292
DYNAMIC MODELS FOR PLANNING TOURIST COMPLEXES
Habib Sedehi
ENIDATA
Via Marconi 29/1
40122 Bologna Italy
Paola Valli, Paolo Verrecchia
TEMA
Via Marconi 29/1
40122 Bologna Italy
ABSTRACT
Planning tourist facilities is a highly complex task. It is ne-
cessary to evaluate carefully, with an interdisciplinary ap-
proach, all the variables of a technical, architectural, commer-
cial, economical and financial nature that may be involved in a
given project, without however ignoring the natural resources
of the environment where the facilities are to Be set up.
For a correct evaluation, these resources must be considered 1i-
mited and seen as a wealth that can be exploited but not wasted,
used but not destroyed.
The approach outlined above is all the more important in coun—
tries like Italy, for instance, where there is a risk of over-
exploiting the natural resources of the environment.
In all but exceptional cases, an evaluation that does not take
the above principles into account will result in a tourist en-
terprise that is ultimately a failure, as it degrades, often ir-
reparably, the natural environment until it ceases to be an ade-
quate source of revenue.
This paper describes an integrated approach which provides, by
means of simulation techniques, tools for a proper implementation
of tourist facilities taking into due account all the variables
and constraints involved, and likewise for the assessment by the
Public Administration authorities of the wisdom and soundness
of projects submitted to them for approval.
1. INTRODUCTION
The simulation model of a firm or company, that can be
used for the design of the company itself or its development,
must have a sufficient degree of descriptive detail to allow
all the necessary evaluations.
Generally speaking it is not enough to consider a company
as merely an economic phenomenon. A company is always a far
more complex phenomenon and it does not usually suffice to know
whether it is able to support itself economically and make a
profit; it is also necessary to know how it uses the resources
at its disposal in order to yield profits and how it interacts
with the market.
A company therefore has to be viewed from at least three
different standpoints, and at least three different models have
to be prepared:
a) A ‘physical model' describing the process according to which
certain raw materials, with the aid of particular resources,
are transformed by the company into the product
b
A ‘market model’ describing the relationship of the company
with its market, taking into account the initiatives of com-
petitors
c) A ‘financial and economic model' translating each company phe-
nomenon into monetary terms and giving the economic balance
of the operation to check its capacity to yield a profit.
Clearly the ‘financial and economic model' will have a
structure that remains unchanged, whatever the type of company.
Since this structure is based on accounting principles and the
juridical grounds of company management, thé nature of the pro-
duct or of the services offered by the company are irrelevant.
293
At the most, there may be different models in that they have a
different degree of detail, according to what one wishes’ to
highlight for evaluation.
The 'market model', and even more so the ‘physical model!
are specific to the type of company to which they refer and are
therefore studied on a case by case basis.
In our case the company that is to be studied offers its
clients tourist services; by using the natural resources of a
site and adding accommodation: structures and the related infra-
structures, it offers its clients the possibility of staying in
a pleasant place in exchange for the payment of an appropriate
price.
Thus the ‘physical model’ must describe the evolution of
the site conditions as a function of time accarding to the use
to which the site is put (number of people present, effective-
ness of the infrastructures, type of clientele and its aggressive
ness towards nature and the accommodation structures, etc.). Con-
versely, the 'market model' must describe the quantitative and que-
litative evolution of the clientele as a function of time taking
into account all the important variables (degree of crowding,
deterioration of the natural environment in the course of time,
price policy, model of behaviour of different types of clients,
ete.).
In this paper we shall briefly describe the approach fol-
lowed for the model of a tourist concern; we shall describe with
a certain degree of detail the ‘physical model’, briefly refer to
the concepts of the 'market model’, and in the present case, leave
aside the ‘financial and economical model’.
This model has been developed according to methods derived
from Industrial Dynamics and it will shortly be tried out for
294
for some practical cases in Sardinia. The results of the ex-
perimentation will be available in the future.
