THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 415
MURCIA A/I, A MIXED SYSTEM DYNAMICS AND LINEAR PROGRAMMING
MODEL FOR REGIONAL INVESTMENT PLANNING
a) a)
(3) (2)
Toval, A.'''; Requena, A.''’; Martinez, S.‘~'; Monreal,J.
(1) Escuela Universitaria de Informatica. Universidad de Murcia
(2) Facultad de C. Econémicas. Universidad de Murcia
(3) Instituto de Economfa Agraria y Desarrollo Rural. Consejo de
Investigaciones Cientificas (CSIC). Madrid.
Abstract. When distribution of economic goods, equipments,... ta
kes place among different regions, it is expected to carry out 7
in an optimal way, considering "optimal" the way of distribution
that assigns more to the neediest regions; thus, numerous fac- /
tors such as economic conditions, actual equipments, social con-
ditions, population, etc, should be taken into account.
‘The presented model has a double aim: firstly to show the pre~ /
sent behaviour of distribution system of investment in Comunidad
Autonoma de Murcia, regionally, and secondly to get this distri-
bution to optimize a linear function that represents the regio-~
nal social welfare as a consequence of the social welfare in /
each region of the Community and dependent on linear constraints
To reach these objectives, a mixed model that combines both sys-
tem Dynamics and Linear Programming techniques is constructed ;
a relation between both procedures is established in order to si
mulate.both the natural behaviour of the distribution system and
those decisions ‘that make this distribution to be optimal.
Along this report the method carried out to handle mixed models/
as well as the particular model MURCIA A/I are described.
INTRODUCTION
In last years a centrifugal process is carrying in the structure
of the Administration of Spain and the Regional governments ta-~
king actions to know the changing conditions and to improve the
dynamics of the economical and social activities.
This paper takes part of an initial study of the Comunidad Auto-
noma de Murcia to establish an optimal way to assign the invest—
ment. The scope of the work is centered in the use of the System
Dynamics methodology combined with the Linear Programming proce-
dures in order to produce a simulation of the behaviour of a dis
tribution system, in which the gap of the several factors deter:
mining the "necessity" is minimized. z
In traditional dynamics systems simulation, various types of va~
riables are handled in order to understand the behaviour of the
systems by means of the behaviour of the variablds along the ho
rizon time. This behaviour is usually depicted trough mathemati-
cal functions which depend on either other system variables, pre
vious values of the same variable or constants.
416 = THE 1986 INTERNATIONAL CONFERENCE OF TRE SYSTEM DINAMICG SULIETY, SEVILLA, ULIUBER, 1900,
As it is known, to build a system dynamics model it is necessary
to find the mathematical relationships or functions able to des-
cribe the real behaviour of the system.
In this way, the "natural" behaviour can be modelled. However, /
sometimes, when we are working with some specific kind of sys~ /
tems, simulation or modelling of the natural behaviour of the /
system may be not enough, because besides to the natural it may
be interesting, or necessary, to simulate the decision-making of
the managers, based on environmental factors, state of the sys—-
tem or policy constraints, in each timestep.
Several examples of this kind of systems have been already stu-
died by the authors; those belong to areas so different as:
Farming policy, Toval,A. (1985), Labor-Market, or which we descri
be below, about regional investment planning, MURCIA A/I.
Section II includes a formulation of System Dynamics and Linear/
Progzamming mixed models and section III relates the Assignement
Investment Murcia model including numerical results for various/
hypothesis.
SYSTEM DYNAMICS AND LINEAR PROGRAMMING (SD-LP) MODELS .
The aim of SD-LP models is’ to incorporate the simulation of deci
sion-making, when this is carried out trough one or several 1i—
near programs, into the traditional system dynamics techniques .
Thus, it is possible to obtain the optimal values of the system/
variables which participate as an objective function or as acti-
vities in some previously defined linear program, so making po--
ssible the simulation of decision-making at each time of the run
Althought the method is shown to use only linear programming, /
there is no problem to apply it to non-linear programming pro- /
blems using the same SD-LP algorithm (fig.1) and the same inter~
faces to the sistem dynamics equations with minor changes.
To simplify, let us assume that we have defined an unique linear
program together with the system dynamics equations, althought /
we could consider as many as we wish, with the only limitation /
of the memory computer size.
The objective consists in simulating the optimal behaviour of a
variable and, in consequence, the corresponding values for those
variables which participate as activites in the definition of /
that variable.
