The analysis of characteristic dynamics of stock management structures

Abstract

Stock management is a dynamic task which is often found in managerial, physical, and biological systems. The aim in stock management is to bring a stock at a desired level and maintain it at that level by taking corrective actions. Stock management task imposes difficulties to the decision maker, which results in unwanted oscillations. In this thesis, different stock management structures are modeled and analyzed. We carry out complete parametric analysis of stock management problems with continuous delays of first, second, and third orders aiming to obtain the range of values for different characteristic dynamics of stock. For parametric analysis, we use control theoretic approaches. We first provide different stock management structures modeled using stock-flow diagrams of system dynamics methodology. Secondly, we obtain the corresponding simplified differential equations of the system dynamics model and, based on the differential equations, we obtain block diagrams. Thirdly, we convert simplified differential equations of the model from time domain to s-domain using Laplace transformation technique and obtain the transfer function. Fourthly, the characteristic equation of the transfer function is determined. Finally, we determine the critical values of the decision parameters at which a qualitative change in dynamics is observed by analyzing the roots of the characteristic equation. The critical values that are reported in this thesis are valid for all durations of the delay between the corrective actions and their eventual results on the stock. We also obtained a few counterintuitive results such as increasing the level of aggressiveness in stock corrections can completely eliminate oscillations in one of the cases. Aiming to build a bridge between system dynamics and control theory, the corresponding block diagrams of many basic system dynamics models are provided in the thesis and also in one of its appendices.