models type SD. The idea of three dimensional structure of experiments was invented by Kasperska. The object of experiments is the model DYNBALANCE(2-2). Many examples of different kind of experiments (from "crossing" different "surfaces" of invented system) were presented in paper. At the end, some conclusions are formulated.
Key words: System Dynamics Method, Optimization and Simulation, Model DYNBALANCE(2-2).
1. Introduction
Model DYNBALANCE(2-2) is the one from "family" of models type "ba-lancing the production and raw materials". Such models were named: DYNBALANCE(1-3) [KMLS00a, KMLS00b], DYNBALANCE(3-1) [KMLS01], DYNBALANCE(3-1-II) [Ka02a]. The model DYNBALANCE(2-2) is the newest member of this family, already described in paper [KaSł03]. Now, authors will present only the general structure of this model and concentrate on extension the simulation and optimization experiments on this model. These experiments were planned according to the idea of three dimensional structure of experiments on models type SD. This idea was already applied by Kasperska on model DYNBALANCE(3-1-II) [Ka02b]. Figure 1 present the general structure of model DYNBALANCE(2-2) and Figure 2 present the idea of the structure of experiments.
Fig. 1. The general structure of the model DYNBALANCE(2-2)
Fig. 2. General idea of three dimensional structure of experiments (invented by Kasperska [KaML03])
The structure of model DYNBALANCE(2-2) was modelled using Łukaszewicz symbols [Łu75, Łu76], which were described dentally in [Ka02b].
In paper [KaSł03] authors have presented two different methods of embed-ding the optimization in simulation on model DYNBALANCE(2-2). They were illustrated by some experiments on this model, but authors didn't pay enough attention to problem of using specific types of experiments for solving specific problem of supporting the decisions in organization. Now, on the base of expe-rience of formulation of three dimensional structure of experiments and on the base of remarks placed in paper [Ka02] authors have performed "putting in or-der" experiments and some conclusions about present below.
Fig. 3. The characteristic of variables: norm, profit, copr1 and copr2 under the
condition: price1=300, price2=350)
Experiment 1 (type of "trials and errors"). This experiment is the example from the "structure of modelling" (see Figure 2). Such interior parameters like: price1, price2 were changed and we explored the influence of that on dynamic of system, in each step of simulation. The characteristic of variable norm, profit and copr1, copr2, upon different condition of price1 and price2, are presented on Figure 3 and 4. This kind of experiment makes possible to study the "sensi-tivity" of parameters and, in consequences, helps in the descriptive - explanatory approaches, which gives the basic information about the structure of the system (and rules of its functioning).
Fig. 4. The characteristic of variables: norm, profit, copr1 and copr2 under the condition: price1=600, price2=700)
Experiment 2 (type of minimalization of cost of production). This experiment is the example from the "structure of optimization" (see Figure 2). The interest-ing point of view is the comparinterest-ing the results of minimalization of cost and max-imalization of profit. The Reader can study the dynamics of system in both cases on Figures 5 and 6. The decision - maker has possibilities to compare and choose the "optimal" decisions and, what is more important, to predict the dynamical consequences of these decisions on the whole system (its behaviour). Such is the strength of System Dynamics method, "enriched" with optimal procedures. Fig. 5. The dynamics of variables: lin1, lin2 and profit in experiment of
Fig. 6. The dynamics of variables: lin1, lin2 and profit in experiment of maxima-lization of profit
Experiment 3 (type of "what if?"). This kind of experiment allows to study the effects of changing the condition of "sources" of system. The equations for sources: rd1, rd2 (rates of demands for product P1, P2), are:
rd1.k = po+step(p1,0), rd2.k = po+step(p2,0).
The results of such demands are presented on Figure 7 and for comparison the option of sinusoidal rd1, rd2 on Figure 8.
Fig. 7. The characteristic of demand and levels of production (demands have "steps" characteristic)
During creating the model and simulating the dynamics, authors have per-formed so many experiments, that it is not possible to present them all in this section. Authors have wanted to show the examples of experiments from struc-ture of experiments and on base of that, stress the specific possibilities different kinds of experiments, for learning process of decision - makers. In conse-quences, this process of learning leads to effective supporting of the decisions. So, it is time for final remarks and conclusions.
Fig. 8. The characteristic of demands and levels of production (demands have "sinusoidal" characteristic)
3. Final remarks and conclusions
The purpose of the paper was to present the extension of simulation and op-timization experiments on model DYNBALANCE(2-2). The specific types of experiments from three dimensional structure were presented and results of changing the specific assumptions for experiments were shown in illustrative form. Final conclusions are as follows:
• the idea of three dimensional structure of experiments is very fruitful, in sense of consequences of different kind of experiments for specific needs of supporting the decisions in economic organizations,
• the size of model DYNBALANCE(2-2) (the complexity of base structure and formalization of optimization procedures) is that, that makes possible ef-fective learning process from man – computer - model chain. The future de-velopment of model can make easier the application of model not only in works with students but in real production~-- trade enterprises as well, • possibilities of languages Professional Dynamo [Pu94] or COSMIC and
COSMOS [Co94], allows to performed simulation and optimization experi-ments, which are the fruitful and progressive way of extending the classical System Dynamics method.
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ROZWÓJ SYMULACJI I OPTYMALIZACJI NA MODELU DYNBALANCE(2-2)
Celem pracy jest zaprezentowanie rozwoju symulacyjnych i optymalizacyjnych eksperymentów na modelu DYNBALANCE(2-2). Autorzy zastosowali ideę trój-płaszczyznowej struktury eksperymentów na modelach typu Dynamiki Systemo-wej. Przedstawiono wyniki wielu ciekawych eksperymentów na modelu DYNBALANCE(2-2), zgodnych z tą ideą. Na końcu sformułowano pewne wnio-ski, w szczególności związane ze wspomaganiem decyzji w organizacjach eko-nomicznych.
Słowa kluczowe: Dynamika Systemowa, Optymalizacja i symulacja, Model DYNBALANCE(2-2).