With this purpose, let us fistly consider the usual linear pro--
gramming form:
(optimize) z = cx a)
subject to:
using matrix form.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 417
We call SD-LP model to the system dynamics one embodying one or /
several linear programs which have the following characteristics:
the coefficients forthe vectors c, b and matrix A, are not obli-~
ged to be constant, as it is usual in linear programming problems
but they can be time-depending functions defined in relation to /
the elements of the system to be modelled. Thus, the usual SD-LP /
model is posed as:
(optimize) z(t) = c7(t) x(t) (2)
subject to A1(t) x(t) s b1(t)
A2(t) x(t) = b2(t)
a3(t) x(t) 2 b3(t)
Some of the coefficients of A, b or c may be constant (constant /
functions) if necessary. We can distinguish two kind of taking /
part in SD_LP models:
sD Lp
Tevels Cost coefficients (c)
Rates Constraints or tech-
Auxiliaries nological coefficients (A)
Exogenous Activity variables (x)
Constants Resources coefficients (b)
Objective function varia
bles {z)
Note that many of the LP-coefficients are included into SD one /
although it may ocurrs that we use some LP~coefficients exclusive
ly in the linear program, without any interest since the system 7
modelling vewpoint.
In this case, they can be performed as auxiliaries or merely as /
computer programming variables non essential for the model.
When we pose a linear program in this "dynamic" way,(2), we can
consider that during an iteration, t, coefficients of c(t), A(t),
and b(t), remain constant and so we Can operate the linear pro- /
gram, in that moment, as an usual one (1), and we can to apply /
the simplex or revised simplex algorithm for the actual constant/
values. At the next iteration, t+1, the values of the coefficients
c(t), A(t) and b(t) will be changed, but during the current t+1 /
iteration, they will again remain constant and well can again a-
pply the same procedure to solve the linear program posed in this
time and so on.
Before the run begins, we should give to the model the initial va
lues of c(0), b(0) and A(0), which will be either ‘fictitious valu
es for those functions which are not constant, or the real values
for the functions being really constant along the time horizon.
Thus, we have defined a dynamic linear program which is different
each’ timestep of the run because its coefficients are changed. How
ever, the structure of the linear program will remain unchanged 7
except if at some iteration we add or substract activities (x) or
constraints to it, although we seldom will do this.
As a consequence of the simplex run, we“ll can obtaint, each time-
~
ee eee eee eee eee OO RE ———E—E—_—_E—————_— OO
Step the optimal values of the variables which participate either
as an objective function or as decision variables. This fact in-~
corporates to the system dynamics model the ability to simulate /
the making decisions at each timestep as well as the results of
applying these decisions, bearing in mind the environment chan- /
ging conditions.
State equa
tions and
linear pro4
grams
Thitialize
LP coeffi-
cients.
‘Start
T=To
LP program
Run the mo
eis 2 Run simple:
~equations lor revised
anes simplex
Convert IF
optimal va
t= lues to SD
variables
Fig. 1 Algorithm to operate SD-LP models
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 419
Figure 1 shows the steps of the algorithm of operating SD-LP mo-
dels.
To finish this section, we are going to give a warning: is nece-
ssary to bear in mind that as the linear program coefficients /
values change, even randomly, it can be produced, at a certain /
timestep, a linear program which cannot be solved because it may
not exist either an optimal or a feasible solution. If some pro-
blem of this kind occurs, it could be a reason some of the fo-
llowing:
- The model (as a set of equations and linear programs) has ina~
ccurately been posed.
Phe chosen scenario is inadequate.
The system will really reach a state where it will not be po--
ssible to make an optimal decision according to the posed li
near program.
It is advisable to provide an alternative solution to prevent /
this event.
It is advisable too, the using of linear programming sensitivity
methods ‘to be able to use the optimal solutions reached at the /
previous timestep, t-1, in order to make decrease the number of
iterations of the simplex algorithm, to compute in a few time, /
the optimal solution at the present time, t, and so on. These /
methods are well known in operations research and they can be
applied when some of the linear program "data" vary. Changes can
be made in:
- b vector (resources) values
- ¢ vector (costs) values
~ A matrix (technological coefficients) values
~ x vector (activities or decision variables) values
- the number of activities or decision variables
- the number of constraints
Study of the variation of the solution with the variation of so-
me coefficients is not difficult, the last two variations are a
more intrincate matter.
