Model of Dynamic Multicriterial Evaluation and Selection - MODES
Branko Greie Ante Munitic
University of Split, Faculty of Economics, University of Split, Maritime Faculty Split
Radovanova 13, Split, CROATIA Zrinjsko-Frankopanska 38, Split, Croatia
e-mail: grcicoliver.efst.hr e-mail: muniticbrod.pfst.hr
Abstract: As the basic field of application of the MODES is selected a process of evaluation and selection of the most favorable
development scenario considering explicit dynamic character of that process. Application of the MODES makes possible evaluation of
efficiency of selected scenario and comparison of efficiency of diverse scenarios in any point of a simulated time horizon in development of
the observed system. Thereby is avoided conventional static approach to the multicriterial selection of the most favorable scenario, and
enlarged potential of their analysis starting from presumption that various scenarios are not equally favorable for the beginning, middle or end
of the simulated period. Application of MODES is facilitated by the existence of dynamic simulation model of the observed system. In this
paper is presented possibility of direct integration of MODES in the structure of system-dynamic model and establishing of active relation
between basic variables of simulation model and criteria for evaluation and selection of the most favorable scenario as a part of MODES
structure.
1. Problem formulation
To design different scenarios for the future dynamic development of a social-economic system is an extremely
difficult and demanding task entrusted to experts. Different variants or scenarios are the result of different forecasts
and assumptions related to the future movement of a number of significant variables, controlled or non-controlled,
which determine the dynamic behavior of the real system. The final goal is identification and then selection of such a
scenario which can provide an optimal encounter of possibilities and wishes in terms of the specified development
aims, considering the fact that it is not possible to meet all the requirements, which necessitates determination of
priorities.
If the experts rely only on qualitative observations in terms of evaluation of variables, it will be very difficult to
evaluate the final effects of these scenarios, as the evaluation and selection of the best scenario will be based
mainly on qualitative, subjective and insufficiently reliable criteria. However, if they take a qualitative-quantitative
model approach to support the management of the social-economic system in question, which is a necessity in
complex systems, they will not only get the more clear, more systematic, faster and more efficient test for the effects
of the potential development scenarios, but they will also be able to use the simulation results as objective and
quantified criteria for evaluation and selection of the best development scenario.
In some of the earlier examples of selection of the best scenario both approaches were used, and sometimes
combined. However, preferring the latter, model approach to support the global management process, in this work
we shall point out the weakness of the results achieved by the simulation model at the stage of multicriterial
evaluation. Namely, the examples of selected exogeneous and endogeneous model variables used as criteria in
scenario selection show that the simulation results of these variables are used partially, i.e. most frequently only
those quantities which express the final effect of a scenario - the effect referring to the end of the simulated period, or
those quantities which express the average value of criteria for the entire simulated period. In this way the selection
has a static character. Besides, the possibilities of a thorough analysis of the expected effects are limited. Since all
these development scenarios are medium-term and long-term ones, we think that it is of great importance to analyse
and compare the effects of individual scenarios at each point of time of the simulated period, starting from the
assumption that different scenarios are not equally favourable for the beginning, middle, or end of the total simulated
period; so one has to take this into account when selecting the best scenario. In other words, it is necessary to
include the dynamic component in the process of evaluation and selection of the best scenario, which would provide
the evaluation of the instant (at each point of time), dynamic (in the continous flow of the simulated period), and
eventually of cumulative efficiency (in the total simulated period) of a particular scenario. Finally, there is a question
of methodology which can include the dynamic component into the procedure. This work will offer an approach
using the advantages of model support to the management process, the advantages of computer simulation of
development scenarios, and the benefits of the system-dynamic simulation methodology.
2. Model of dynamic evaluation and selection (MODES) of the best
development scenario
Design of MODES is based on all the known achievements of the multicriterial decision-making methods, and it
includes all the characteristic stages i.e. procedures with the same or altered content. Figure 1. shows the global
procedure of design and use of the model.
2.1. Simulation model of a real system
To test the dynamic approach practically this work uses the system-dynamic simulation model (SDSM) of
development management in Split-Dalmatian County. It is a very complex, non-linear, multidimensional, multisector,
and subregionally disaggregated model of the regional social-economic system.
