.1.C. Description
visited Minimum List
Heading
a 368 Electric appliances
primarily for domestic
use
6 399/9 Domestic gas appliances
3 381 Motor vehicle
manufacturing
. 3 365/2 Broadcast receiving
, equipment
1 339/4 Space heating,

ventilating and air
conditioning equipment

1 39/9 Other machinery
1 351 Photographic equipment

1 399/12 Miscellaneous metal goods
24

In any ‘syatem dynamics study, the initial phase must be devoted to
acquiring knowledge of the structure and operational policies characterizing
the system of interest. This initial phase, although all. too often not
accorded sufficient importance, can generate quite considerable difficulties.

In the project described here, considerable time was allocated to this
particular initial aspect. Accordingly, several firms in the consumer durables
manufacturing industry were invited to cooperate in the study. The response
rate was low, but although our request entailed spending up to three days at
each firm during a boom period in the cycle, within one year (January 1972-
January 1973) 24 firms had been visited and 119 executives interviewed.

“the Standard Industrial Classification index is a method of classifying
activities that go on at places where people work; it is based on the types
of products made or the service given at each place. Set up by U.K.
government statisticians in 1948 it is revised every 10 years. The 1968
edition covers 181 Minimum List Headings which are written as 3(or 4) digits.
Minimum List Headings for Vehicles (e.g.) are from 380-389 while those for
Mechanical Engineering are from 331 to 349,

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‘The interviews were structured around a preprepared questiorinaire
which served primarily as a catalyst for discussion, Such departments
as Production Planning, Purchasing, Production Control, Marketing, and
Distribution delegated their personnel and, although political factors
appropriate to individual firms tended to taint some responses, by the
end of the year a collective written description of how a typical firm
in the consumer durables manufacturing industry operates had been prepared,
Much of the information obtained was qualitative, but such data has-been
especially useful in determining the broad shape of table functions
contained in our model.

The reference mode which it is the purpose of the model to depict
is an oscillating pattern of behaviour which conforms to the periodicity
of the typical business cycle. The organising concepts which give rise
to this type of behaviour are shown in Figure 1 which is a much-simplified
influence diagram of the model as described in Section IL.

Paspuctions
‘Send G

+
Finisved, IN 1SSupaste
Coops Stott \, paars

Decay
SarsFyinte

Ga 6G beng

Figure 1, Influence diagram depicting organising concepts within the model

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The interplay of three significant negative feedback loops is responsible

for the observed oscillations. For example, an increase in the sales rate
will lead to a decrease in the stock of finished goods and thereby an increase
in the delay in satisfying demand, This in turn will ca

a corresponding
decrease in sales back towards the original rate.

The fall in the level of stocks of finished goods will cause an increase,
in production designed to correct the shortfall of stock. After 4 delay in
manufacture these goods will be available to replenish the industry's finiehed
goodsstocks. The equations incorporating ‘the variables in these negative
feedback loops (loops 1 and 2:Figure 1) are discussed in Part A of the
following section, Part A deals with the marketing and production planning
sectors of the model.

Loop 3 in Figure 1 is covered in Part B which describes the materials
management sector.” This negative loop showe that an increase in production,
designed to rectify the shortfall of finished goods stock, leads to a reduction
in the stocks of available parts and materials with the result that the delay
in issuing parts increases thereby in turn bringing about an eventual decrease
in production.

Me
i, DESCRIPTION OF THE MODEL

The mode] is designed to simulate the effect of changes in demand for
industry products oh production, stocks, and the derived demand for parts
from supplying industries. Demand for industry products is an exogenous

variable.

Appendix I provides a DYNAMO flow diagram of the model, showing the
interrelationships in the consumer durables manufacturing industry. These
interrelationships include variables and interactions commonly acknowledged
in the literature, as well aa others established by observation of the system
through fieldwork at the 24 firms mentioned earlier. Particular numerical values,
where quoted, are based on information obtained through the fieldwork. The
model equations are written in the DYNAMO language, with units expressed
as equivalent product units at constant prices. Time is expressed in
months. A documentor listing of the current version of the model is
presented in Appendix III, with an on-line listing in Appendix IV.

To understand the model, the logic underlying the fmportant equations
must be understood. The explanation offered here begins with the sales/
demand input and works backwards to the purchasing of replenishment parts
and materials from other industries.

AL The marketing and production
planning sectors

The flow into the industry of orders, in thie case originating from the
distributive trades, has been designated the primary demand rate PDR in the
model, The equation for thia variable is:

R PDR.KL . PDRI + STEP (STH,STT)

PDR . Primary Demand Rate (units/month)

PDRI - Primary Demand Rate Initially - 1000 (units/month)
STH - STep Height = 200 (unita/month)

stt = STep Time = 12 (months)

This equation permite the modeller to introduce ‘a STEP input function*
to investigate the effects of an arbitrary 20% increase in primary demand.

*A STEP function in the DYNAMO language has the form
X= STEP (H,T) STEP = 0 if TIME <T
STEP = H if TIME 2T ~

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While 4 real-world analogy is unlikely to be found, a change of thia nature
approximates the aituation attendant upon significant reflationary action by
the government such as the stimulation of consumer spending. On euch occasions,
s although the consumer durables manufacturing industry experiences a sudden -
external shock, the actual change in demand is unlikely to be so abrupt. The
Primary reason for using a simple input signal to drive the aysten is to
simplify the task of analyzing system behaviour.

The delay in

tisfying primary demand DSPD is inversely proportional
to the ratio of actual to normal finished goods atocks (APGS/NFGS), and is
ascuned to vary as indicated in the table function aelov. The delay is
leant, equal to the average time required to process orders (1 month),

when actual stocks are 50% more than normal, However, when stocke diminish,
during the boom phase of the economic cycle, the delay in supplying
Soods from stock increases, For example, the table function shows that

the industry takes, on average, 9 months to satisfy demand when the ratio
of actual to normal stocks falls to 0.25,

toRto

°

cory os os v0 ae Ve 15

Figure 2, Effect of finished goods stock availabili
ty
satisfying primary demand piemienesdelay tn

Ravin of
AEGLINEGS

x
‘Table functions are an extremely useful feature of the DYNAMO rr
opral
Janguage. They enable the sodeller to incorporate non-linear rele levers
: fe rede + Moreover, they frequently permit an interpretation of qualitative
lata, which otherwise might be neglected. But qualitative data can often
at least indicate the overall shape of the function. Then even if the
Parsi sulae faor of the function cannot be justified directly, the
naitivity of the system to changes in the oes ,
Prior to a substantial expense of effort on their accarcte davennite fed,

Somaymiesienernenmntes omits

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The value of 10E60, for the delay in satisfying primary demand vhen
the ratio of actual to normal finished goods stock is zero, is used in the
computer program to represent infinity. Although that portion of the curve
is not usually operational, if the model is subjected to a large enough
shock, low values for DSPD can cause AFGS to assume negative values through
the operation of the equation for the sales rate SR.

A oDSPD.K TABHL (TAB6, AFGS.K/NFGS.K, 0, 1.75, 0.25)
T TABG - 10E60/9/6/3.25/1,5/1.25/1/1
DSPD =  " Delay in Satisfying Primary Demand (months)
AFGS - Actual Finished Goods Stock (units) .
NEGS . Normal Finished Goods Stock (units)
TABG - Table of delay in eatiafying primary demand (months)

‘The gales rate SR from the consumer durables manufacturing industry to
their customers (almost wholly in the distributive trades) is shown as
the primary demand rate backlog PDR divided by the delay in satisfying
primary demand DSPD, For a given backlog, as the delay in meeting demand

increases, the sales rate decrea:

R ‘SR.KL a PDRB.K/DSPD.K
SR - Sales Rate (unite/month )
PDRB - Primary Demand Rate Backlog (units)
DSPD - Delay in Satisfying Primary Demand (months)

Production demand PRD, oze of the most important decision functions in
the system, expresses the rate of planned industry output. Our fieldwork suggests
that PRD contains two components viz. an amount based on current forecasts
which could be expected to be sold, and an amount to adjust any discrepancy
in the finished goods stock. The delay in adjusting finished goods stock
DAFGS: increases aa the ratio of actual to normal finished goods stock
approaches 1.5 and thereafter is constant.

A PRD.K - MFS.K + ((NFGS.K - AFGS.K) / DAFGS.K)
PRD - Production Demand (units/month)
MFS = Modified Forecast of Sales (unita/month)
NFGS - Normal Finished Goods Stock (units)
AFGS - Actual Finished Goods Stock (units)
DAFGs - Delay in Adjusting Finished Goods Stock (months)

= hh -

In aggregate production planning, firms face a choice between keeping

< production steady while allowing finished goods stock to absorb any sales rate
variations, or keeping tight control of finished goods stock levels vhile
allowing production to fluctuate. In the consumer durables industry, firms
unanimously opt. for the former course of action, The preference for steady
production ie reflected in the increase in the finished goods stock adjustment
delay, described in more detail below. The increased delay has the effect

of mitigating any sharp downturn in planned production.

