A simulation nodel of system dynanics for evaluating
dynanic changes of priority sectors in county industry
Wang. Yixiang
Department of Management Engineering
Wuhan University of Technology
Wuhan 430070, P.R. China
Abstract
As the developing speed of the county industry economy depends to a large extent
on the developing speed of the whole county economy,.it is the key of success of the
county economy planning that how to bring the region superiority into full play, and
that which of priority sectors in industry should be developed under the circumstances
of limited funds, resources and sources of energy. For this reason, it is difficult to
get a united opinion when discussing that which is priority sector in undertaking a
county economy planning.
A system dynamics model (SD2 model) suggested in this article is actually one of
the model group of system dynamics. The model can be used to evaluate those priority
sectors dynamically through being introduced the method of multiobjective decision
analysis. In the article the writer also introduce a simple method of preference rank-
ing about equality or inequality weight targeted values in a period of time, so the
scientific quantitative basis can be supplied for working out the county economy
planning.
There are several characteristics of SD2 model. It can be used to dialogue bet-
ween person and computer conveniently, to compare and analyse multi-plannings, to
give the user dynamic economy indicators and benefit indicators, e.g., fixed assets,
labors, rate of profits and taxs to funds, etc. If cutting out the rate of output
values of sectors in the evaluating indicators, we can obtain an evaluating indicator
for general economy benefits.
The simulation results of the SD2 model have supplied an important reference for
working out a county economy planning used in practice effectively. Of course, this
model can still be used for the same questions in other sectors or in larger regions.
THE WHOLE MODEL DESIGN
The SD model group composed of three system dynamics models is set up according
to real circumstances of a county. The total computer programs of the SD simulation
are compiled in DYNAMO language. The developing sketch of the national economy and
the changes of the industrial structure of a county between 1980 and 2000 are all
drawn up.
The SD2 model described emphatically in this article is only a part of the real SD
model system, which is composed of a forerunner model group and a SD model group, and
the former term involves a predicted model set and an industry production function
model set. The SD model group involves the SD1 model to the national economy of the
county and the $D3 model to the supply of the sources of energy of the county in
addition to the SD2 model to the synthetical evaluation of the priority industry
sectors. A diagram which illustrates the relationships among the factors is shown in
Figure 1.
Page 700
System Dynamics '91 Page 701
National Economy Indicators
Gross industrial Gross agricultural
output value output value
am |
National income Gross national
product
Forerunner Model Group SD Model Group
Predicted model set f SD1 model r
Industry production SD2 model [27] SD3 model
function model set
i] Y
Scientific and Future industry
technological structure
progress
Output and input Game of energy -~+—
relationship 1 sources
————=| Planning decision [-<*————~
FIGURE 1 SD Model System
DESCRIPTION OF THE SD2 MODEL
1. Introduction of the problem
The national economy system of a county, though small, is a complete open system
involving a satisfactory variety of sectors. A great quantity of industrial and agri-
cultural products have to be sent to the markets outside the county to change into
the funds of flowing back. Those necessary mechanized equipment, electric power, etc.,
have to be imported from outside and some funds, of course, also flow out of the county.
The importance of open system is that it ensures the efficient exchanges from material
flow to capital flow and then accelerates the expanded reproduction. The funds of
developing county economy principally depend on accumulation itself in addition to
the opportunity (foreign funds, etc.). The greater part of county revenues still rely
upon the county industrial accumulation. In the period of the Sixth Five-Year Plan,
six priority lines, i.e., chemicals, machines, building materials, food products,
textiles, glass and ceramics, have been formed in Qichun county industry. However,
how to identify the more important one in the six sectors? Which of these will become
a lead line in the county industry once the investment decision is fixed? What are
future general layout and state? There is an important referential sense for working out
Page 702 System Dynamics '91
the county economy planning in the policy analysis about these problems, and there is
also great significance for the county decision-makers who are working out the present
policies. For the purpose of solving similar problems, the model SD2 is set up.