The structure of SDSM for SDC is based on total inclusion of fundamental dimensions: economic and
demographical, and on partial inclusion of other dimensions such as e.g. ‘politics’ in the part related to limited
measures and instruments of economic policy, or e.g. ‘space’ used as one of determinants for dynamics of
demographic processes. Thus we may conclude that the focus of thus research and modeling is on the dynamic
process of economic growth, i.e. the speed of entire socio-economic and demographic development, with a special
emphasis on solutions for elimination of disruptions and imbalances between the given dimensions.
Economic dimension and demographic dimension are disaggregated into sectors to enable identification of potential
intradimensional and intersector disruptions and imbalances.
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This primarily refers to structural disproportions in economic development of the region and to the question of
optimal allocation of investment funds, as well as to disproportions in population age structure with consequences
on the long-term dynamics of demographic flows, etc. Besides, each of these dimensions is subdivided into
characteristic subsystems or functions important for establishment of a single management mechanism. These
subsystems or functions are represented by separate model sectors or submodels: population sector, production
sector, social product distribution sector, investment funds sector, labour supply and demand sector and
exogeneously determined influences sector.
The SDSM for SDC explains the basic interdependence and interactions in economic and demographic structure of
the SplitDalmatian County with a great degree of validity and represents a good basis for a fast and effective
generation of different forms of dynamic behaviour of the region modelled in order to test the different development
scenarios.
Inputs and outputs of the simulation model are assumed or generated series of values of different exogeneous and
endogeneous variables in the chosen simulation period, which to a greater or lesser extent determine the future
development of the system modelled. Therefore, when we reach the stage of evaluation and selection, the
mentioned exogeneous and endogeneous variables will become criteria for that evaluation and selection.
2.2. Selection and definition of criteria (Ki)
In this example a number of selected criteria is divided into two characteristic groups - the first one comprising
criteria related to outputs, i.e. crucial endogeneously defined variables in SDSM which provide an image of the
speed and achieved level of social-economic development of the Split-Dalmatian County; - the second one
comprising criteria related to inputs, i.e. crucial exogeneously defined variables which determine the speed and
achieved level of social-economic development of the County.
Selection of preference (P,j): When considering the preferences related to the observed groups of criteria, we can
generally state that ‘desirability principle’ is most important for the first group of criteria, while the second group of
criteria deals with ‘evaluation of realization probability’ or ‘evaluation of reality’ of input. As already pointed out, our
intention is to use the well known achievements of different methods of multicriterial decision-making, so in this
case, i.e. when selecting the preference function we shall use the ‘generalized criteria functions’ from the
PROMETHEE method Brans and Vincke, 1985 allowing some corrections in accordance with nature of the criteria
chosen.
Coefficients of the relative importance of criteria (Wi): As all criteria do not have the same relative importance,
when evaluating efficiency of a particular scenario, they have to be given appropriate weights. The technical
condition here requires that sum of all weights equals to one.
The chosen criteria and the coresponding preference functions are as follows:
1) K1 = Gsr_DP - refers to the ‘annual growth rate of the domestic product’. The choice of the corresponding
preference function (P,;) for this criterion starts from the assumption that ‘criterion with linear preference and
indiference area’ - 5th generalized criterion from PROMETHEE method would be most suitable, where the
indiference threshold is linked to zero Gsr_DP, the area of linear preference between 0% and 10%, and the area of
maximal and constant preference exceeding 10%.
2) K2 = SN - refers to ‘unemployment rate’. The preference function (Pz) in this case starts, with minimal
corrections, from 6th or Gauss generalized criterion from the PROMETHEE method, i.e. from the assumption that the
area of maximal preference could be between 0% and 5% for the unemployment rate, and the preference curve of an
inverted S form would be 30%, while the indiference area would be above the unemployment rate of 30%.
3) K3 = S_BINV - is the only chosen criterion related to inputs in SDSM and it refers to evaluation of reality of 'gross-
investment rate’. When defining the preference function (P,3) one has to take into account some commonly known
trends in the movement of this rate, as well as the general assumptions related to the definition of scenario for the
future development of Split-Dalmatian County Grcic, 1996. This results with the following assumptions:
- S_BINV should not be less than 10% which is the compulsory allocation for depreciation, i.e. simple reproduction
of capital funds. Therefore, the value of preference function under 10% S_BINV is 0. At the same time it is highly
improbable that S_BINV could exceed 40% - therefore preference function over 40% is also equal to 0.
- Considering the general characteristic of the mentioned scenarios it would be realistic to expect that S_BINV
would move between 10% and 40%, the most preferable being the usual rates of cca 20-30%, which are also the
most probable ones, therefore within that range the preference function has the maximal value.