Note that the last two kind of changes involve changes in the /
structure of the initial linear program, what will not be usual/
but provides more flexibility to these models. Procedures to pro
gram these methods can be found in Prawda(1982), Sakarovitch
(1983) and many other books about linear programming.
420
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, UCIUBEK, 1¥%0
7 MURCIA A/I MODEL FORMULATION
Murcia A/I model has been designed to provide a tool to assist in
decision-making to the "Consejeria de Pol{ticia Territorial (cPT)"
( Department of Territorial Policy) of the Comunidad Autonoma in
Murcia in Spain, about the distribution of investment in the co-
mmunity. This distribution will be carried out bearing in mind /
the twelve regions wchich constitute the community of Murcia. (See
Appendix I) 7
Figure 2 shows the hierarchy of the organs of government over the
community of Murcia including the Central spanish government.
Where are five basic aspects to distribute the investment, in or-
der to
1) Decrease the differences between the regions about the follo--
wing eleven equipments goods and infrastructures: transporta-—
tion, housing, urban planning, supply, road network maintenan-
ce, road network improvements, ports, river edges and irriga——
tion channels, public health, water depuration and environ— /
ment.
2) Guarantee the minimum investment according to the weight of /
the regional population with respect to the total population /
in the community.
3) Guarantee the minimum investment according to the region geo--
graphic size.
4) Maximize a regional welfare index either using linear progra-~
mming, when possible, or unless, an equation as the European /
Social Fund does.
Description of model components
Murcia A/T model, or simply A/I model, uses about 600 variables ,
500 constants, 11 tables and 500 equations. This is the reason /
because well merely describe the most important relationships /
and the general aspects of it. For further details about the mo-
del, and software used to run it, the readers may look up Murcia/
A/T (1986).
From a geographical viewpoint, the model is thought of two le-~ /
vels: the upper one, or aggregate, which is constituted by the /
global community and the lower one, or disaggregate, which is /
constituted by the twelve regions.
The advisable time horizon is the period of three years, making /
corrections every month and every year in the data set. However ,
the model is run for the period 1983-1986 because of the availa—
ble data.
Figure 3 shows a very simplified loop diagram of the model A/I .
The four major submodels are: Population, Labor, Aggregative eco-
nomics and Distribution of CPT-investment. .
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 421
CENTRAL ADMINISTRATION
COMUNIDAD AUTONOMA DE
MURCIA
CONSEJERIA DE
POLITICA
TERRITORIAL
(cpr)
Fig. 2 Hierarchy of the organs of government
POPULATION
+
+ *
LABOR ——————-
+
AGGREGATIVE
ECONOMICS
+/- +
cpr —t
INVESTMENTS
Fig. 3 A/I Simplified causal diagram
422 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
Each one of these, includes variables which belong either to the
aggregate or to the disaggregate level.
A) Population model (regional and community)
- The vegetative growing depends on the difference between the /
birth and death rates
~ Migrations are obtained ‘by means of an equation describing the
statistics behaviour of them, which includes three aspects: a~
verage familiy size, unemployment (with a certain delay struc-
ture) and the growth rate of the regional per capita income.
B) Labg; model (regional and community)
- Regional active population is obtained by multiplying the ac--
tivity index by the corresponding population.
- Once we have got the community active population, by adding /
the regional one, active population per major sectors (fourth)
are computed by fractions obtained from an Active Population /
Sampling.
- The difference between active population and available jobs de
termines the employment level per each major sector, respecti=
vely.
- Employment net variations, per major sectors, depend on sto- /
chastic equations, which are based on the following causes: /
previous new jobs, Lq coefficient of population variation, to
tal employment variation, irrigated land variation and indus-~
trial land variation.
Regional unemployment is determined by the difference between/
the active population and the total employment. The recorded /
historical unemployment data, by extrapolating, determine the
youthful unemployment.
C) Aggregative economics model (regional and community)
At the upper level (community) the economic network is modeled .
The essential relationships are:
- Foreign, Comunidad Autonoma, Business and Central Administra--
tion investments are exogenous. Comunidad Autonoma investment/
should specially be simulated.
- CPT investment is computed as a fraction of Comunidad Auténoma
investment. This fraction will be one of the basic parameter /
to simulate the system.