0 ig ta as tee tas Se FIT de Ratio of APASEINFAS

Figure 3, Effect of finished goods stock availability on the finished goods
stock adjustment delay
The delay in adjusting finished goods ‘stock DAFGS is shown in Figure 3.
The table shows that DAFGS increases as the ratio of actual to normal finished
goods stock increases to 1.5 and thereafter DAFGS 1s constant at 3.5 months.
‘The delay increé
stock increases from 0.75 to 1.0, This reflects the industry's desire to

8 sharply as the ratio of actual to normal finished goods

avoid sharp cuta in planned production as finished goods stock builds up
when demand falls off.

A -DAFGS.K = TABHL (TABI, AFGS.K/NFGS.K, 0, 2, 0.25)
tT TABL *  0/0.25/0.5/1.0/3.0/3.3/3.5/3.5/3.5
DAFGS = Delay in Adjusting Finished Goods Stock (months)
AFGS = Actual Finished Goods Stock (units)
NEGS = Normal Finished Goods Stock (unite)
TABL =‘ Table of delay in adjusting finished goods stock (months)

= hs

ALL firms in the industry employ sales forecasts aa a starting
point for planning production. Therefore a forecasting routine has been
built into the model, The equation for the raw forecast of sales RFS .
extrapolates by determining the slope of the smoothed (delayed) curve, and
then uses thie slope to calculate the change in sales over the forecasting
horizon. This procedure is representative of the largely unsophisticated
forecasting methods common within the industry. In certain situations in

the model, the forecasting equation is subject to modification, as explained
below.

A RES.K =) SS.K + FH * ©((SS.K ~ PSS.K)/CSPS)

RFS = Raw Forecast of Sales (units/month)

ss = Smoothed Sales (units/month)

FH = Forecast Horizon = 3 (months)

PSs = Past Sales Smoothed (units/month)

csPs = Constant for Smoothing Past Sales = 1 (months) —

Modifications to the raw forecast of sales are treated by multiplying
the raw forecast by the factor for adjusting raw a of sales FARFS.

A OMFS.K =o RFS.K * FARFS.K F
MFS = Modified Forecast of Sales (units/month)
RES = Raw Forecast of Sales (units/month)
FARFS = — Factor for Adjusting Raw Forecast of Sales (dimensionl

PARFS is represented ty a table function (Figure 4) which is operational
in the model when smoothed primary demand SPD exceeds smoothed sales SS or is leas
than 75% of smoothed sales. (Smoothed values of the variables are employed to
reduce the magnitude of random disturbances in the ratio, Smoothing the
variables ensures that only significant and continuing changes are taken into
account in any adjustment of the raw sales forecast). Smoothed primary demand

SP) can easily exceed smoothed sales SS when the government reduces personal

taxation or eases credit controls. The consumer durables manufacturing
industry knows from past experience that the effect of such a decision will
in demand. They need not wait until a shift in the

be a fairly rapid incre
sales trend appears on the historical sales graph.

Governmental tightening of credit restrictions has the opposite effect,
but the equation for FARFS assumes no modification to the raw forecast of
sales RFS unless smoothed primary demand SPD is less than 75% of smoothed
sales SS. In other words, any downward shift in the primary demand rate PDR
will not be reflected in a modified forecast of sales MPS (and, therefore,

= kG -

an altered production demand) unless the shift is welatively severe. This
reasoning coincides with the industry's policy of delaying production
cutbacks for as long as possible,

ry FARFS.K = TABHL (TAB2, SPD.K/SS.K, 0, 2, 0.25)
r TAB 2 = 0/0.5/0.75/1/1/1.2/1.6/2.6/1.8
* FARFS = = Factor for Adjusting Raw Forecast of Sales (dimensionless)
SPD = Smoothed Primary Demand (units/month)
8s = Smoothed Sales (unite/month)
‘TAB2 ™ Table of factor for adjusting raw forecast of sales

(dimensionless)

2S oso Ors tee. fas t¥o rts 200
. Retio of SPHISS

Figure 4, Factor for adjusting the raw sales forecast following a marked
change in demand

The SMOOTH* function is employed to first delay the signal for the sales
vate SR and then delay the smoothed sales SS. Alternatively, past sales smoothed
PSS can be viewed as a "doubled-sncothed” version of the sales rate. The equations

are smoothed because decisions in industry are based on information about rates
which is averaged (smoothed) over a period of time, rather than on instantaneous
rates which by their very nature would be impossible to measure anyway.

z
The SMOOTH function has the form X = SMOOTH (IN,DEL) where IN = input and
DEL = smoothing constant or delay. Tt provides a way to exponentially smooth
a quantity.

mone con“ commnnrmnee eet poten iemeeeensmimenieentsie meee

>it

a 88.K = SMOOTH (SR.K,CSS)
A PSS.K = SMOOTH (SS.K, CSPS)

ss = Smoothed Sales (units/month)

SR = Sales Rate (units/month)

CSS = Constant for Smoothing Sales = 3 (aontha)
PSS = “Past Sales Smoothed (units/month)

CSPS = Constant for Smoothing Past Sales = 1 (months)

The production rate PR is a delayed version” of the parts issuing
rate PIR. All consumer durables firms manufacture their products by an
assembly-type operation on the constituent parts. Thereby, the flow
of products from the end of the assembly line can be viewed as a delayed
on of the parts issued at the beginning of the production lines.

R PR. KL = DELAY 3 (PIR.K, DPR)
PR = Production Rate (units/month)
PIR = Parts Isauing Rate (units/month)

DPR = Delay in Production = 3 months

Our fieldwork showed that, averaged over all the investigated firms,
desired finished product stocks were the equivalent of 6 weeks (1.5 months)
average sales. Such stocks may not necessarily be held at the factory
but may be dispersed among one or more distribution depots, For this
reason the normal finished goode stock holding NFGSH vas set at 1.5 months
and the normal finished goods stock at the equivalent of 1.5 months long
term sales rate LTSR, The long term sales rate was found to be a fairly
long term average of the sales rate and has been represented by smoothing

the ales rate using a 12 month smoothing constant.

NEGS.K = NFGSH # LTSR.K
A LISR.K = SMOOTH (SR.K,CLTS).

NFGS = Normal Finished Goods Stock (units)

NEGSH = Normal Finished Goods Stock Holding = 1.5 (months)

LTSR = Long Term Sales Rate (units/month)

SR = Sales Rate (unita/month)

CLTS = Constant for Long Term Sales = 12 (months)

“rhe DELAY 3 function performs much the same operation as the SMOOTH
function, However, DELAY 3 is employed to delay physical flows, whereas
SMOOTH is employed to delay information flows.

“and tak

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‘a, The materials management sector

“Having described the main equations relating to sales and aggregate
production planning, we can now move backwards in the manufacturing operation
to the equations embodying materials management.

The majority of firms in the industry pursue a requirements planning
Procedure which involves exploding the aggregate production plan into all.
the constituent parts and materials required for assembly of finished
Products. The parts demand rate equation reflects this procedure: the
parte demand rate PADR is a delayed version of production demand PRD.
The model specifies a constant 1-month delay to allow for the clerical
Procedures entailed in receiving and exploding an aggregate plan and
tabulating parts requirements, Obviously, some firms with computerised
systems may be able to conduct this operation much more quickly, but
an average delay of 1 month seems reasonable for the industry as a

whole.
R PADR.KL © = ~—DLINF 3 (PRD.K, DEXPRD)
PADR = PArts Demand Rate (units/nonth)
PRD - PRoduction Demand (units/month)
DEXPRD =. Delay in Exploding PRoduction Demand = 1 (month)

The equation for RDPR represents industry demand for parts and materials,

the same form as the equation for production demand. The replenishment

demand for parts rate RDPR. contains two componente: the parts demand rate
PADR satisfies current demand, and the variables ((NPS~APS)/DAPS) account
for stock adjustment. The adjustment delay in the latter term increases as
actual parts stocks APS exceeds normal parts stocks NPS.

The MAX function* employed in the RDPR equation prevents negative values
for RDPR.
term have exceeded the current demand for parts.

In some preliminary runs, negative values of the stock adjustment
Such negative values, when
However,
although cancelled orders could be straightforvardly incorporated in the model,

multiplied by ~1.0, represent cancelled orders for parts and materials.

for the time being the model us

@ value of zero whenever the RDPR equation
goes negative. By implication then, in some time periods no orders for parts
and materials are sent to suppliers.

*h MAX function in DYNAMO has the form
X = MAX (P,Q) where MAX = P if P > Q and MAX = Q if P< Q

ween

eg

R —-RDPR.KL = MAX (0,PADR.JK * ((NPS.K ~ APS.K)/DAPS.K))
RDPR = Replenishment Demand for Parts Rate (units/month) |
PADR == Parts Demand Rate (units/month)

NPS © Normal Parts Stock (units)
APS = Actual Parts Stock (units)
DAPS = Delay in Adjusting Parts Stocks (months)

DAPS
(moans)

° 00
1 fas 150 195 tata OP aps mrs
Figure 5. Effect of parts stock availability on the delay in adjusting parte stocks

From a minimum length of 1 month when actual parts stocks APS are less than
or equal to normal parts stocks NPS, the delay in adjusting parts stocks DAPS
increases to 6 months when actual parts stocks are twice the normal requirement.
This is depicted in the tablefunction in Figure 5.