- In the remaining areas, i.e. for the movement of S_BINV within the range of 10-20% we assume linear or
exponentially increasing preference, and within the range of 30-40% we assume linear or exponentially decreasing
preference, i.e. evaluated probability of realization.
The importance of particular criteria, i.e. determination of coefficients of relative importance of each criterion (Wi) is
the matter of subjective judgement of expert working on evaluation and selection of the best scenario variant. In this
case, the initial value of weights will be: W1=0.4, Wp=0.2, and W3=0.4.
2.3. Definition of dynamic function of efficiency
If we mark the particular development scenario with Sj the value of criterion Kj in scenario Sj will be defined as Vij-
However, when selecting the optimal development scenario acording the simulation results, where each scenario is
simulated on the corresponding model of the real system, the value of criterion Vij is dynamized, i.e. one criterion
value is substituted by a series of values Vij). t=1,2,3,...,N, where N is the lenght of simulation period, or the time
horizon of the scenario.
By dynamizing the criterion value Vij), the value of preference function is also dynamized for the corresponding
criterion value - Pyj Vij), which means that now the preferences of scenario Sj are changed according to criterion K;
at the every point of the simulated period. If the same approach is applied to all the criteria used in evaluation and
selection of the optimal scenario, the final result will be the dynamization of the total preference function of the
corresponding scenario, which shall be called ‘dynamic efficiency function’ of the scenario Sj - DEFj(t). Therefore,
the formula defining the ‘dynamic efficiency function’ of the scenario Sj is:
DEF; (t) = Pxi Vit) Wi
2.4. Integration of MODES into the real system simulation model
Considering the starting hypothesis on complementarity of MODES with the model approach, or simulation
approach to testing of potential effects of the scenarios defined, where the outputs of the simulation model are used
as Criteria for evaluation and selection, it is logical to integrate the MODES into the structure of simulation model. In
that way we can not only ensure fast and efficient testing of particular scenario effects, but we can also provide the
possibility of effective multicriterial analysis and comparison of these scenarios. For that purpose we used the
expectional benefits of the system-dynamic simulation methodology and simulation programme language
POWERSIM. In that way all the components of MODES were integrated directly into the structure of SDSM of Split-
Dalmation County.
The flow diagram of MODES is:
cerpesor SkSor Say sor
‘Oo 04 G2 03 O4 OS DFE_SDZ
ed
Figure 2. The flow diagram of MODES
On the top of the flow diagram there are the chosen variables, i.e. three criteria which are the direct output of the
SDSM of the Split-Dalmatian County. On the left there are preference functions defined for each of the criteria, which
in POWERSIM-notation can be represented by corresponding GRAPH-function as follows:
aux P_Gst_DP = GRAPH (Gsr_DPa, 10, 2, (0,0,0,0,0,0,0.2,0.4,0.6,0.8,1,1,1,1,1,1))
aux P_SN = GRAPH (SN, 0, 0.05, (1,1,0.96,0.85,0.63,0.37,0.16,0.07,0.02,0,0,0.0,0,0))
aux P_S_BINV = GRAPH (S_B_INV, 0, 0.05, (0,0,0,0.39,0.81,1,1,0.81,0.41,0.13,0.04,0.02,0))
On the right there are importance coefficients for each of the criteria, which in POWERSIM-notation are defined as
constants:
const W_Gsr_DP = 0.4
const W_SN = 0.2
const W_S_BINV = 0.4
Finally, ‘dynamic efficiency function’ (DEF), as the basic structural component of the flow diagram in POWERSIM-
notation will be:
aux DFE_SDZ~= P_Gsr_DP*W_Gsr_DPsP_SN'W_SN+P_S_BINV'W_S_BINV
3. Simulation, analysis, and comparison of development scenarios
based on the MODES
Process of simulation, analysis, and comparison of different development scenarios requires previous formulation of
scenarios. To test the model practically, we shall use two characteristic scenarios for the future development of Split-
Dalmatian County presented in the previously mentioned work Grcic, 1996.
But, just before we show up the results of dynamic multicriterial evaluation of these scenarios, let's examine (using
one of the criteria - 'gross-investment rate’, S_BINV), how in fact MODES operates. This is explained in Figure 3.
Ba
—Fs.BINv
02 03 04 0s 1995 2.000 2.008 2,010
S_BINV Time
° ° ° 2
8 & * a
1980
$_BINY
1995
2000
2005
2010
Time
Figure 3. How does MODES operate?