- Inner private investment is assumed to be equal to the inner /
saving. Also the inner saving depends both on the regional in-
come and the per capita income.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 423
= The distribution of the total investment per the fourth major
sectors is one of the main aim of the model. The functions to
distribute the investment are the following:
IA = FUNCTION(IA/II, EXA/EX, TEA/TE)
IC = FUNCTION(IC/IT, TEC/TE) (3)
IZ = FUNCTION(II/IT, EXI/EX, TEI/T5)
Is = IT- Ia- Ic ~ 1
the meaning of the variables is
IA: Agriculture investment
IC: Building «
II: Industry
IS: Services
IT: Total
EXA:Agricultural exports
EXI: Industrial exports
EX :Total exports
TEA:Agrarian employment level
TEC:Building * "
TEI: Industry " "
TES:Services " ”
TE :Total " ”
- The investment is converted to production by means of the frac
tion ICOR(Incremental capital-output relation) using the rela—
tions:
ICORA = DPA/IA — ICORC_= DPC/IC ICORI = DPI/II ICORS =DP:
‘i Ts
ICOR(X) means the fraction ICOR per each of the major sectors /
and DP(X) means the increment of production. Note that these in-
crements may, jpossibly, be negative.
+ The total production per major sectors (defined as the gross /
added value) is obtained by adding the increments per year to/
the previous production. In this way, the productions per sec~
tor are xate variables, but they work as level variables and
in this manner is as we are going to operate with them (from a
system dynamics viewpoint) .
- The total employment per sector is computed by dividing the /
sector productions by the corresponding average productivity.
~ Community income depends on the sum of the sector gross added/
values, computed as the net added value and it is added to the
remaining income originated by the CPT investment. Per capita/
income is computed from the regional income previously defi-~ /
ned.
424 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
D) Consejerfa de Politica Territorial (CPT) investments
This model is the main subject and the justification of the pre~
sent work. The current release accurately formulates the main /
questions.However, a completely satisfactory solution is not yet
given. According to the CPT-criteria, the expected objective to
be reached by the distribution is a double one: firstly, to a~
ttend to the regional deficits due to the absolute shortages in
equipment and infrastructure; and secondly, to close the gap due
to the differences between the twelve regions.
In case of having information enough about both potential needs/
and actual equipments, we could find out both the relative and
overall deficits. However, this-is not the case, and well be /
forced to operate, in this first release, with the inter-regio--
nal relative deficits which have been subjectively estimate by
the experts and political in charge of different areas in rela--
tion to equipments or infrastructure.
On the other hand, inter-regional priorities to decrease the de-
ficits in equipments and infrastructures will be determinated by
political criteria and they will be established by the CPT.
There are two main formular investing for the investment direc-
tly depending on CPT:
al
By using an economic equation which distributes the invest-~/
ment in a proportional way, as the European Social Fund does.
b) By using a SD-LP model to obtain the optimal distribution ta~
king into account some linear constraints.
In both cases, a regional discomfort index is used, which is de-
fined as
0.30, j=1..12 a)
IZ} = 0.7 (0.8 PAROT} + 0.2 PAROAJ) + Tepory
Note that variations in IZj are dynamics, and they depend, among
other causes, on the quantity of investment assigned to the re--
gion.
In fact, this investment contributes to decrease the unemployment
and to increase the income.
The variables in (4) mean:
124 : Regional discomfort index
PAROJj : Regional youthful unemployment
PAROA] : Regional adult unemployment
IRPC} : Regional per capita income index
Now, well superficially describe both possibilities.
a
Economic equation
In this case, the criteria to distribute the investment are to
1) Assign an investment ratio to be proportional to the popula-~
tion size.
2) Assign an investment ratio to be proportional té the economic
size, which is measured by.the total employment.
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 425
3) Assign an investment ratio to be proportional to the regional
geographic size.
4) Compensate the differences between the regions due to the re-
lative deficits in equipment and infrastructure.
5) Distribute the remaining investment -once we have substracted
from the total investment the first three ratios- to be pro--
portional to the regional discomfort index.
