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.

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 Split.Dalmatian 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_Ki): 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_K1) 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 (P_K2) 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_K3) 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, W₂=0.2, and W₃=0.4.

2.3. Definition of dynamic function of efficiency

If we mark the particular development scenario with S_j, the value of criterion K_i in scenario S_j will be defined as V_ij. 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 V_ij is dynamized, i.e. one criterion value is substituted by a series of values V_ij(t), 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 V_ij(t), the value of preference function is also dynamized for the corresponding criterion value - P_Ki V_ij(t), which means that now the preferences of scenario S_j are changed according to criterion K_i 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 S_j - DEF_j(t). Therefore, the formula defining the 'dynamic efficiency function' of the scenario S_j is:

DEF_j (t) = P_Ki V_ij(t) W_i

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:

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_Gsr_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_DP+P_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.

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^th 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).

Comparing the efficiency curves it is 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.

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4 B. Grcic, Simulacijski model upravljanja razvojem regije, Ph.D. Thesis, Split, 1996.

5 B. Grcic, Z. Babic, E. Jurun, N. Plazibat-Tomic, Multicriterial analysis of development scenarios,

Proceedings of the 7th International Conference of Information Systems - IS '96, Varazdin, 1996.

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ModellData AS, Norway, 1993.

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