2. Procedure of building models
Let the essential element set of industry economy S.be denoted byT’(S)=(A; /ASRS
i=1,2,...,m}, and let the relation set for the elements above be denoted by R(M')={R;./
Rs SAXA,, 1, j=1,2,...,m}. Note that the essential element set and the relation set
here,’ which don’t involve any quantitative values, are all the concept sets. Then the
system S can be corresponded to the S)system of system dynamics through mapping
(single-valued mapping in general) as follows:
f: S=Sp, O: RR".
so that, I(S)=(0,/QCR", i=1,2,...,m},
RYT )={RE /RESOXO; , i,5=1,2,... 0).
Through the above exchanges the qualitative elements in S$ are converted into the
quantitative units in Sp and the qualitative casual relations in S are converted into
the quantitative flows (material flows or information flows). So the language- models
have been changed into the Spflow diagrams, then the key factors are found out and
the variable types are ascertained. Obviously the funds of influencing the circulation
of the county system are the key factors of limiting and promoting the county industry
economy. Funds are the critical points, since they can be considered either the course
of production, or the results of production. Thus the fund should be determined to be
a level variable. The decision variable is generally denoted by CLIP function or. TABLE
function. Its changes directly affect the accumulations of levels and then affect the
circulations of all the units as well as the whole system.
In order to be clear it can be showed below with the method of set theory:
Varible set: ['(Q;)={X; .R; .W, PU; ,Y;}
Relation set: [™(R5)=(Fl;z /FL,=0,xO}
where, X -- state variable set
R -- decision variable set
V -- auxiliary variable set
PU-- parameter set or input variable set
Y -- output variable
FI--. flow coupling variable
Some decision variables in SD2 model are defined by forerunner model group according
to the practical indicator values of the county in the period of the Sixth Five-Year
Plan. A few-of external variables needed to change into internal variables can be
denoted by TABLE functions in time series. In the course of determining the structure
and parameters of the system, we lay stress on listening to the opinions of relative
decision-makers who have rich practical experiences.
3. Model Structure
SD2 model is a system dynamics model of evaluating dynamic changes comprehensively
in the county industry. Funds play a leading role and the benefit indicators are
prominent in the model. Let the fixed capital of each-sector be a level variable, and
System Dynamics '91 Page 703
Figure 2 The flow diagram of the SD2 Model
the changes of future industry structure are implicitly involved in the changes of
growth rates of fixed capitals for the six priority lines. Let the other benefit
indicators be auxiliary variables.
Figure 2 shows the model flow diagram in which there are 14 flow rate variables,
93 auxiliary variables, and 320 equations. The simulation period of time is from
1980’s to 2000's.
It is the principal character that a dynamic objective function of evaluating sectors
comprehensively is set up through introducing the decision analysis of multiobjective
function. They are represented as follows:
6
Max U; COL TNp: (t)/Ny; (t), (i=1,2,...,6),
where, Ny; (t)=1V, (t)/FC; (t), Noy (t)=1V, (t)/IV(t),
Ngg (E)=NIV, (t)/IV, (t), Naz (t)=PT, (t)/IV, (t),
Ng; (t)=NPC, (t)/FC; (t), Ng; (t)=PT; (t)/ (NEC; (t)+FFC; (t)),
Nj, (t)=WH; (t)/IV; (t), (i=1,2,...,6).
IV -- gross industrial output value of county
IV;-- industrial output value of i-th sector
FC -- fixed assets
WM -- labor number
NIV-- net value of industria] output
Page 704 System Dynamics '91
PT -- profit and tax yields
NFC-- net fixed assets
FFC-- circulating capital
is1,2,...,6 above represent chemicals, machines, building materials, food products,
textiles, glass and ceramics, respectively.
SIMULATION RESULTS AND EVALUTATION ANALYSIS
We design fifteen distinct investment schemes to proceed to the policy simulation
in using the SD2 model on an IBM Personal Computer. After considering the county
industry base, natural resources, external circumstances, etc. in the course of simu-
lation, the planning people and the county decision makers determine a wore ideal
scheme about which plot-outs and table-outs of simulation results for U;(t) illustrated
in Figure 3 and Table 1 respectively.