The’ corresponding equations to these criteria are:
ICPT} = -ICPT*( FPOBLA*P}/P + FEMP*E}/E + FSUG*SG}/SG + FEQ*Cj)
j21..12 (5)
Tepyp = f 1cPTj riz = 7 123
ICPT} = ICPT}] + (ICPT - ICPTP)*IZj/IIZ (6)
The variables not described yet mean:
IcPT : Total CPT-investment
ICPTj: Regional CPT-investment
P "+: Total population
E : Total employment
SG + Total geographic surface size
Pj + Regional population
Ej: employment
sGj : geographic surface size
Cj: Equipment and infrastructure deficit index
FPOBLA:Minimum fraction of ICPT per population
FSUG a E vee geographic surface
FEQ : ss " equipment and infrastructure
Let us see now the other option
b) SD-LP model
Now a linear program is formulated where the objective function/
which we wish to maximize is the total welfare, IB,(7), defined/
as the sum of the regional welfare coefficients, (1/I1Zj)*ICPT} ,
which can be understood as the profit resulting from the invest-
ment ICPT} in the region number j, which has a discomfort (wel--
fare) index 12} ( 1/123). Decision or activities variables are
IcPTj and cost coefficients or profitabilities per invested unit
value are IZ}.
The interpretation is not difficult: let us assume the next sin-
gle case, where T is the time
- Tsk and 12Z3(k) < 125(k)
In this time it is more profitable to invest more in the re-~
gion number three better than in number five, because number/
three is more depressed, in this period.
~ Tek+1 and 123(k+1) > 125(k+1)
426 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
Now it is more profitable to invest more in the region number
five because in this timestep it is more depressed.
In this way, taking into account that each timestep the system
environment is different, the linear program computes the opti
mal distribution for each timestep of the run.
The constraints beared in mind, (8), are similar to the repor—
ted above, for the option (a). Thus, the linear program would/
be: -
maximize Bes f (1/123) *1CPT} oa)
subject to ICPT} = ICPT
ICPT} 2 FPOBLA*(Pj/P) *ICPT
ICPT] 2 FEMP*(EMJj/E)*ICPT
ICPT] = FSUG*(SGj/SG) *ICPT
IcPT} 2 FEQ*C}*ICPT
Note that the optimal solution, whether exists, should be on /
the hyperplane EICPT} = IcPr.
Note also that all the inequations are in the same sense ( 2 );
to avoid redundancy we“1l consider the inequation which has the
highest value on the right part.
Perhaps the best way of formulating this model would be using /
the SD-LP way, but the option a) is not lost of sight to cover/
the iterations where the linear program doesn“t give a right so
lution, because either unfeasibility or unboundedness or other/
problem.
MURCIA A/T Scenarios
In order to show the possible uses of the model, various diffe-
rent scenarios are formulated. Suggestions are made in order to
manage to the future users and specially to the CPT-technical /
staff.
Firstly, the constants and tables which are more adequate to ma-
nipulate the model behaviour are suggested. These constants and
tables are in relation to exogenous economic policy variables ,e-
quipment and infrastructure (to be modified when information /
will be available) and CPT-investments variables.
Five different scenarios are used to run the model.
MURCIA A/T Images
An image is the set of results corresponding to the model run /
with a scenario given. In order to compare the results of the /
run, some tables have been included'in this paper, which show /
the most important consequences of the different policies to aig
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 427
tribute the investment: tables 1 and 2 show the values. correspon
ding to both the relative per capita income indices (IRPC) and 7
the discomfort index (IZ) generated by the chosen scenarios. Outs
tanding remarks could be:
1) IRPC“83 fluctuates between 1.126 and 0.764 with a standard de~
viation 0.105
2) For any image the disparities are minimized
3) The discomfort indices on 1983 fluctuate between 0.440 and /
0.310 with a standard deviation 0.041
Unlike it happens with IRPC, in I-4 (1986), the differences /
are maximum, with limits between 0.332 and 0.457 and a stan-~
daré deviation 0.0400
4
5) It is noted that the minimum IZ corresponding to any image on
1986 is higher than the 1983 minimum one. However, changes are
not measurable.
Finally, tables 4(a) and 4(b) show the percentage distribution of
CPT-investments, per region, depending on the policy (or scenario)
chosen. It is obvious to note how remarkable differences exist. /
Such differences involve very different impacts on both the gene-—
rated remaining incomme and the generated employment. To facilita~
te the comparisons the reader could see the bars diagram on appen-
dix II.