Firms may actually be able to adjust stock deficiencies more quickly than
the I-month minimum figure used here. For example, they can contact their
respective suppliers by telephone and so short-circuit the once-monthly
requirements scheduling process. While acknowledging this practice, especially
during the boom phase of the cycle, auch a refinement has been omitted for the
present, particularly since the model does not yet include a variable lead time

for parts and materials.

eee 08

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‘The increase in the delay in adjusting parts stocks DAPS to 6 months
reflects the fact that firms in the industry want to retain the goodwill

, of their suppliers when demand is depressed. Lengthening the adjuatment

delay prevents any marked reduction in demand for supplies.

A -DAPS.K = TABHL (TABS, APS.K/NPS.K, 1, 2, 0.25)
T ‘TABS = 1/1.8/3.0/3.9/6.0
DAPS = _— Delay in Adjusting Parts Stocks (months)
APS = Actual Parts Stocks (units)
NPS = Normal Parts Stocka (unite)
‘TABS = Table of delay in adjusting parts stock (months)

‘The equation for PRR may embody a shortcoming of the current version of
the model. The equation below describes the parts receiving rate PRR

4 delayed version of the replenishment demand for parte rate RDPR. The
average delay is set at 3 months. Obviously, the lead time on parts/materials
cannot be constant, especially since a characteristic of boom conditions in
the economy is a lengthening of lead times with a consequent effect on order

rat

Rg PRR.KL = DELAY 3 (RDPR.JK, DRRP)
PRR = Parte Receiving Rate (units/month)
RDPR = Replenishment Demand for-Parts Rate (units/month)
DRRP = Delay in Receiving Relenishment Parts = 3 (months)

. Stocks of parts and materials held by firms are proportional to their
use in production. Therefore, the normal parts stocks NPS equals a number
of months of normal parts stockholding NPSH multiplied by the smoothed
production demand SPRD. In other words, the industry tries to maintain a
parts/materials stock that will cater for a certain number of months of

average production.

A NPS.K = NPSH.K * © SPRD.K
NPS = Normal Parts Stocks (units)
NPSH == Normal Parts Stock Holding (months)
SPRD = Smoothed PRoduction Demand (units/month)

Firms in the industry are galvanized into strict control of parts/materiale
stocks in times of tight liquidity, During such periods, in order to preserve
cash flow, the growth of stock levels must be contained. Usually, as a result,

IER AAT LOOT NTT oT CURTRIINORERIETEEN:  RNORE
~51-

senior management issues directives to-reduce stock holdings. In the main,
parte/naterials atocke are the focus of attention, aince attempts to cut
finished goods stocka are inextricably bound up with aggregate production
planning. :

The particular mechanisms adopted to improve control of parte/materials
stocks range from creating a more efficient data base on stock levels,
purchases, and usage rates to the use of decision rules designed from
operational research investigctions. In most cases, improved procedures
should have a lasting benefit on firms within the industry, although, |
no doubt, pressures to contain stock levels are very much less in the
boom phase of the cycle when cash flow is usually healthy.

To incorporate this important stock control feature into the model,
normal parts stockhplding NPSH is related to the ratio of the smoothed
parts receiving rate to smoothed sales (SPRR/SS) by means of a table function.
According to the table, when sales are sufficient to generate cash to pay
for purchases, normal parte stockholding is 3 months. However, if sales
fall off for any reason, and parte/materials continue to be delivered,
:the pressures on cash flow reduce the normal parts stockholding. The
table function is shown in Figure 6,

NPSH.K = TABHL (1AB4,.SPRR.K/SS.K, 1, 2, 0.25)
T TABS = 3/2.75/2.5/2.0/1.0
NPSH ==“ Normal Parts StockHolding (months)
SPRR = Smoothed Parte Receiving Rate (units/month)
ss = Smoothed Sales (units/month)

TABS = Table of normal parts stockholding (months)

1
° 1 i 7 :
1 das 450 145 200
Robie of SPRRISS
Figure 6. Effect of liquidity changes on normal parts stockholding

-52-

For a given parts demand rate backlog PADRB the parts issuing rate
PIR is invereely proportional to the delay in issuing parts DIP. This

equation, identical in form to that for the sales rate, represents the

effect of changes in the delay in issuing parte (resulting from variations
in stock availability) on the ability of the industry to issue parts for
mbly into finished products.

R PIR.KL = PADRB,K/DIP.K
PIR = Parts Issuing Rate (units/month)
PADRB == ~—- Parts Demand Rate Backlog (units)
DIP = Delay in Issuing Parts (months)

oa too. vas 130 Vt

°o o-2s O-So
. Patio of APS: NPS
Figure 7, Effect of partes availability on the delay in issuing parts

The table function for DIP shows that, as actual parts stocks exceeds
normal, the delay in issuing parts decreases from 1 month to a minimum of 0.5
months when actual parts stocks are 75% above normal. The curve for DIP
continues to fall as the ratio of Actual Parts Stocks APS to Normal Parts
Stocks NPS exceeds 1.0 because of the desire by firms in the industry to
prevent sharp reductions in the parts issuing (and hence production) rate
and enable the manufacture of finished gooda for stock during recessions.
The table function is shown in Figure 7.

mri: meneame gh

a
~53- Ill. SIMULATION EXPERIMENTS AND MODEL VALIDATION
decreases tovards revo then the delay in

As the ratio of APS to NPS dec: A Peawane RAGE indadd

issuing parts DIP increases tovard infinity, As with the equation for the

Delay in Satisfying Primary Demand DSPD described earlier, the value of % As a prelininary experiment to reveal dynamic behaviour characteristics
10E60 is used in the table function to represent infinity and thus ensure that the of the model, # 20% STEP input is inflicted on the model system in the 12th month.
level of APS ie not driven negative by any large shock imposed on the model. Figure 8"shows the effect of such a sudden increase in demand on some of the
‘ important endogenous variables, This particular signal clearly induces
A DIP.K = TABHL (TABS, APS.K/NPS.K, 0, 1.75, 0.25) cyclical behaviour with a periodicity of between 30 and 34 months. Although
TABS = 10860/4/2.25/1.5/1,0/0.75/0.65/0.5 the 20% increase occurs at the end of the 12th month, the fluctuations, albeit
DIP = Delay in Issuing Parts’ (months) considerably damped, are still continuing after the 100th month, An explanation
APS = Actual Parts Stocks (units) will be forthcoming shortly. :
NPS = Normal Parts Stocks (units)
TABS = Table of delay in issuing parts (months) ‘As expected, the finished goods stock exhibits peaks significantly

greater than the production peaka. The former peaks. show 43.12%, 28.142,
22.33% and 20.48% increases on’ initial values,compared to 33.64%, 24.54,
21,34 and 20.39% for the latter. This result is consistent with the stated
industry policy of using finished goods stocks, rather than production, to
counteract flunctuations in sales.

| Production exhibits an interesting feature which is compatible with
observations from our fieldwork! production momentum, once started, is
difficult to arrest. As a result, after each cyclical peak in sales hi

passed, production continues to increase (or at least does not decrease
simultaneously) » Perpetual "overshooting" of production in this manner is
@ major problem for production planners in the industry.

The model has also been run with a demand signal incorporating data
generated randomly from a normal distribution with a mean of 1000 units
and a standard deviation of 40 units, The results, (shown in Figure 9),
are quite interesting. Even with randomly generated demand, industry
output sales and stocks still exhibit cyclical behaviour. Such a result
implies that the system possesses characteristics which are sensitive to
certain input frequencies, an entire spectrum of which would be found in
normal random noise, for example. We must identify these characteristics and
whether revised policies adopted by firms in the industry are likely to
reduce amplification of the sensitive frequencies.

*
The figures on the following pages, which depict the time series plots, do not
all exhibit the same acale, but where the reader is invited to compare two or
more graphs their scales are consistent. .All the values printed are in terms
of percentages of initial valués (i.e. index number form).

ibe Si om EERE

meee

Wo

Primary Demand
Finished Goods Stock
Sales

Production

Yo of initieh values

60 months >

Figure 8. Fluctuations generated by a 20% step increase in primary demand in month 12

s

% of initial values

Finished Goods Stock
Seles

mouths —>

Figure 9. Model behaviour resulting from a normal random noise demand signal

aége
dogg

To further illustrate the system's sensitivity to certain input
frequencies, the model has been driven by a demand signal comprising a pure
sine wave vith an amplitude of 200 unite and a periodicity which changes

in successive runs. Figure 10 shove the resulting amplification in finished
goods stocks and production, The figure anticipates a serious amplification
when a signal with a periodicity of between approximately 15 and 55 months
perturbs the system. The critical or natural frequency’of the system vould

appear to be elicited by a signal with a period of about 25 months.

Anlifiaing
fo
~ me me Finished Goods Stodes
; 1 \ Pre
{ \
t
é {
s |
| j
“|
2 t
ti
!