The U;(t) value of sequencing of each line in the industry at any time point can be
directly attained on the curves or in the table. Usually these output results can be
immediately supplied for the decision reference. However, it is necessary to proceed
to mathematics analysis if the sequencing results of the period of time must be
supplied, whereas the 0; (t) values of the six lines transform alternately. A useful
method is described below:
Firstly axn AP dynamic matrix of ordering value (n time points and p sectors) is
defined as: AR (as; lp » natural number set Pole 2,.-.J, Set Ep=(q/q=1,2,...,p}SE,
gj Ep, the weight ordering value vector P=(p,p-1,...,1)". Thus the frequency row
vector of p-dimensional ordering value can be established according to the emergence
frequency of elewent q of each column vector A; in the matrix A, then p row vectors
of p-dimension form a pxp matrix S of ordering’ value frequence. Hence the column
vector R=S-P is a ultimate ordering vector of p-dimension that we expect to obtain.
Using the above-mentioned method we can-proceed to the quantitative analysis as
follows:
The sequencing results between 1981 and 1985 canbe derived first. Here n=5 and p=6.
» P65 4 3.2 1)
7
NYY
Oe oe
wow rom
Arman
PNW AD
Hee
The A matrix of ordering value above can be easy obtained from Table 1 (where, a;;
is the weight ordering value of the j sector in the i year).
The first column of matrix A-shows that the number of emerging frequency of element
"1" is equal to 0.4, that the number of emerging frequency of element "2" is equal to
0.6. Thus the frequency row vector of ordering value S =(0 0 0 O 0.6 0.4), The
other five row vectors can be got alike. Thus
Hence R=S+P=(1.6. 4 3.4 5.6 4.8 1.6)".
System Dynamics '91 Page 705
Table 1 The U;(t) values of synthetic evaluation function
Ui
TIME U, U; Uy Yu U, Uy
1980 2.2510 36.601 | 7510 | 162.37 T1380 15467
1981 01044 | 3.522- “T3864 130.80 149.87 | 3.6281
1982 0.4554 15.919 “13227 70.83 1663 [2.7958
1983 0.8304 18.959 6.012 31S 13.16 0.6203
1984 1.4268 21.307 8.218 37.10 27.06 | 0.6867
1985 1.8455 25.066 6.461 29.17 23.10 ~ 6.0328
_ 1986 1.8308 24.427 6.637 29-71 23.93 0.0314
1987 18150 23.786 6.812 30.23 24.77 0.0300
1988 11979 23.145 6.987 30.74 25.62 0.0287
1989 1.7797 22.505 7.161 31.24 26.49 0.0274
1990 1.7604 21.868 7.334 372 27.36 0.0262
1994 1.7672 21.161 7.826 32.13 29.20 0.0353
1992 17721 20.456 @343 32.51 312 0.0245
1993 17784 19.754 8.886 32.86 33.15 0.0236
1994 1.7768 19.058 9.454 33.18 35.27 0.0228
1995 1.7767 18.369 10.049 33.48 37.49 0.0220
1996 T7HR2 17.128 10.331 32.67 38.54 0.0205
1997 1.6594 15.943 10.607 31.84 (39.57 00191
1998 1.6006 15.824 10.876 30.99 40.57 0.0177
1999 1.5419 13.766 11.138 30.12 41.55 0.0165 _
2000 14835 12.767! ‘11.392 29.24 42.50 0.0153
60 10.0
Baw 3s
Fig. 3. The diagram S30 2S 50
of curves of the U;(t) _« =
values (is1,...,6) = 15 2 2.5
0 0
1980 1985 1990 1995 2000
A conclusion can be drawn as follows from the six-dimensional ordering. vector gained
ultimately: During the period of the Sixth Five-Year Plan the sequencing of important
degrees of the six sectors is separately food products, textiles, machines, building
materials, chemicals, glass and ceramics.