2. PHYSICAL MODEL
2.1 Description of the 'trend' of the natural species present
Let us assume that we start with conditions in which a
small local population lives in equilibrium with the environment
using the existing housing and infrastructures that are ade-
quate for its requirements. A tourist complex (for example a
village) able to accommodate clients on an assumed seasonal basis
is built is this location (for instance a seaside village near
@ pre-existing fishermen's village). It is assumed that the system
is delimited by an ideal line circumscribing the surrounding
area up to the distance that can be reached on foot by the
clients.
In such a situation the natural environment can be des-
cribed by a vector of variables y,,V,.-.¥,, each of which re-
presents quantatively the presence of a living species, whether
animal or vegetable, which is characteristic of the environment
and which indicates, with its increase or progressive disap-
pearance, the present conditions of the environmental system
one wishes to study.
The equation that governs the trend overtime of one of
these species is of the type:
ay,
i
GQ)
i i 2
= 8,4 (K)- Kj) yy, - ag ny - ay yy
where:
8, : stands for what is imported (for examplt, in the case of a
vegetable species, S is the contribution made to species
y, from outside by a team of gardeners);
OSD, : represents the contribution of nature to species
i doe get pt
y, in terms of birth (Ky) and death (K3)5 Kj-kK, isu
sually expressed as OKs
represents the destruction brought by man to spe-
cies y, (n = the number of people present) which is
found to be proportional by means of a coefficient
a, (the specific aggressiveness of man towards spe-
cies y,) at product n y,, which represents the pro-
bability of an encounter between a man and an indi-
vidual of species y,;
E stands for the self-limitation of the species that
occurs when individuals of the same species y,, con-
tend for living space.
This first version of. equation (1) contains an oversim-
plified term, in respect of reality. Indeed, in the termo, ny,
we have considered that all the people present have an equal ag-
gressiveness towards species y,. In practice one should consider
a vector of classes of people:
AoMy ress oMy
where at index 'o' we insert the value referring to the local
inhabitants. In this case equation (1) becomes:
ay, m 2
ae 8+ OK yy “Ee 5 715 5 7 YG (2)
where 0, Tepresent the specific agressiveness of the class
of men n, towards species y,.
J
It should also be noted that we have qonsidered the effect
of the relative interaction between two different y, species to
be nill. If we wished to take this effect into account, equation
(2) would become:
dy, n
ae 28, HOR y 54 Vy ~Yoctix WX
where coefficients 4,, represent the specific agressiveness of
species y, towards species y,.
A series of general equations like (3) can become very
numerous if we wish to consider in detail the species present
on the site. Since one is likely to find a few hundred living
species in any natural place, it is clear that a complete appli-
cation of (3) would raise great difficulties, also in deter-
mining all the coefficients. If then we think of the other se-
condary effects that have been overlooked, such as, for example,
the indirect effect of man on species y, by means of his refuse,
it will be readily understood that before long the systems of
equations can become unpracticable.
However it should be borne in mind that the objective of
this model is not to evaluate in depth the evolution of the na-
tural ‘environment; it can very well be limited to detecting symp
toms of deterioration that would already indicate reliably an
excessive exploitation of the natural resources available.
It is therefore possible to have many simplifications that are
not far removed from our objective. In the present case, owing
to the limits imposed by this paper, we shall only deal with a
very simple case.
First of all it comprises only two species. One of these
will be indicative of the average situation of the natural en-
vironment: on the one hand it will be the most characteristic and)
evident.one, and on the other it will have the characteristic
295
of an average resistance to deterioration (in the case of a vil-
lage on the coasts of Sardinia this species could be the "ME-
DITERRANEAN MAQUIS").
The second species that we shall examine is a species that
is characteristic of very good conditions from an environmental
point of view. That is to say, it is a very delicate and 'nobie!
species that does not stand up well to even slight changes in
the environmental conditions (there are numerous examples of this
type in many areas: the red algae that give colour to the waters
of lake TOVEL in the Alps in spring, some types of butterflies
or flowers, etc.).