Period of Sine wave aput (aonils)

Figure 10. Graph of the degree of amplification of two system variables
as a function of periodicity of a’ sine wave input

One factor contributing to instability in the industry appears to be
the forecasting procedures adopted by the constituent firms. Few sophisticated
procedures are in use, firms merely extrapolating from current trends and
focusing on an excessively short forecasting horizon. To illustrate the impact
of forecasting procedures, Figure 11 shows the response of the system to a
20% step input when the sales forecasting routine, which until now has been
used to determine production demand, is replaced by a smoothing process on
the only “hard information available ~ the inflow of ordera. The equation
for production demand PRD now becomes:

*
The natural frequency’of a system is the frequency of a disturbance to which
the system is most sensitive, In this case iv is a frequency corresponding to
an input signal with « period of about 25 months. ~

ary demand in month 12 when smoothing of incoming

60

4
3
8

6
a
i
3
2

a

4
a
me

j
|

---=- Sales
orders, as opposed to forecasting sales, is used to determine production demand

Figure 11. Results of a 20% step increase in prim

Sammon “yorqiut “Jo Yo

- 59 -
A PRD.K =~ SPD.K + ((NPGS.K - APGS.K)/DAFGS.K)
[Ceap.x = MPS.K + ((NPGS.K - APGS.K)/DAFGS.K (previous equation)

‘SPD = Smoothed Primary Demand (units/month) *

NFCS = Normal Finished Goods Stock (units)

AFGS “= Actual Finished Goods Stock (units)

DAFGS' = Delay in Adjusting Finished Goods Stock (months)

MS = Modified Forecast of Sales (units/month)

months

Comparing Figure 8 vith Figure 11 clearly shows the reduction in instability.
Indeed, fluctuations of any significance disappear after 50 montha or so when the
smoothing of incoming orders is used to determine future production demand, whereas —
they continue through the 100th month when sales forecasts are used for the same

purpose. The continuation of fluctuations in Figure 8 must therefore be the

. Finished Goods Stock

direct result of the sales forecasting procedures adopted by the firms in the

consumer durables manufacturing industry. Nothing else but these procedures
have changed between the two figures.

——_—— Primary Demand

Sales
——— Production

Figures 12 and 13 further illustrate the differential effect of alternative ~

modes of determining production demand. Both depict the behaviour of the system

when driven by an input signal composed of random fluctuations superimposed

upon a sine wave. This type of input signal more nearly approximates the effects “
+ on demand of periodic stimuli applied to consumer spending by the government in

its overall management of the economy. Figure 12 illustrates the effects ina

system practicing forecasting, while Figure 13 shows the effects in the same

system when orders are smoothed instead. Once more; the smoothing policy has

the effect of damping fluctuations in comparison with the sales forecasting

policy. E

Inevitably such results raise the question of why firms in the consumer
durables manufacturing industry bother with forecasts at all. Yet every firm’ weve
of those visited pays attention to such forecasts when formulating their aggregate
Perhaps fear of competition motivates individual firms.

opposed to extrapolation of the

production plans
Smoothing of data,
that the information obtained will lag a change in trend. Therefore, a firm

Effect of sales forecasts as a determinant of production demand when

primary demand is a composite of normel random noise and e sine vave

me data, inevitably means

that adopts 2 smoothing system for aggregate production planning could discover
during an expansion phase of the demand cycle that its delivery dates were

Figure 12.

extended compared to competing firms using forecasting systems. As a result,
ite market share could shrink. However, whether the adverse affects of a reduction
“in market share outweigh the negative effects of instabilities (such as the

inefficiencies introduced by fluctuating workloads) is open to question.

Actually,most firms probably do not even consider the costs associated with

‘
instabilities beyond saying that,given a choice between fluctuations in production 07 oo!
and fluctuations in finished goods stocks, they would prefer the latter. SIMA Fwrpur jo . %

6 -

~Ore

A firm which replaced ite production planning system based on forecasting by
‘one based on the smoothing of incoming orders would probably remove the
need to have to make such a choice.

A second experiment has been undertaken to assess the effect of :
removing the modification to the raw forecast of sales. For this test,
forecasts consist only of an extrapolation of past movements in the sales

months

rate. The system ignores further information from changes in incoming
orders, Figure 14 displays the results of this experiment.

Finished Goods Stock

The effect of removing the forecast modification can be seen by

comparing the percentage increases on initial values of the successive
peaks in actual finished goods stock, production rate, and sales rate series
in Figures 14 and 8, respectively. The figures are tabulated below:

——— Primary Demand
----- Sales
———=— Production

20% Step Increase in Demand

No Modification to Forecast Modification to Forecasts

Figure 14 (% Increases) Figure 6 ( increases)
nl

| Ist peak 2nd peak 3rd peak 1st peak 2nd peak 3rd peak

Finished Goods Stock 55.85 36.90 28.71 43.12 28.14 22.33
Production 38.1 29.47 24,82 33.64 ° 24,54 21.34
Sales 33.70 27.31 23.65 30.14 23.39 20.99

Not modifying the sales forecasts increases the system instability. The

implication is that, when account is taken of rapid changes in demand, the

industry responds in advance of changes in sales, thereby eliminating information
delays and preventing the destabilisation induced by excessive adjustments to

output.

Effect of smoothed incoming orders as a determinant of production dewand vhen

primary demand is a composite of normal random noise and a sine wave

Two experiments have been conducted to assess the sensitivity of the
modelled system to varistions in delay times. Firet, the delay in adjusting
finished goods stock DAFGS is increased to two, and then to four times, its

213.

original value, As a result, the delay function ranges up to between 0 and
14 months, instead of between 0 and 3.5 months originally.

With a pure sine wave for input, the periodicity of fluctuations in
production does not change, but the amplification of the input signal is
considerably reduced as the delay increases. Figure 15 illustrates the

results of this experiment.

“aapiatin
1 —  — Finithar Croeds Stork

a reduction

>

months

° =
fe a ae FO Gece by oie the in
WS increased’

