Optimal Dynamical Balance of Raw Materials - Some Concept of Embedding Optimization in Simulation on System Dynamics Models and Vice Versa

摘要

The purpose of this paper is to present the optimal dynamic balance of raw materials in two formulations. The model DYNBALANCE(3-1) appears in two cases, named I and II. The main idea of case I of model DYNBALANCE(3-l)concist in optimal control of supplying three raw materials according to productivity of three technologies, by taking into consideration possibilities of sources of raw materials and actual demand for product on market. This optimal control lies in optimal balancing of raw materials, according to plans: cost of raw materials, cost of production and according to forrecast of demand. The objective function in optimizing process (in Coyle's sense) is consisted of three main components and one component which has "penalty" function. The optimization experiments were performed usying COSMOS package (Computer - Oriented System Modelling Optimisation Software), which is software tool automatically linking a dynamic simulation model to an optimization package. In this paper authors present the whole structure of model DYNBALANCE(3-1) case I, with the legend and list of variables and parameters. The equations of the model reader can find in program output in Appendix B.The main idea of case II of model DYNBALANCE(3-1) concist in replecement of problem of solving of balance of raw materials, which minimize the norm ‖Ax - b‖ (at the condition x ≥ 0) by the problem of solving pseudosolution of extended balance of raw materials, which minimize the norm ‖Ax - b‖ (without condition x ≥ 0). The benefit of such solution of problem is that we can embedding optimization in simulation on System Dynamics model by using language Dynamo. In each step during simulation theprogram solves the x by the Legras formula: (A(T)A)~(-1)A(T)b, step by step. Such a solution (balance of raw materials) we can named "dynamic", so the embedding the optimization in simulation, on System Dynamics models, has dynamical character.Many interesting experiments were undertaken by authors and discussed in paper. At the end of paper some conclusions were formulated, specially concerning the problem of simplificationes of models.