When applied to the two selected species, equation (3)
becomes:
Whe: 4 bx
© Bot Oy My
wes tax
ae ~ F2 OK YQ ~
It will be seen that the multiplicity of classes of clients
is maintained in both equations and that (5), which represents
the trend of the noble and more dslicate species, maintains
also the term that expresses the agressiveness of species y,
in respect of y,.
Before proceeding with other variables, it should be noted
that in our case it is difficult to operate with the variables
chosen: an absolute definition of the quantity of species pre-
sent is a difficult task.It will therefore be preferable to oper-
ate with adimensional variables.
In order to do this wé shall take as a reference condition
one in which only local inhabitants are present (n,=n,=...,n_=0)
2
and equilibrium is assumed. Under these conditions (4) becomes:
. oy ce
0 8K, ¥ - 819 MQM Ay
*
where y, is the value of y, that is reached when only local in-
habitants are present on the site. From (6) we get:
¥, = 0 (when the local population totally destroys species
y,, which is a case we can rule out)
Moreover, in order to make all the other variables adi-
mensional, we assume:
S = O.5 75 yy (which means that 8° is the value given to
what is imported in order to compensate for
the destruction caused by the local inhabi-
tants alone)
y.
y= (quantity of species y, in relation to the
yy quantity present in the above conditions of
equilibrium)
n,
No = (quantity of class j tourists in relation
2 to the local inhabitants)
a o
y° a (agressiveness of class j tourists in re-
10 :
lation to the aggressiveness of the local
inhabitants)
*
If we divide both the members of (4) by y,;, we get, after
some simple algebraic transformations:
296
o "0
8K,
040%,
+ “10% s
~ (7)
6K, §
In this form the equation relating to species y, is now much
easier to tackle. Let us now have a look at the coefficients:
6K, + can be expressed as aoa where T, is the regeneration
time, that is to say the time required for species
y4 to reappear throughout the territory after serious
damage (eg. a fire).
is the relation between the capacity for destruction
of species yy by the local inhabitants and the ca-
pacity of the same species for self-generation. We
can assume y,< lotherwise this would mean that the
inhabitants had already completely destroyed species
y, in the past.
ij constitute a vector of values to be estimated which,
with 1 as the aggressiveness of the local inhabitants
towards species y,, assign a relative value to the ag-
gressiveness of the various classes of tourists to the
same species.
Equation (7) thus becomes:
i
7 2
fp - ys 4] Ye =) ¥ +
(8)
Following a similar process, equation (5) can be trans-
formed into adimensional variables, and becomes:
a} og 2
a” "| [: “% Ys (a, Ny) }e ~ BYY, — GQ ~ ¥y-B,)¥,
s
+ 1, (9)
Ps
2
In (9) the symbols have a meaning analogous to those in
(8), with the further introduction of:
~ ie Ya
6K,
which represents the relation between the aggressiveness of spe-
cies y, in respect of species y, and the capacity of species
Yp for self-generation.
In the case of the 'noble' species y,, which is assumed to
be very delicate, we can introduce another simplification by
supposing that the aggressiveness of the various classes of
tourists is equal. This amounts to considering that this species
is so delicate that the mere presence of man is harmful to it,
regardless of the specific behaviour of the various classes of
tourists,
With this simplification (9) becomes:
1 = 2
oe t, [Lh - 7, 8) N]¥, - 8Yy¥, = (1 - 7 - 8,)¥8 +
~
Ino”
(10)
a
we
’
297
+
lL
2.2 Other variables that are indicative of the environment
Two other variables are needed in order to complete the
description of the environment surrounding the tourist complex
that one wishes to evaluate; one of these defines the ‘trend!
of the refuse produced, and the other the appearance of possible
parasite species marking the beginning of a situation of environ
mental deterioration.
Naturally, in the case of these variables too,it would be
necessary to identify a vector of magnitudes. In point of fact,
different types of refuse behave in a very different manner, and
thus the appearance of every species of parasite may not only
announce the beginning of a different degree of environmental
degradation, but may also have a very different effect on the
various types of tourists present. It is therefore only for the
sake of simplicity that we shall refer to only one variable to
identify refuse and also to a single parasite species.