iables as the delay in adjusting

~~~ Sales
———— ‘Production

Figure 15. Amplification of two system
; finished goods stock increa

The finished goods stock is amplified at first up to the point where the
delay in adjusting finished goods stocks is 1.75 times as great as the original
In effect, up to that maximum point,

delay, and then progressively decreas:
delaying the adjustment of discrepancies between normal and actual finished

gooda stock leads to a reduction in production fluctuations only at the expense
of greater fluctuations in the finished goods stock. If the delay increa!
still further, oscillations in both production and finished goods stock are
diminished.

Fluctuations generated ty a 20% step increase in primary demand in month 12 when sales

forecasts, without modification, are used to determine production demand

For a second experiment, the delay in satisfying primary demand is
successively increased to two and then four times its original value, in
the same way as the delay in adjusting finished goods stocks was changed

Figure 1h,

for the preceding experiment. This means that the delay, when the system

is in equilibrium, increases from 1.5 months to 3 and then 6 months respectively.
‘A pure sine wave provides the demand input. The resulting amplification of
production and finished goods stock is shown in Figure 16. This time the effect
is to considerably reduce the amplification in both series as the delay increases,

decane es nanindie” SRA eNtaciumumreN rmmmersenngnntcentiy: tanto

-65-

Finished Goad Starle
a Prodnct ion

$0 to to 4-0 Faator by whith te delay

| fs Naerensed

Figure 16. Amplification of two system variables as the delay in satisfying
primary demand increases

Although both increases in the delay in adjusting finished goods stock and in the
delay in satisfying primary demand have beneficial effects on system behaviour,
the Likelihood of ‘their being implemented in a practical situation is certainly
questionable. No firm would readily implement a policy of lengthening the delay
Even given

in fulfilling customer orders, a strategy the latter case require
“general agreement among individual firms, a most unlikely event, any significant
delay in supplying customer requirements would lead to orders being switched to
foreign competitors in the consumer durable goods field.

There is slightly more scope for delaying adjustments to finished goods
stocks, Such a policy is already extensively used during @ cyclical downturn.
However, during an upturn, competitive pressures strongly impinge on policy-making
because the sales departments of consumer durable gooda firms continually insist
on healthy stock levels in order to be able to offer goods for supply off-the-shelf.
Any policy which we
creating a larger backlog of orders than stock available ~ for any length of time

seen to create a negative free stock situation ~ that is,

would bring heavy protests from the sales people.

= 6
In 1965, Brechling and Wolfe published a paper containing a closely

reasoned account of why the U.K. economy experiences such severe “atop-go”

cycles? One important conclusion was that. the speed of the cyclical

upswing is a primary determinant of ensuing fluctuations. To throw further

Light on this. point, which has important implications for governmental control

of the economy, the model has been tested with a demand input in the form

of a ramp. This ramp drives demand up from 1000 units per months to 1200 units

per month over periods ranging from one to three years, With this addition, the |

model can be viewed as a microcosm of the entire economy ~ the increase in

demand being analogous to a general increase in consumer spending.

The behaviour shown in Figures 18 (a-c) aupports Brechling and Wolfe's
viewpoint. The figures show the effects of a 20% demand increase spread
over one, two and three years, respectively, Fluctuations are diminished
as the slope of the demand signal decreases, Figure 17 embodies the general
principle exhibited by Figures 18 (a-c). The decline in the amplitude of
fluctuations in finished goods stocks and production is graphed against

the lengthening of the period of time over which the demand increase is |
spread. On the basis of Figure17, the considerable destabilising effect

of the extremely fast expansion of consumer demand in the U.K. economy

in 1971/1972 is perhaps not surprising.

fo

Moin

eof
Frsteation 4 | ~N a
Cetemge ~~ ;

fists). a

ye nett
; ae
20 |
TT Finished Goods Sho

6 —— Praduchion

2 23 3
Pevind of Line over wich 10% dennad tatrtase is spread (Ves)
Figure 17. Decline in the range of fluctuations of finished goods atock

and production as a 20% demand increase is spread over a longer
period

sore or ”
BE RR ARE 8 RE ARIES

seRsRemREeaNny MARL ees

months —>

vo Finished Goods Stock

—---— Sales
m= Production

—— = Sales
———— Production

Fluctuations generated by e 20% increase in primary demand

Fluctuations generated by © 20% increase in primary demand spread
spread over 24 months starting at month 12

over 12 months starting at month 12

a a |
s g j
= ee}

2 i |
4 2

a a

cl

ont 001 , : Ont oo!

samen yoy Jo %. srmyon yoymut Jo %

--

B. Historical time eeries inputs

A recurring controversy in eystem dynamics is model validation. Some
\ practitioners argue against attempts to ascertain the ability of a model
to re-create observed dynamic behaviour embedded in published statistics.
However, if past data is available (souething that for sufficient model
variables may not be the case) why neglect it entirely? Good agreement
between the simulated and actual behaviour of important variables would give

the modeller greater confidence in his model. The question then becomes:
What represents "good"?

Usually, @ comparison between simulated and actual behaviour takes into
account periodicity, amplitude, time of occurrence of turning points and phase
relationehips among variables. In many vays this approach is somewhat subjective
and unscientific. Moreover, with highly variable data series, statements about
turning points, amplitude and periodicity may be uncertain if not completely
indeterminate. |

Spectral analysis, a technique commonly employed in modern statistical
practice and with origins in the physical scienc

» may be able to play a
useful role in helping to validate system dynamics models where the behaviour

of the variables is such that visual inspection of the series may prove unreliable.
However, there are no reported accounts of the use of spectral analysis in

this way. Therefore, a review of the advantages and difficulties of the

technique, by réference to an actual case study, should throw some light on

the admittedly huge problem of model validation.

ceemeee Finished Goods Stock

§
23
3
ak
'
1
i)
|
1

This paper will not go into the theory of spectral analysis in depth. Pease
reader can refer to other sources for a detailed description of the techniqae.’
However, its essentials, as well as the procedure used in the spectral analyais

computer program, are described in Appendix II.

Fluctuations generated by e 20% increase in primary demand spread

over 36 months starting at month 12

Even though some attempt should be made to assess the model by its ability
to recreate the dynamic behaviour of the industry as depicted in published
statistics, problems still abound in the case of the consumer durables industry.
First, the government does not publish statistics which can be identified

with a definition of “consumer durables manufacturing industry"; second, the

Figure’18(c).

existing statistical coverage extends to only one or two of the important
variables in the study. Neverthele

imulation runs have been conducted with

! i rane SteA?
A RRA RRNA

-n-
the model driven by an exogenous historical time-series. The results,
together with comments on the usefulness of spectral analysit a model
validation technique, are reported below.

The exongenous input to the model is the flow of orders which emanate
largely from the distributive trades. However, no government~published
statistice are available on the flow of orders; indeed, only one major
firm of the 24 visited during our fieldwork kept data on orders booked.
This omission from U.K. economic statistics does seem significant»and not
only from the modelling point of view. A cyclical upturn in the flow of
orders from distributive trades to the consumer durables manufacturing