1-1 I-2 1-3 1-4 1-5
DATE FRPCB IRPCB IRPCB IRPCE IRPCS pate Rpcgs
1985 1 .976 .969 .969 .963 969
2 1870 1869 1869 1972 lege 1788 «978
- 3 1876 185 1865 1e67 ‘865 s, eee
4 1900 899 .900 ‘901 ‘900 ; =
5 .806 .802 .803 .803 .803 5 ee
S 1960 1963 1963 1969 1963 a lee
7.768 753. 1753. 1753 1753 5 oe
8 910 .908 .909 .909 .909 8 lo
1,026 1.019 1.019 1.014 1.019 ieee
10 1.060 1.060 1.060 1.060 1.060 ee
11 1.116 1.106 1.106 1.105 1.108 Hage
12.900 896 .896 .900 .900 ers
Table 1 Regional per capita income
IRPCB3
COUNT 12
MINIMUM 4746
MAXIMUM 1.128
MEAN 49245
VAR +0109
STD DEV .1047
RANGE: 1983 1 TO 1983 12
IRPCASI1 IRPCB6I2 IRPCB6I3
COUNT 12 12 12
MINIMUG +766 +753 1753
MAXIMUM 1.116 1.106 1.108
MEAN +9305 92575 2926
VAR D999D999 292999299 97222222)
STD DEV .09777226 .09850983 .09636835
RANGE: 1986 1 TO 1986 12
IRPC8SI4 IRPCASTS
couNT 12 12
MINIMUM +753 +753
MAXIMUM 1.105 1,106
MEAN = -.92633333 .92633333,
VAR 292099292 999999999
STD DEV .09746908 09827286
RANGE: 1984 1 TO 1986 12
gable 2 Statistical analysis of the per capita income
I-1 3-2 1-3 1-4 1-5
DATE =» -'1283_— DATE =—-'12861- 12861 12861 12861 12861
1983 1.350 1986 1 1370 373.374.382.374
2 415 2 424 419 419.424 419
3.380 3.380 4381 .381 .383 .381
4.435 4.455 450.450.457.450
5.420 5S 430 432.432 437.432
S$ 4365 $ «365 362.362 1363 .342
7 440 7? .440 4445 6445 448 4445
8.365 8 .375 4374 1374 378.374
9.320 % 330 «328 .328 .332 .328
10.345 10.365 6364 364 370.365
41.310 11.330 4330 330.334 1330
120.365 12.385 375.375.378.375
Table 3(a) Regional discomfort indices
ory
eR! WAGQIAN “WIA LITINNS COIAYWAIC III CAS 241 40 FONAMIINO) TWNOILYNHAINI ORG1 JHI
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 429
1283
COUNT 12
MINIMUM 431
MAXIMUM 444
MEAN 4.3758
VaR >>>)
STD DEV .0413
RANGE: 1983 1 TO 1989 12
Table 3(b)
“DATE
1983
i
It 1-2 153 1-4 15!
10PT%
7.83
Table 4(a)
1cPT%
6.82
PAP
4
9.86
6,00
5.69
3.47
3.96
6.26
23,16
15.81
5.50
129611 128612128613
COUNT 12 12 12
MINIMUM +33 +328 +328
455 245 145,
MEAN — ,38741648 .984608333 ,38616666
VAR DD>D9D929_D9D2I2D9)_ 992999292
STD DEV .03937100 ,03958210 .03955551
RANGE: 1984 1 TO 1986 12
i
I-1
ICPT% 1CPT% 1CPTZ %
gen worn Worms aE cP
9.29 6.38 9.79 2 9.04
4.10 2.27. 4.71 3 8.21
9.94 9,51 10.46 a 9.72
5.96 4.88 6.57 3 9.3f
5.66 4.93 4,29 % 7182
3.61 1.33 4.27 7 958
3.91 1,83 4,58 8 8.06
6.22 6.35 4.86 9 7209
23.17 34.19 18.96 10 787
15.82 19.68 14.01 110713
146 3.92 6.10 12 8.10
128814 128615
COUNT 12 12
MINIMUM +332 +328
MaxIMunt -457 45
MEAN 13905 98625
VAR >>>990999_ 92929299,
STD DEV .04004684 .03950975
RANGE: 1986 1 TO 1986 12
Statistical analysis of the discomfort indices
Ing, I-3 I-4 I-65
1CPT% ICPT% ICPTA ICPT%
6.87 6.92 4.72 7.47
914 9.25 6.32 9.74
4.06 4,04 2.23 4.66
9.98 9.51 10.51
5.95
5.60 4,89 6.23
3.54 1.33 6.20
3.89 1,83 4.55
6.22 6,39 6.86
23.26
15.88
5.45 3.91 6.10
3
o
&
a
cPT- investment distribution
430 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
In 1-2 1-3 1-4 15
ICPT% ICPT% ICPTA ICPT% ICPTZ YePT/8314 ICPTZ8315