The basic equation for refuse is:
nm
aw
ae Ya -aw - f(w) (a1)
where the first term represents the production of refuse by the
various classes of people present, the second term the self-
disposal of refuse by natural processes and the third the dis-
posal of refuse by means of a cleaning service; to f(w) is at-
tributed a 'trend' of the type shown in Figure 1:
12
t(w)
tlw) =e
Figure 1
The inclination of the sloping part of f(w) depends on the
time the cleaners can operate. Thus
w
ifw<w, fw) =F
w
ifwo>w, tlw) =
in the second case the cleaners cannot eliminate all the refuse,
that will continue to accumulate.
Expressed in adimensional variables and assuming that the
refuse is the same for the various classes of people present,
(11) becomes:
aw
cE (12)
where ifw<w, f(w) woe i
298
w is the quantity of refuse present under equilibrium conditions
with only the local inhabitants
w is the present quantity of refuse referred to w
The basic equation for the parasite species (y,) is as fol-
lows:
¥a
- % fg(t) +8, (13)
It will be noted that this equation is similar to the ones used
for the other natural species present. The following type of pro
cess has been assumed. Originally the parasite species was not
present; it is continuously imported from the, surrounding en-
vironment (S,); it is subject to the negative effects of the
ny), of the self-
actions of the people present ( - 6, y4 ~
of disinfestation
limitation of the species (- 4, va),
(- = #,(t)); the only term that is positive and hence favour—
able'to the parasite species is g(w).. y, because we should nor~
mally introduce (by means of g(w)) a threshold below which the
positive effect becomes nil. However since we have only one para
site species, it is worth taking the species that is most likely
to appear, and thus the term g(w) . y, can be replaced by K, y,
3
where K is a constant. With regard to this is made up
y.
Seb,
Vo ™ 3
of a factor q that represents the decline in the action of dis
j 3 _
infestation, and by a function (£3 (t)) with a square wave con-
figuration that represents the action of disinfestation itself.
Expressed in adimensional variable, (13) becomes:
|
& a) W Ya Ma bss *
3
T,
3
~ = Bel) tye OD (14)
In the above equation Y, refers to the quantity of parasite
species present with only the local inhabitants, without refuse
removal and without taking self-limitation into account (which
is negligible in such conditions): the reference value is y,.
the regeneration time of the parasite species in the
presence of quantity of refuse w (generated by the
local inhabitants only)
: the relation of T, with the time T,, needed for the
local inhabitants alone to destroy the parasites with
out taking their’ regeneration capacity into account
s the presence of the parasite species under equili-
brium conditions in the site considered completely un
inhabited
Bigg the time needed for the area to return to equilibrium
conditions, after a total. destruction of the parasite
species,only with S, imported from the surrounding
environment.
2.3 Other variables not relating to the natural environment
Three other variables that complete the physical model
framework have been introduced.
The first refers to the state of the buildings and related
equipment by means of an equation of the type:
299
15
2 OZ NAL 2 (15)
where 2 represents the quantity of a certain type of efficient
equipment, S, is maintenance carried out by man, e@2 is the de-
terioration due to use, and 4,2 is the deterioration due to aging.
The second is the level of crowding that greatly affects the
degree of satisfaction of some classes of tourists, and is ex-
pressed by an equation of the type:
2
ig ef-n/ny) (16)
j
where (n being the total value of people present), oy is the cha-
racteristic value of each class of tourists and represents the
environments greater or smaller capacity to withstand the level
of crowding. .
The third is a variable that identifies the cost on the
site of indispensable goods and commodities and identifies the
rise through a series of thresholds (with greater crowding)
from a normal cost to a higher cost level, due to the fact that
supplementary structures have to be introduced.
The trend of the variable (c) is shown in figure 2.
Also these equations have been translated in adimensional
variables for a homogeneous use in the model.