induatry would be a useful leading indicator of improvement in the business
confidence of retailers/wholesalers. Such a trend would normally be coincident

with the restocking phase of the cycle.

Since data on orders booked is not available, the series for retail
sales in durable goods shopd has been taken as a proxy. However, there
are grave dangers in using proxy variables not least being the lack of
any assurance that the variable is a suitable proxy. The choice of retail
sales here has the major disadvantage in that sales lag ordera by several
months. The characteristic behaviour.of the two series may not be similar
because over-ordering ie common during a boom phase of the cycle. Neverthele
the retail sales series should at least reflect the respective periods of
boom and slump in the durable goods industry, as suggested by Figure 19 which
uses rétail sales to drive the model, (The series consisted of 70 quarterly.
observations from 1958(1) to 1975(2), Unless otherwise stated, all actual
data series used here take this form),

A significant point to be drawn from this figure concerns the peaks in
finished goods stock, Statistics are not available for finished goods stocks
disaggregated into the consumer durables manufacturing industry. However, a
finished goods stocks-to-production ratio series for the U.K, manufacturing
industry in aggregaté is available from 1959, Each peak in finished goods
stocks in the model occurs shortly after a boom phase in the U.K. economic
cycle. While thie pattern is encouraging, since finished goods stocks
would be expected to build up aa a boom comes to an end, the behaviour is not
in exact agreement with the occurrence of finished goods stocks peaks in the
historical ratio series. Figure 20 below shows the relevant quarter of each
year that exhibited peaks in the model series and the actual historical series,

respectively.

----- Seles

——— Production

Behaviour resulting when the model is driven by a historical
data series of retail sales in durable goods shops

Figure 19.

-n-
MODEL OUTPUT SERIES ACTUAL RATIO SERIES
1960 (3) 1961 (4)
1966 (3) 1966 (4)
. 1969 (2) 1971 (4)
1974 (3) 1975 (2)

Figure 20. Comparison of peaks in finished goods stocks series in the
model with those published in the finished goods stock :
output ratio series for manufacturing industry in aggregate

The greatest discrepancy occurs where the 1969 peak in the model output
series falls 10 quarters avay from the peak in the actual ratio series, However,
given the unavailability of relevant data for the actual series and the fact
that @ proxy is being used as an input signal in the model, the overall result
of producing the same number of peaks as the published data is relatively
actory+

The motor industry is one of the most important homogenous sectors: of the
U.K. coneumer durables manufacturing industry{ Therefore, available dal ri

on new car production for the home market would be useful in helping to asse:
the validity of the production series given by the model. Since retail sales
~ would not be a suitable proxy to drive the model in this instance, the motor

industry's counterpart to retail sales, new car registrationé, has been
adopted instead.

The reoults*of spectral analysis of the historical data series on new
car registrations and car production for the U.K. market are shown in Figures 21
and 22, respectively. As expected, the power spectrum shows large peaks
corresponding to high frequencies and alao to @ seasonal cycle. However,
there is also a peak corresponding to a cycle of about 52 months -~ the

Power

“se voters

UsING meorrten Manteut aIsOe®

070neat

acaeceeccaceceqatess

generally accepted periodicity of the busit cycle in the U.K. This r
periodicity agrees with research reported elaewhtid’as well. 1 i

The plots of the spectral density functions for the simulated production ey
and finished goods stock seria (Figures 23 and 24) do not lend much support Bs ‘3
: 3 C&
The graphs of the spectral density functions reproduced below are read as 2& .
ae power (expressed on a logarithmic scale) as a function of frequency. ne
The values x; across the bottom are the exact points on the logarithmic y-axis,
represented as CL. The significance of peaks at certain frequencies is indicated
by an arrow together with the periodicity of the corresponding cycle. Figure 21.

a emapereaminenigiais. Lemecvmins menrhaonRbNinSck AAC RSMIIRR Ronin tem

wuvevesvecvereey

=the

Seasons

wuevveuverevery

saereset

sr0ntoar

S323

Power spectrum of new car registrations 1959-75

en

eto

mene

|

sneaege® leoasee*

-16-
i

Power spectrum of the simulated production series
when the model is driven by new car registrations

SAmonth 23eronth

Figure 23,

ngoute iataNa 0741008
Santos Of AY adI8mZ0 Wald2et 60 901 60 40%

aneed ewataresetaze avd ades aututneae x5t12000
: :
2 !
i i
Beg
a t
: 23
senses! teoatets 38 H
i - . . = !
susnasonenenspensnynenvnennnnonenneanonsnnennonnononnn en 8 i
i
wane ¢ ,
; 7 i
> 3 i
: 3 i
: ;
: & i
2 5
: 5 i
: Hy i
3
4 3 '
Y : % 5
> 4
ms . i
. 3 H
: 5 ‘
: 2 i
Y {
g {
2
:
a u
8 j
: }
. 3 L
>vsnppovepvsponnnsoneazonsnnononsnosonenozonsnonnonpenezannzenensnnneperepezenan or =) i
: . Wiss . Lesaeet® * t
soostn Viatwra odisiee anton i
Gintos 95 an ALttq2y Yal2ReR 40 407 40 10% i
Anaya gaom woe MOLL INODuE OVD HTN |
# PINTSHED GOOD STORK AFSULTING FROM Cam HEGEBTAATIONS IWPUT

Powe

vornre

ry

Ler oF Loe OF Secret veWsrty At

ant oet
anesecet

wsgereny

Smo Baonth Seasonal

USING MODIFIED OOMTELL *tS0re

S76beat

Figure 24, Power spectrum of the simulated finished goods atock series
, when the model is driven by new car registrations

|

to the existence of a 52-month cycle. Indeed, although there seems to be

@ peak corresponding to such a cycle, it is minor compared to the peaks
corresponding to a 23-month cycle and to the seasonal cycle. The significant
23-month cycle does not appear in either of the power spectra of new car

-B-

registrations or car production for the home market. In fact, a comparison
of the power spectrum for car production for the home market (Figure 22)
with the power spectrum for simulated production (Figure 23) generates no
conviction that the two series are in any agreement, apart from seasonality
influences.

Data obtained from firms participating in our fieldwork is generally
unsuitable for spectral analysis because the data series are not of a
significant length. To produce evidence for 4 52-month cycle would ideally
require something like a minimum of 200 monthly observations. An unfortunate
fact of economic life is that industrial firms see no need to retain monthly
data for several successive years. Consequently, the modeller hoping to
acquire statistical information from such a source is unlikely to meet
with much succe:

+ The longest series obtained from an individual firm
consisted of 92 monthly observations, These observations have been
subjected to spectral analysis with some misgivings, and, as expected,
the plots of the power spectra are not very useful for detecting cycles
with a periodicity corresponding to the buainess cycle:

The results reported in this section have to be viewed in the light
of the fact that proxy variables have been used for the primary demand
input. This expedient distorts what in other circumstances might be a
reasonably successful method of testing dynamic models of industrial or
economic systems.

One possibility which might be tried,in order to avoid the need to employ
proxy variables for demand input in this model, is to add a retail/distributive
sector. This would then mean that the primary demand flow to the industry
would be determined endogenously as the distributive trades reacted to
exogenous changes in customer sales. Certainly it would seem to be premature
at this stageto reject

ther the model itself or spectral analysis as a
means of testing it given our inability to obtain the necessary demand input
data.

-9-

WW. CONCLUSION

‘The work reported in this paper has attempted to serve two important
purposes, First, it has stressed the importance of the consumer durables
manufacturing industry in the national economy, and explained why efforte
to control instability in the economy should ideally etart with a close
managerial policies

examination of government policies toward, as well
adopted by, this industry. From recent indications, this view is apparently
beginning to be taken seriousl}~

Second, and perhaps more importantly, our work has served notice of
