# THE EXTENSION OF SIMULATION AND OPTIMIZATION ON MODEL DYNBALANCE(2-2)

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1 THE EXTENSION OF SIMULATION AND OPTIMIZATION ON MODEL DYNBALANCE(2-2) Abstract ElŜbieta Kasperska, Damian Słota Institute of Mathematics Silesian University of Technology ul. Kaszubska 23, Gliwice The purpose of this paper is to present the extension of simulation and optimization experiments on model DYNBALANCE(2-2). An interesting point of view is to apply on this model the idea of three dimensional structure of experiments on 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 "balancing 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.

2 256 Metody formalne w SWO 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].

3 The extension of simulation and optimization 257 The idea of three dimensional structure of experiments on models type SD, was invented by Kasperska on the base of her considerations about different kind of approaches within System Dynamics method (this problem was undertaken in paper [Ka02a]). Now, authors want to pay attention on some experiments on model DYNBALANCE(2-2), which represent the different "crossing" of the surfaces of structure of experiments. 2. The extension of simulation and optimization on model DYNBALANCE(2-2) In paper [KaSł03] authors have presented two different methods of embedding 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 experience of formulation of three dimensional structure of experiments and on the base of remarks placed in paper [Ka02] authors have performed "putting in order" 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 "sensitivity" 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).

4 258 Metody formalne w SWO 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 interesting point of view is the comparing the results of minimalization of cost and maximalization 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 minimalization of cost

5 The extension of simulation and optimization 259 Fig. 6. The dynamics of variables: lin1, lin2 and profit in experiment of maximalization 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 performed 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 structure of experiments and on base of that, stress the specific possibilities different kinds of experiments, for learning process of decision - makers. In consequences, this process of learning leads to effective supporting of the decisions. So, it is time for final remarks and conclusions.

6 260 Metody formalne w SWO 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 optimization 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 effective learning process from man computer - model chain. The future development 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 experiments, which are the fruitful and progressive way of extending the classical System Dynamics method. References [Co77] [Co78] [CoWo80] Coyle R. G., Management System Dynamics, John Wiley & Sons, New York Coyle R. G., System Dynamics - The state of the art, Dynamica 5 (1978), Coyle R. G., Wolsterholm E. P., Modelling discrete events in System Dynamics models - a case study, Dynamica 6 (I) (1980),

7 The extension of simulation and optimization 261 [Co94] Coyle R. G., ed., Cosmic and Cosmos. User manuals, The Cosmic Holding Co, London [Co96] Coyle R. G., System Dynamics Modelling. A Practical Approach, Chapman & Hall, London [Co98] Coyle R. G., The practice System Dynamics: milestones, lessons and ideas from 30 years experience, System Dynamics Rev. 14 (1998), [Co99] Coyle R. G., Simulation by repeated optimisation, J. Opt. R. S. 50 (1999), [Fo61] Forrester J. W., Industrial Dynamics, MIT Press, Massachusetts [Fo69] Forrester J. W., Urban Dynamics, MIT Press, Massachusetts [Fo71 orrester J. W., World Dynamics, Wright-Allen Press, Massachusetts1971. [Fo72] Forrester J. W., Principles of Systems, Cambridge Press, Massachusetts [Fo75] Forrester J. W., Collected papers of Jay W. Forrester, Cambridge Press\Wright Allen Press, Massachusetts [KaSł00] Kasperska E., Słota D., Metody matematyczne w zarządzaniu w ujęciu Dynamiki Systemowej, wyd. II, Wyd. Pol. Śl., Gliwice [KMLS00a] Kasperska E., Mateja-Losa E., Słota D., Some extension of System Dynamics method - theoretical aspects, in: Proc. 16th IMACS World Congress, M. Deville, R. Owens, ed., IMACS, Lausanne 2000, , 1-6. [KMLS00b] Kasperska E., Mateja-Losa E., Słota D., Some extension of System Dynamics method - practical aspects, in: Proc. 16th IMACS World Congress, M. Deville, R. Owens, ed., IMACS, Lausanne 2000, , 1-6. [KMLS01] Kasperska E., Mateja-Losa E., Słota D., Some dynamics balance of production via optimization and simulation within System Dynamics method, in: Proc. 19th International Conference of the System Dynamics Society, J. H. Hines, V. G. Diker, R. S. Langer, J. I. Rowe, ed., SDS, Atlanta 2001, [KMLS02] Kasperska E., Mateja-Losa E., Słota D., Optimal dynamical balance of raw materials - some concept of embedding optimization in simulation on system dynamics models and vice versa, in: Proc. 20 International Conference of the System Dynamics Society, P. I. Davidsen, E. Mollona, V. G. Diker, R. S. Langer, J. I. Rowe, ed., SDS, Palermo 2002, 1-23.

8 262 Metody formalne w SWO [Ka02a] Kasperska E., Cybernetic formulation of some functions of management - types of simulation and optimization approaches within the System Dynamics method, in: Proc. 20 International Conference of the System Dynamics Society, P. I. Davidsen, E. Mollona, V. G. Diker, R. S. Langer, J. I. Rowe, ed., SDS, Palermo 2002, [Ka02b] Kasperska E., Supporting the decision in organization by the inteligent simulation package Cosmic and Cosmos}, Pr. Nauk. Akad. Ekonom. w Katowicach, "Support Systems in Organization" (2002), [KaSł03] Kasperska E., Słota D., Two different methods of embedding the optimization in simulation on model DYNBALANCE(2-2), in: Proc. 21 International Conference of the System Dynamics Society, SDS, New York 2003 (in print). [KaML03] Kasperska E., Mateja-Losa E., The structure of simulation and optimization experiments on model DYNBALANCE(3-1-II), in: Proc. 21 International Conference of the System Dynamics Society, SDS, New York 2003 (in print). [Łu75] Łukaszewicz R., Dynamika systemów zarządzania, PWN, Warszawa [Łu76] Łukaszewicz R., The direct form of structure models within System Dynamics, Dynamica 2 (1976). [Pu94] Pugh A. L., ed., Professional Dynamo 4.0 for Windows. Tutorial Guide, Pugh-Roberts Associates, Cambridge [Se98] Senge P.H., Piąta dyscyplina, Dom Wyd. ABC, Warszawa [Se02] Senge P. H., Piąta dyscyplina zbiór ćwiczeń, Oficyna Ekon., Warszawa [St00] Sterman J. D., Business dynamics - system thinking and modeling for a complex world, Mc Graw-Hill, Boston 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 trójpłaszczyznowej struktury eksperymentów na modelach typu Dynamiki Systemowej. Przedstawiono wyniki wielu ciekawych eksperymentów na modelu DYNBALANCE(2-2), zgodnych z tą ideą. Na końcu sformułowano pewne wnioski, w szczególności związane ze wspomaganiem decyzji w organizacjach ekonomicznych. Słowa kluczowe: Dynamika Systemowa, Optymalizacja i symulacja, Model DYNBALANCE(2-2).

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