16
Ge
oy
C,
23
c
Lr “
cy
|
n,n, An 1
+ 4 n
a a 0
0 ‘0
Figure 2
3. MODEL OF RELATIONS WITH CLIENTS
The ‘market model' that has been prepared is at present
extremely simple and has the sole aim of allowing a first ex-
perimentation of the model with a view to focusing and adjusting
the physical part and the related parameters.
Consequently the model that describes relations with
Clients is simply a function of the ‘image' offered by a tourist
enterprise.
The present model has been developed on the basis of the
following principles:
a) It is assumed that the demand for tourist services is plenti-
ful (this is true of Italy).
b) It is assumed that there will be no promotional activity ex~
cept when the initiative is launched and that thereafter the
300
7
advertising message will be transmitted by the Clients who
have already made use of the service.
c
Three classes of clients have been defined, with a different
sensitivity to the different variables of the physical mo-
del and differentiated according to the trend over time of
client attendance.
The curves of client attendance shown in Figure 3. have
been preliminarly assumed.
CLIENT
MONTHS
JFMAMJIS
Clients type 1
Figure 3
The ‘image' is determined as a function of the variables
of the physical model - i.e. natural species, crowding, equip-
ment, and cost of living - in the period under consideration.
This image is measured in terms of the number of people,
subdivided by type, who request the tourist service. It will be
recalled that adimensional variables are adopted also for the
market model. Thus, the number of tourists is expressed in re-
lation to the local population.
At the end of each season, an evaluation is made of the
level of satisfaction of the various classes of clients as a
function of the image offerted. At this point the user can in-
fluence the image variable, as it has been proposed by the model
for each type of tourist for the following year; it can be con-
firmed or modified on the basis of the constraints imposed by
the structure, the state of the environment and also commercial
decisions.
4, SIMULATION MODEL
fhe mathematical model described up to now has been trans-
lated into a computer simulation model by means of the MDS
methodology that has been developed by TEMA on the basis of
Industrial Dynamics concepts.
It is not possible here to go into the details of this
methodology and the models management package that was developed
in BASIC on HP 9845 and in FORTRAN on IBM in TSO and CMS environ
ment. However, the attached bibliography can be consulted for
further details.
We shall merely give a graph of the main subsystems that
constitute the model at its present stage of development, in-
301
dicating also the state variables (levels) and their variations
(rates) .(see figures 4, 5 and 6).
The coefficients of the equations are the parameters of
the model that can be checked and/or programmed for all the
duration of the simulation.
The results are given hereinafter of two simulations made
in different conditions of refuse collection, considering all
the other conditions unchanged, namely:
- curve of tourist attendance (Figure 3);
- sensitivity of classes of tourists to the quality of the en-
vironment (greater for class 1 and decreasing for the others);
- behaviour of natural species.
The simulation is made for a ten-year period at monthly.
intervals. ‘
At the end of each year the ‘image! proposes a certain
number of requests, The tourists present the following year are
limited to 3 times the local inhabitants. The surplus of requests
is refused subdividing it between the three classes of tourists
at the rate of 20% in the first, 30% in the second and 50% in
the third.
The graphs represent the trend of the species and refuse
(Figures 7 and 9) and the trend of the image, that is to say the
number of requests for the tourist service (figures 8 and 10).
5. CONCLUSIONS
The model described in this paper is, as we have already
pointed out, a first approach to the problem of evaluating a
tourist enterprise. ~
20
This approach can have two different lines of development.
It can be used as a planning tool by the public administration
to evaluate the impact of tourist enterprises on its own ter-
ritory, as well as the corrective action that it must take or
require of entrepreneurs, It can also be developed along com-
pany lines by constructing a model with which to evaluate the
economic return of a tourist enterprise, thus keeping under con-
trol the costs of the investments represented by both the in-
frastructure and maintenance of attractive environmental condi-
tions.
The following phase will be experimentation of the model.