the usefulness of system dynamics for conducting such an examination.
Indeed, system dynamics could prove to be a far more valuable tool for
policy evaluation at the macro-economic level than the large-scale
econometric models which consume such a large proportion of economic
research efforts today. Econometric models are primarily forecasting
models. Morever, although some attention ig now being given to their
use in simulating the effects of alternative economic policied,the
primary characteristic of current econometric models is an ability to
forecast the symptoms of economic problema rather than to identify the
root causes which are almost certainly connected with the structure of
the economic system and the policies adopted by the system managers.

Attempts to validate our model have unfortunately been inconclusive,
Mowever, given the non-availability of relevant data, especially that on

orders booked by the consumer durables manufacturing sector, the results
are perhaps not surprising. Nevertheless, the use of spectral analysis

to compare an actual and a simulated series seems to offer considerable

advantages in situations where the behaviour of the simulated and actual
time series is such that ,if a visual comparison was made, it could reault
in disagreement as tp whether or not the two series were actually the same.

The technique is, in effect, a quantitative way of assessing qualitative

behaviour. However, it has a significant disadvantage in that, to produce
@ power spectrum which highlights business cycle behaviour, a fairly lengthy
data series is required, Such lengthy data series are not commonplace in the
U.K.

tone inca aceos ” Sulaeone apa

~ 80 -
Finally, we are planning an enlargement of the model to incorporate

the ateel and steel stockholding industries. This work is being conducted

in pursuit of the major objective of viewing the economy as an interconnected

network of major industries. With a finished composite model, policy-makers

should be able to assess the simultaneous effects of cyclical ‘demand

fluctuations on three major industries in the U.K. economy.

PRnee 1976

=m

REFERENCES

1, BALL J "Some aspects of the nature of large scale economic
: dynamic systems", in the proceedings of the symposium .
“The Dynamics of Economic Systems" held under the auspices
of the Institute of Measurement and Control, Imperial College,
London, 1976, (Proceedings available from the’ Institute of
Measurement and Contro}, 20 Peel Street, LONDON W8 7PD,
price £6.50.)

2, BRECHLING F and WOLFE JN "The End of Stop-Go", Lloyds Bank Review, No.75, pp.23-D,
. 19

3. CABINET OFFICE"The Future of the British Car Industry’ A report by the
Central Policy Review Staff, H.M.S.0., London, 1975,

4. CENTRAL STATISTICAL OFFICE Economic Trends Annual Supplement,
London, W.M.5.0.,1975.

5. CHATFIELD C The Analysis of Time Series, Chapman and Hall, London, 1975.

. 6. DANGERFIELD BC and STEPHENSON E “Inventory Behaviour in U.K. Manufacturing
Industry ~ Consumer Durables’! Private Paper
University of Liverpool, School of Busine:
Studies, 1973.

7. FORRESTER JW Industrial Dynamics, M.I.T. Press, Cambridge, Mass., 1961.

8. GRANGER C WJ and HATANAKA M Spectral Analysis of Reonomic Time Series,
Princeton University Press, 1964.

9... INGHAM I Balancing Sales and Production ~ models of typical business policies,
Hanagencet Publications Lid for the British Institute of Manegement,
London, 1971.

10, JONES Rt "A Reappraisal of the Periodogram in Spectral Analysi
Technometrics, Vol.7, No. 4, pp.531-542, 1965.

11, LUN $T "Trade Cycling ir U.K. Industry", Measurement and Control,
Vol. 8, pp. 152-156, 1975.

12, NATIONAL ECONOMIC DEVELOPMENT OFFICE "Cyclical fluctuations in the U.K. economy,”
: London, 1976,

13, NAYLOR TH Computer Simulation Experiments with models of Economic System
(Chapter 9), John Wiley and Sona, London, 1971

14, PARZEN E Time Series Analysis Papers, Holden-Day, San Francisco, 1967.

15, SAMUELSON P A Economics, 9th Edn., McGraw Hill, U.S.A,,1973.

16. TUKEY JW "An Introduction to the calculations of numerical spectrum analysis"

in Warrie B (ed.), Spectral Analysie of Time Series, John Wiley and
Sons, New York, 1967.

17, WILLDER NJ R "Manpower Planning in the light of economic cycles", in the
proceedings of the symposium, "The Dynamics of Economic
Systems," (See Ref. 1), London, 1976.

nated + AAS TERETE “TTR RCT

= 83 -
APPEND Ts DEMAND FLOY DIAGRAN-OF <I, NODE.

~

raw
forecast of
Sales

Smoothing
constant

(>)

DELAY:
3 Devays  |RDPRGI
\ eplenis
: PR ‘ u
“ds <———-—predoction NPRR, _ ened
vate, a Parks vecei- for pads
) 18 ing rate. acta
oR |) Beh im :
R 1 ely i a aa a }
Sales rcnihicnent pep 22 ’
fis) ae
a

- 85 -
APPENDIX IT
Spectral Analysis

down a given time series

The spectral: analysis method essentially brea!
into its component frequencies and estimates the relative strengths of these
frequencies. A plot of component frequencies against component strengths ~
called the power spectrum (or spectral density function) ~ provides a convenient
means of comparing two or more time series. In other words, two series are
compared in the frequency domain, where a time series is the sum of many sine
waves of differing frequencies, rather than in the more conmonly employed
time domain. If the spectral density function of an actual and a corresponding
simulated time series of a variable exhibit similar profiles, the simulated
and actual series must be in agreement with regard to that particular variable.

The computer program adopted here estimates the spectral density function
by smoothing the periodogram, following a method suggepted by P J Daniell (and
described by R H Jones}°which incorporates a fast Fourier transform. Daniell's
approach is generally viewed as an advance on earlier methods which operate by

transforming a truncated autocovariance function. Such methods require the

choice ofa suitable lag window such as those suggested by Parzed’ and Tukey
The program incorporates a routine for pre-whitening the data by extracting
any trend in mean and then taking firet differences of the residuals.

= 06 -

APPENDIX III: DOCUMENTOR LISTING OF THE MODEL,

DYSHAp DOrUNEWTOR,

ares
on
cy

APS nears.

HW ADSaHPS,
APR
an
om

n
feTARHLCTABE ARGS. R/N

paras,
Tans eb/0.287065/9 873

Tan
Arce

wens

AMPS ccuy ACTUAL uy

WAFGS. JODTOCOR, dKegn ged
68

#CUY ACTUAL BINISNED Go0ds stoce
FCUPNTHS) PaOBUCTION RATE
SCUINTHE) BALES RATE

DT OCPRR, IK=PER. JED

CUD ACTUAL PATS STOCK

SCUPATHSD paRT, RECEIVING RATE

SCUMTHAD PARTS 135UING RATE

ake PR de

sroce

= CUIMTHSD paRTS ESSUING MATE

eCUTHTHSD

ueTRUN RATE

Ko 0260.59)
%

73.13.3573, 975,
AFGS = CHTHS? BELAY Tu ADJUSTING FINIGHER Conds grocK.

2. Oe
Rtn

NCATNS) TABLE OF DELAY EM ADJUSTING FINISHED Gooos sr0ce

CU) ACTUAL PIUIBNED €nods gtOCK
CUD MORAL FTutBHeD Goods BT0CK

AMPS T64 42.0,259
PCMTHE) DELAY 1m ADJUSTING PARTS syocK
SCHTHSD TABLE OF DELAY IM ABJUSTING PARTS srOCK

Ape #CUD ACTUAL PARTS stOEK
WOR =CUD NORMAL PARTS STOCK
LCTABS APR AZUPS C4000. 7: ~
7412. 2518318 I0.78/0.45 058
° Saha) DELAY aw T.8UING pants
TAM —SCHTHS) VARLE OF DLLAY 1M ESSULKe paar
APR CUD ACTUAL PARTS s1O0CK
MPS CUD NORNAL PARTS STOCK

ADDER ReTAMML TARO ARGS,
Y VAbsmtO1 60/9 /6/3,.25/44
bebo
Tana
Aras

uegs

HAUGS ON Ie 2T
reer ray
HS) DELAY iW SATISFYING ParMaRY DENAND.

SCNYHS) CARVE OF DLUAY ON QATENEVING ORtMAnY BrHaND
CUD ALPUAL PInESHrD GuODe gTOVe

107 NOMHAL FIATSHED GunDs STOVK

3. Ga
ee

%. On
me

- 81 - :

A FARES He TABWECTARZ -RDD. R/S 746042 60,75),

VvAnzeD S70 PSNI 2/8 dd Ast,
FABER UCTY FACTOR FOR ADJUSTING RAW FoRFeAT
Tan2 44) ARLE OF CACTOR FoR ADJUSTING RAV FORECAST
SP) NCUZHTHG) guOOTHED PRINARY BEMAND.
ss SCUINTHS) EMOMTHED SALES
ALTSR ReSMOOTH CEMLIE CLT RD
© rarest?

LYSR | CUPHTHGY Lond TERN SALES WATE

se AQUINTAS) GALES RATE

Crys wChtns) LOMA T.

ALES RATE SOOTHING CON

AMES RO FS WOFACEE.K
HF5 —— ACUHTHS) MMOH TED FORECAST OF HALAS.

aes CUPHTHS) RAW FOREQAST OF SALES
FARE @C4) FACION 60x ADJUSTING RAW FORPEAST.

AONEGS KenpuSHoL TERK
C MeGchet Ss

Wres — eCUy MURMAL FINISHED Goods ETOCK
WEGEM « =CHYHSD NORMAL FINISHED GOODS STOCKEHOLOING
ATSR — @CUAHTHAY (ONG TERN Saved RATE

AMPS OND SH.KeBP ROLE
hex CUD MORDAL PARTS STOCK

WPSH —-MCIITWE) WORMAL PARIS GTOCKHOLDING
SPRD — #(WANTHS) guOO™WED PRODUCTION DEMAND

AMP TW KETABRLCTARA. SPAR. K/SSTI

WNPSHad,

VAM 403777517 .5/2.0/9 60
fiogu

1,2,0,299

ACNTHS) NORMAL PARTS ATOCKHOLOINE