As we can see, the basic input of MODES is a continuing time horizon of the simulated values of the chosen
criterion inside the x'" scenario (Sx). To show how MODES operates, we have chosen just four characteristic points
of that time horizon and named them as A, B, C and D. The simulated value of the S_BINV criterion in the year of
1995 (point A) according the chosen function of preference, or according to 'generalised criterion’, adds the
preference of the approx. 0.2, that is 'registrated' on the third graph as the matching ‘value of preference function’ of
the chosen criterion in 1995. Point B is a similar thing but only for the year of 2000, ponit C is for the year of 2005
and point D is for the year of 2010. Well, the curve that represents ‘simulated value of criterion’, indirectly transforms.
itself into a curve named ‘value of preference function’ of the chosen criterion with the help of 'preference function’, or
‘generalized criterion function’. On the basis of the previous remarks, and considering all the criteria used, we came
out with the summarized waged value of the function of preference, or so called ‘dynamic efficiency function’ of the
scenario Sx.
By simulation of the earlier mentioned variants, i.e. scenarios for the future social-economic development of the
Split-Dalmatian County for the chosen time horizon from 1991 (95) to 2010, the previously defined ‘dynamic
efficiency function’ will result by the corresponding ‘efficiency curve' for each of the scenarios (Figure 4).
4-DFE_S0Z_¥1
=p DFE S0Z_v2
Figure 4. Efficiency curves of the chosen scenarios
Comparing the efficiency curves itis easy to conclude that a particular scenario variant is not equally favourable
within the characteristic sub-periods of the simulation time horizon, and that in terms of evaluated efficiency the
chosen variants are not equally interrelated during the simulated period.
Here we shall not go into detailed consideration of all the factors determining the efficiency of the concrete
development scenarios, as that is not the purpose of this work.
4. Conclusion
Summarizing the basic characteristics, the benefits previously mentioned, and some additional possibilities of the
expounded MODES we can point out that:
a) The ‘efficiency curves' generated by the MODES provide the evaluation of efficiency of a particular scenario, as
well as the comparison of efficiency of different scenarios at every moment of the simulated future period. In that way
the simplified, static approach to scenario selection is avoided. This provide the basis for a complete analysis of
scenario efficiency during the sub-periods of the total simulated period. The results of such analysis can be used not
only for evaluation and selection of the 'best scenario’, but also for combination of positive characteristics of the
existing scenarios with an aim to find out a new and even better one for the total simulated period.
b) Direct integration of the MODES into structure of the simulation model affirms the advantages of computer-
simulation model support in managing the complex social-economic systems. In this way conditions are created for
a fast and efficient testing of change effects in any of the controllable or non-controllable variable within the
simulation model structure.
c) Integration of the MODES into the structure of computer simulation model provides also a past and efficient testing
of change in any component of the MODES (narrowing or widening of criterion group, change of preference
functions, change of criterion importance coefficients, etc.) on the preference of the corresponding scenario.
d) The MODES offered can also generate 'the cumulative efficiency curve’ for each scenario. Such curve shows the
sum of preferences at subsequent time points of the simulated period, and it represents the basis for the so called
‘total’ comparison of efficiency of particular scenarios.
e) Finally, questions and observations related to improvement of particular elements or components of the MODES
remain to be discussed: e.g. a greater number of criteria should contribute to ‘smoothing’ (elimination of significant
oscillations within the total simulated period) of the ‘efficiency curve’; there is possibility to introduce 'dynamized'
weights assuming that during the simulated period a change in criterion importance is expected, etc.
References:
1 Y. Barlas, Multiple tests for validation of system dynamics type of simulation models, European Journal of
Operational Research, 42(1989), p. 59-87.
2J.P. Brans and P.H. Vincke, A preference ranking organization method - The PROMETHEE Method for
Multiple Criteria Decision-Making, Management science, Vol. 31, No 6, 1985.
3 M. Babic, Makroekonomija, MATE, Zagreb, 1995.
4B. Grcic, Simulacijski model upravijanja razvojem regije, Ph.D. Thesis, Split, 1996.
5B. Greic, Z. Babic, E. Jurun, N. Plazibat-Tomic, Multicriterial analysis of development scenarios,
Proceedings of the 7th Intemational Conference of Information Systems - IS ‘96, Varazdin, 1996.
6 POWERSIM - The Complete Software Tool for Dynamic Simulation, User's Guide and Reference,
ModellData AS, Norway, 1993.
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