This experimentation will be carried out with the aid of inter-
disciplinary expertise to make in the first place an accurate
check of the environmental model, with the identification of
the appropriate species relating to a specific ‘case and measure-
ment of the related magnitudes.
Next the analysis of the market model will be developed
in greater detail so as to determine, also through the direct
experience of operators in this sector, any further variables
that may affect the choice of the tourist service offered.
Lastly the model is completed by the financial and economic
subsystem that determines the return of the tourist enterprise
in economic terms.
302
22
au ten
SPLOIS SURGYSTIM LQUPMLNT SUBSYSILA
Equipment
installed
State
of.
species
92: —: average species (Y,) ——» Equation (8) Equipment : (2) —————> Equation (15)
: noble species (¥,)* ——» Equation (10)
: parasite species (¥,)——» Equation (14)
: refuse species (w) ———» Equation (12)
Figure 5
Figure 4
303
23
THRGL SUBGYSILH
(noe Tage due
i to crowd
lining total ‘tat
St; - Clients type 1
nm 3
” "og
Figure 6
24
Trend of SPECIES
a
Pe 8
AVERAGE SPECIES
NOBLE SPECIES
PARASITE SPECIES
REFUSE SPECIES
Figure 7
Trend of IMAGE
CLIENTS TYPE 1
CLIENTS TYPE 2
CLIENTS TYPE 3
Figure 8
304
25
@s
AVERAGE SPECIES
NOBLE SPECIES
PARASITE SPECTES
REFUSE SPECIES
Figure 9
Trend of IMAGE
eo?
CLIENTS TYPE 1
CLIENTS TYPE 2
CLIENTS TYPE 3
Figure 10
305
26
BIBLIOGRAPHY
{11
lal
{3
141
ts]
l6}
\7t
Is]
Ig
{101
faa
J.W. Forrester, Industrial Dynamics, New York (N.Y.),
John Wiley & Sons Inc., 1961
J.W. Forrester, Principles of Systems, Wright Allen, Cam-
bridge Mass., (trad, It, Principi dei Sistemi, Etas Libri,
Milano 1974)
E. Bertezzaghi and S. Mariotti, Modelli per le decisioni
strategiche aziendali, I1 sistema MDS-TEMA (ENI), Angeli,
Milano, 1983
R.G, Coyle, Management System Dynamics, New York (N.Y.),
John Wiley & Sons Inc., 1972
1. Popper, La Dynamique des Systemes, Paris, Les editions
d'organisation, 1973
De Maio A., Barezzaghi E., Brivio 0., Zanarini G., Infor
matica e processi decisionali, Angeli, Milano, 1982
V. Marrama, A. Iovane, M, Tenenbaum, Economia del Turismo,
Angeli, Milano, 1982
E,Bertezzaghi, S. Mariotti, S. Vassallo, MDS, un modello per
le decisioni strateghiche; L'Impresa, n.1, 1982
E. Bartezzaghi, S. Mariotti, S. Vassallo, Come usare il
modello MDS per le decisioni strategiche, L'Impresa, n.3,
1982
H. Sedehi, Progettazione delle risorse umane con 1'aiuto
del computer, DATA MANAGER, 1983
G. Selva, A. Trebeschi, $, Vassallo, Tecniche decisionali
ed informatica: Modelli dinamici per strategie (MDS), Con
gresso Iseo, St, Vincent, October 1980
112]
1131
ja41
lis]
27
E. Navone, S. Vassallo, Evaluation of Investment Project
in a New System in the Chemical Industry, VARNA 22-26
September 1980
Various authors, Dynamique des Systemes et Analyse du
Changement, 6éme Conference International, Afcet, 5-7
November 1980
V. Gervasio, Esperienze di sistemi di supporto alle de-
cisioni nelle imprese, Convegno Aica, Padova
E, Bartezzaghi, S$; Mariotti, H. Sedehi, A Dynamic Simula~
tion Model for FIRM-System Strategies, 7° Symposium tiber
Operation Research, St. Gallen, 19-21 August 1982
306