TABS — SCHTHS) TABLE OB NuRMAL PARTE SrOCKHOLA!

SPRR —-SCUPHTHY) GMOO-WED PARTS RECEIVING RATE
ss SCUINTHED -BrOOTHED SALES,

RPAH. KLeDLINFS (01
W PADeetO.

cK DENBKOD

© neypRvet
PADR —-=CUPHTHS) PARTS DENIAND RATE
Pun ECUPHT HS) PRORICTIUN DEMAND
OFKPRD SCHTHES HELAY 1M E,.PLODING PRAPUCTION nEnand
L Pann ane

Ke PARE, Je0T= (PADR ska
b

W PAURAND DAE KIR

PADDH TUL BACKLOR O% PALS OEMAND

PADRE ACUIHT HRD AAT DEWAN RATE

%. On

10. 08

15. One
Sl te

| pong xevnah gonretene dneseZsn
w potusbap
neuy maretos 0) PRIMARY BFRAND

SEUINTHR) POTHAAY GEMAND RATE
sn SAUINTARD BALES RATE

A CUIMTHS) paRTs 18,UING RATE
CUD BAFKLOE Oy PAKTE DEMAND

MCHTNS) DELAY rw Te 8UINe PAMTS

ROR. KLMDFLAVS(PIR, JK, DPRD

Coheed
on SCUsHTHED paODUCTION RATE
Pin ECUINTHS) PARTS IS.UING RATE
DPR = #CHITHSD DELAY tH PRODUCTION

ey

APRD KeSUTTCH MES. Ke (OMFGR, RaahGS.£D/DAFQE.K)y SPD. ROC MEGS

X PABAS. KD RD

Cnet s
Pap ECUSHTHS) PRODUCTIUN DEMAND

Hea *CUsHTHe) MADIFIED FORECAST OF SALES

ees (uD NOMMAL FIuTSHED Gonds STOLE

AEGS — #CUD ACTUAL FINESHED GuODs sToCe

CARES ACHONS) DELAY IN ADJUSTING FINISHER @Qons ATOCK

Shp BEUIRTHS) BHOOTHED PRIMARY DEHA
8 CU) CONSTANT 70 PERMIT EVALUATION OF > POLICIES

SPRLAYNUERDPR, JK eDRRY
4.

PRR MEUSHTUSD DARTS RECELVING BATE
RDpR —-ACUIMTAS) REPLLMTSWMENT PARTS ORNAND RATE
RRP <CHTHS) DELAY tw RLCETVING REPLONIQHMENT pants

PABA. KLOCENPSTE@APS EDAD ALEAK.

8 ROPR.KLEMAKE
W PuPrettcn

Rope CUPNTHN) AE PLINES)MENT PARTS DEMAND RATE
PARR ECUPHTHRD PARTS DENAND MATE.

NPS EU) NORMAL PARTS 4TOCK

ApS CUD ACTUAL PARTS STOCK

DAS ECHTHSD DELAY rm ALJUSTING PARTS ByOCK

AR, JeDTe(POPR, vKaoRR, Jn?
cry
Opn CU) RFPLEMTSHNEMT DEMAMD FOR FARTS BArKLaG

AnpR —-LUsHTAS: QEDLIWESKHENT PARTS DEMANR O4TE
Pen | ACUAMTHS) PART, RECEIVING MATE

1“
16) Ne

’

7. Oo
IP tn

20, Om
20, 18
70. ac

24, On
atl tan

am
2 PoRPC ee CPOR.oke800) JehAE
 epareioon

‘ nape SAVE PutMtay OLWANE RATE

anes

Curae CHANEPS

cH
 FSpeet

. bi AST E: eokeh: ope SCUTH THR PREMaeY LEKI are
fe curetany asoteued sas . out stupatesy ontnsey steayn ave seurnauey :
Peony vonsenttna anton
toe seurnraey avocado oany sus
Caen ents) osu Sqc88 o4tr tneateree eonteaey oon 00170088 wots

1nPE BEAD PRORUETEAN DEMAND PERCENTAE CHANGES

P.reFtO DEMAND
Y DEMAND RAYE IMITEALLY

rn CUNT

agen
pont ecusHT HS) alt

© Farmed

or

y
PCUIMTAS) GROOMED PATHARY DEKAND

ACUPRTON) PRIMARY DEMAND MATE

«PR, 40408) JOKE
sawnsy yan0

Parc aC) Pannliernay Rare DEAceHTAGL Cwaut
Pe AEUHTHRD PRODUCTION RATE

PoRd — SCUPMTHE) PRIMARY DEMAND CATE WIT PALLY

1” 1b
Bott
tures) qnatrare PanpueTiou vnene
ntainiasi seabed inate 4 iaee aii itosanbe He. es
Pret on M6. tee
“SCHTHED PRODUCTION DEMAND GHOOTHING CONeTANT eoeperetens tape SCD) SAVES WATE PESCENTAGE CHAKGES,
. ;  kamanNacER
Seurnranyioeencavcvenain sare iabtia
an 7 corntusy onthay venue ate suttnatay
ett .
turns geonrate anse enceivine ante
SCUPATASY Ponts RE EIViNG Mate 8 PESRE ROC CAPE KOAMEPS EDO INAH 6r10 He Gon
Tee aN ESE aes ave snail hind

SCWTWS) DARTS ACEI VENG BATE SHiDOTWEMG CONSTANT

scutes

OTWED PART BALES.

SCUIMTHED GROOTHED Batt a SIZES WEAne Kent Cun Tate satcony aoe . €
SCMTKOD PAST BALES % roy STUD ACTUAL PANT S1OCK
s AUTRE CUD ACTOR we stk
Tae
i na hcl a azepsusaseneaamiats - Rebs
Uma) ntLar 10 ertarvtve paimany semana finest : BORE
ca SianaeaRcara cemteE
; seal, ae SNNMAY SEMA WATIANNY
HG Pete. dadi
ey
fi Gaba gaanes
<stuo WT
ha, "seni anion sandcanaciaing- itd
4 Acer rocaes.aetendtntton oan
eet
BE By
APGEPE ETD ACTOR PIQISHED GoODS STOLK PERCENT cuaners
Arak cus Actny patton fanny ance
ae
WEGAM  ReMTHED 9 A PENISHEL GOMDS stOCeNOn INE 7 . : J

APPENDIX IV mal?
LISTING OF CONSUMER DURABLES MANUFACTURING INDUSTRY MODEL

DYSNAP HHITE+USESCALES:

oc
8 CONSUMER DURABLES MANUFACTURING SECTOR

NOTE a
NOTE EQUATIONS OF THE MODEL :

AGS .J#DT CPR, JK-SR. JK)

APS .K=APS , JHDTAC PRR. JK-PIR «JK?

AUIPS .K=AMIPS . HDT RCPIR. JK-PRJK?

DAFGS .k=TAGHLC TABI +AFGS .K/NFGS .K»012+8.25)
DAPS .K= TABHLC TAB3+ APS .K/NPS Ks 19 298.25)
DIP.K=TAGHL( TABS: APS .K/NPS Ky Qs 1 .7598.25)
DSPD..k=TABHLC TABS + ATGS -K/NFGS K+ Or 1.7510.25)
FARTS .K=TABHLC THB2s SPD.K/SS .Ks@>2+8.25 >
LTSR .K=SMODTHC SR. JK» CLTS>

ES KERTS .KATARTS

NF GSHALTSR.K

TABHL( TAB4, SPRR.K/SS.K» 1920.25)
PAOR .KL=DL INF 3¢ PRO Ks DEXPRD >

PRO.K=SHITCHCHES .K+¢ CFOS .K-AFES .K )/DAFGS .K 2» SPD.K4¢ CNFGS.K-AFGS.K 27

DATGS.K>4R>
PRR.KL=OELAY3CRDPR IK »DRRP >
ROPR..KL-NX¢ Gy PADR .KL+¢CNPS..K-APS..K)/DAPS.K >>
ROPRB.K-ROPRB. JFDTXCROPR . JK-PRR «JK >
RFS.K=SS Ks FHACCSS .K-SPS.K 2/CSPS9
SPD, K=StIOOTHC FOR. JK» CSPD>
SPRU .K:-SMOOTHCPRD «Ks CSPRD?
SPRR .K=SHOOTHCPRR JK» CSPRR >
SPS .K-SHOOTHE SS.KsCSPS >
SR.KL=PORB.K/D5PD.K
95 .K+SHOOTHCSR .JKsCSS>
8/0 ..25/0.5/1 073 .0/3.3/3.573,5/3.5
O8.5/0.757171/1 271.471 6718
171,6/3.0/3.96.0
372:75/2.5/2.0/1.0
TABS= 196607472 .25/1 .571/0.75/8.65/8
TABG=18E60/9-6/3.2571 571 .287E71
note »
NOTE INITIAL URLUE EQUATIONS

L
t
L
a
a
a
A
a
A
a
a
a
a
R
L
L
R
R PR.KL*DLLAT3C PIR. JK» DPR>
a
x
R
R
L
a
a
A
A
a
R
A
T
T
T
T
'
tT

N
NAPS:
NN ALIPS-DPRAPIR
N PIR=1000
N ROPR: 1020
NY PADR=-1000
N NPSH-3.0
N PADRD:-DIFAPADR
N
N
N

PORD=DSPOXPUR

posta se 0

-92-
LISTING OF CONSUMER DURABLES MANUFACTURING INDUSTRY MODEL

NN RDPRB=DRRPARDPR

WN SREPDRIN

NN PORINS1600

NOTE

NOTE SUPPLEMENTARY OUTPUT EQUATIONS
NOTE

§ AFGSPC .K=¢AFGS .KR100>/CPDRINNFGSH>
§ PORPC .K=<PDR.JK™1@0)/PDRI

S PROPC..K=CPRO.K™1009/PDRT s
S PRPC .K=(PR.JKR1G@>/PORT

S SRPC.K=(SR .JKH18)/PORT

S TFSPC.K=CCAPS .K+RUIPS .K 8100/6080
S TFS.K=APS .K+AHIPS .K

NOTE

NOTE CONSTANTS OF THE MODEL

C CSPRR=3
C CSPRO-6
Cc csPS=1
© css=3
© DCXPRO=1

Cc PORI=10@0
NOTE
NOTE DOCUMENTOR EQUATIONS
NOTE
D AFGS=(U) ACTUAL FINISHED GOODS STOCK
APS=(U) ACTUAL PARTS STOCK
AUIPS=CU) ACTUAL H.1.P. STOCK
DAFGS=(MTHS> DELAY IN ADJUSTING FINISHED GOODS STOCK
DAPS=(MThS> DELAY IN ADJUSTING PARTS STOCK
DIP=CMTHS) DELAY IN ISSUING PARTS
DSPD=CHTHS> DELAY IN SATISFYING PRIMARY DEMAND
FARTS=(1) FACTOR FOR ADJUSTING RAN FORECHST
LTSR=CU/MTHS> LONG TERM SALES RATE
HFS=CU-NTHS) MODIFIFD FORECAST OF SALES
NFGS<CU> NORMAL FINISHED GOODS STOCK
NPS=CU) NORMAL PARTS STOCK
NPSH=CHTHS > NORMAL PARTS STOCKHOLDING
PADR=CU/MTHS) PARTS DEMAND RATE
PADRB'<U> BACKLOG OF PARTS DEMAND
PORB-CU) BACKLOG OF PRIMARY DEMAND
PIR<CU/NTHS) PARTS ISSUING RATE
PR=CU-MTHS? PRODUCTION RATE
PRO-CU/NTHS) PRODUCTION DEMAND
PRR=CU/TITHS > PARTS RECEIVING RATE
ROPR(U/NTHS> REPLENISHMENT PARTS DEMAND RATE
ROPRB-CU) REPLENISHMENT DEMAND FOR PARTS BACKLOG
RFS-CU/TITHS > RAW FORECAST OF SALES
SPD-CU/TITHS > SMOOTHED PRIMARY DCVAND

soDD0DDD oD SESS OEDOOOODOCD

-93-
LISTING OF COrSUNER DUSAOLES MANUFACTURING INDUDTRY MODEL

SPRR=CU/MTHS) SHOOTHED PARTS RECEIVING RATE
SPRD-CUCHTHS > SHOOTHED PRODUCTION OENAND
SPS=CU-MTHS) SMOOTHED PAST SALES
SRCUCMTHS) SALES RATE
SS=CU/NTHS? SMOOTHED SALES
TABI=CHTHS> TABLE OF DELAY IN ADJUSTING FINISHED GOODS STOCK
TAB2=¢1) TABLE OF FACTOR FOR ADJUSTING RA FORECAST
TAB3=CMTHS> TABLE OF DELAY IN ADJUSTING PARTS STOCK
TAB4=(MTHS> TABLE OF NORMAL PARTS STOCKHOLDING
TABS=CHTHS> TABLE OF DCLAY IN ISSUING PARTS
TABG=(NTHS) TABLE OF DELAY IN SATISFYING PRIMARY DEMAND
AGSPC=(1> ACTUAL FINISHED GOODS STOCK PERCENTAGE CHANGES
PORTC=C1) PRIMARY DEMAND RATE PERCENTAGE CHANGES
PROPC=C1) PRODUCTION DEMAND PERCENTAGE CHANGES
PRPC=(1> PRODUCTION RATE PERCENTAGE CHANGES:
SRPC=C1) SALES RATE PERCENTAGE CHANGES
TFSPC=C1) TOTAL FACTORY STOCKS PERCENTAGE CHANGES
TFS=CU) TOTAL FACTORY STOCKS
CLIS#CHTHS> LONG TERM SALES RATE SHOOTHING CONSTANT
CSPD-CMTHS) PRIMARY DEMAND RATE SMOOTHING CONSTANT
CSPRD=(NTHS) PRODUCTION DEMAND SMOOTHING CONSTANT
D CSPRR=CHTHS> PARTS RECEIVING RATE SMOOTHING CONSTANT
© CSPS-CHTHS> PAST SALES RATE SMOOTHING CONSTANT
D CSS-CHTHS> SALF'S RATE SMOOTHING CONSTANT !
0 DEXPRD-~CMTHS> DELAY IN EXPLODING PRODUCTION DEMAND
D DPR=CNTHS> DELAY IN PRODUCTION
D DRRP=CHTHS> DELAY IN RECEIVING REPLENISHMENT PARTS
D+ FH-CHTHS> FORECASTING HORIZON
DD PDRI=CU-HTHS> PRIMARY DEMAND RATE INITIALLY
DD NFGSH-CRITHS > NORMAL FINISHED GOODS STOCKHOLDING
o
o
o
.

eoscopDoS sooo oOSCOOOD

R=€1) CONSTANT TO PCRMIT EVALUATION OF 2 POLICIES
POR=(U/NTHS >) PRIMARY DEMAND RATE
OT=CHMTHS) SOLUTION INTERVALCO.2)
TINE=(NTHS > MONTHS:
NOTE i :
NOTE INPUT VARIABLES AND CONSTANTS
NOTE
R FOR.KL=FORI+STFPC 200+ 12>
noe :
NOTE GUTPUT INSTRUCTIONS
NOTE
PRINT AFGSPC»PORPCs PROPC»PRPC+ SRPC» TFSPC
PLOT PORFC*D) PRPC=P 1 AFOSPC=Gs SRPC=S¢ 89s 160)
SPEC DT=@.200/LENGTH-1SG/PRTPER=1/PLIPER=1
RUN STEP INCREASE IN PRIMARY OENAND
+
ia)

~oh =