The sequencing of the priority lines in the county industry from 1990 to 2000 is
given below. In order to simplify the question, the matrix of ordering value is set
up corresponding to U;(t) value at three points (i.e., A.D. 1990, 1995, 2000).
0 0 0 6 1 0
2 4 3 6 5 1 0 0 1 08 oO 0
Ae} 2 4 3 5 6 11], S8*]}0 0 8 1 0 0
2 4 3 5 6 1 1/3 2/8 0 0 6 0
2/3 1/3 0 OO 0 O
o 0 oOo 0 6 1
Hence R=S+P=(2 4 3 5.3 5.7 1)7
Page 706 System Dynamics '91
Consequently the sequencing of important degrees of the six sectors are textiles,
food products, machines, building materials, chemicals, glass and ceramics, respec-
tively.
It is necessary to explain the SD2 model additionally as follows:
1. The market sales of products and the supplies of raw materials are not involved
in the objective function for synthetical evaluation. Of course it is such a result
to the past production and management, and we suppose that the future production and
management can be satisfied through making efforts.
2. The consuming indicator of source of energy power is not represented in the
synthetical evaluation objective function because of the compatibility between the
sequencing of econosy consuming of source of energy power and that of the SD2 model.
Any change will not happen to the sequencing of the model even if the indicator above
is put in the objective function.
3. The multiplication-division analysis of multiobjective function is applied in
the article when the synthetical evaluation objective function needs: to be calculated.
With application of the method, each indicator in the counting formula has an average
weight generally, but the differences of the importance among the indicators are pre-
sent in the real system. Therefore the article presents an exponent weight method.
The multiplication-division method is a method with which a multiobjective question
cau ibe changed into a single objective one. Usually its representation is in the
ollow:
N
Max ra] f,@/1Tf,@,
i ae cI
where k objectives must be maximal to the numerator and n-k ones must be minimal to
the denominator, and the exponent of each indicator is equal to 1. Suppose the expo-
nent weight (i=1,2,...,k) is showed to the k objectives in the numerator, the
follows can be got:
kK a. Hl
Fol] (£; (x)) seats (x),
then La (F(x) Son (x))- Seat, (x)).
4=k+1
Now a linear weight shoréseatntinn ee been gained through the logarithmic conver-
sion.
if f,(x)>1
where nf =1 if f, (x)=1 to the key objective.
* if 0<f, (x)
Usually the rate of the net output value and the ratio of profit and tax to funds
are considered as key objectives, since N3;<1, Ne, >1 (illustrated with the profits
and taxs to a hundred yuan (the monetary unit of China)).
Thus A3 <1 andAg>1.
The various simulation solutions of U;(t) value can be obtained with corresponding
to the variousA;. When 2; =0.7 and Ag= 1. 3, for example, the ordering vector in the
period of the Sixth Five-Year Plan is R=(1.6 3.8 3.4 5.6. 4.6 1.6)" after being
computed. Comparing this vector with the former one under the condition of the equal
weight above we know that the two sequencings are more or less alike, and the sequen-
cing in the time period between the 1985’s and the 2000’s can be got. directly from
the curve diagram and the table.
System Dynamics '91 Page 707
4. The model can also export various dynamic indicators of each sector, e.g., net
value of output, net fixed assets, profit and tax yield, labor number, circulating
capital, etc. between the 1985's and the 2000’s according to the decision needs.
5. The simulation can be used for evaluating the synthetical economy benefits of
various sectors if the ratio of output value Np; is rejected from U;(t).
CONCLUSION
The SD2 mode] introduced in this paper is a key one in the SD model group. Combining
with the relative time series data collected and a number’ of parameters derived from
the forerunner model group, the model has sought to show that the method of decision
analysis of multiobjective function is introduced in the system dynamics model to
proceed to the dynamic evaluation for the priority sectors. The model also gives us a
simple method about the sequencing in a time period under the condition of the equal
weight or the non-equal weight. The simulation solution of the model provides a quite
good quantitative basis for working out the Qichun county economy planning.
The applying region of this model can be extended into the same questions of the
other sectors or the larger regions.
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