COUNT 12 12 12 COUNT 12 12
MINIMUM 6.91 3.67 3.61 MINIMUM 1,33 4.27
MAXIMUM 9.87 23.16 23.17 MOXIMUL 34,19 18.96
MEAN 8.334 8.335 8.334 MEAN — 8, 3341466 8.333393
var +8402 30.37 30.59 VaR 2.537457 17.579138
STD DEV .9166 5.511 5.531 STD DEV 9.0850128 4.1927483
RANGE: 1983 1 TO 1983 12 RANGE: 1983 1 TO 1983 12
Is 1-2 1-3 1-4 T-5
ICPT/B6I1 ICPTAB612 ICPTZB413 ICPT%8614 1CPTX8615
COUNT 12 12 312 COUNT 12
MINIMUM 7.09 3.6 3.54 MINIMUM 1.33
MAXIMUM 9.72 23.26 23.26 MAXIMUM 34.25
MEAN 8.3333333 8.3941666 8.3316666 MEAN 8.3325 8.500833,
VAR +71800549 30.852474 31.032497 VaR 83.029202 16860974,
STD DEV .84735204 5,5545003 5.5706819 STD DEV 9.1120361 4.1062116
RANGE: 1986 1 TO 1986 12 RANGE: 1986 1 TO 1986 12
Table 4(b) Statistical analysis of investment distribution
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 434
CONCLUSIONS
As we said above, this work is about a first releag of the mo-
del for the investments planning. To. improve the currentrelea
se it will be necessary to dispose more statistic data about /
the actual community of Murcia state. Moreover, some ideas and
suggestions could be useful: to
a) Establish an average productivity of the regional” employ--
ment with actual regional income data
b) Introd ze an economic distance index associated with the (
distribution percentage of the constant FDE (minimum frac—
tion of ICPT due to economic distance) whose current value/
is 0
c) Use welfare indices associated with known- ‘equipments (te--
lephones, roads, hospital beds, sewer system, schools, etc.)
a) Recalibrate the model when 1983 information from Bilbao = /.
Bank for our region will be available
REFERENCES
Martinez, S. (1983) Murcia 2000/II/. Pensando en el futuro. Un
modeb de dinémica de sistemas para la Re- /
gién de Murcia.
Prawda,J. (1982) Métodos y modelos de Investigacién de Opera
ciones. Ed.Limusa ~
Sakarovitch(1983) Linear Programming. Springer Verlag
Toval, A. (1985) Uso de técnicas de programaci6én iineal en /
dindmica, de sistemas. Actas del VI Congre-
so de Intormftica y Autom&tica. Servicio de
Publicaciones E.1.8.I. de Telecomunicacion
Cdad. Universitaria, s/n. (28040) Madrid
432 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
APPENDIX I. GEOGRAPHIC SITUATION
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 433
APPENDIX II. BARS DIAGRAMS
DISTRIBUCION DE LA INVERSION. 1983
40
36
% 26
18
IZQUIERDA "“IMAGEN-4"
DERECHA "IMAGEN-2"
DISTRIBUCION DE LA INVERSION. 1962
~IZQUIERDA "“IMAGEN-S"
DERECHA "IMAGEN-2"
434 THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986
DISTRIBUCION DE LA INVERSION. 1966
38
26
1a
DISTRIBUCION DE LA INVERSION. 1986
48
38
w
268
16
ZQUIERDA "“IMAGEN-4"
DERECHA "IMAGEN-2"
THE 1986 INTERNATIONAL CONFERENCE OF THE SYSTEM DINAMICS SOCIETY. SEVILLA, OCTOBER, 1986 435
DISTRIBUCION DE LA INVERSION. 1S66
38
26
N
14
RDA “IMAGEN-S"
HA "IMAGEN-2"
“TIT kidiadaw _ u
La fi7e) WeDuid SETSaihid:
9861 ‘Y3GO.L9O 'VTHAS ‘ALIIDOS SOINVNIG W3LSAS 3HL 40 3ON3H3INOD TWNOILVNHALNI 9861 3H. = 9EP
