Abstract for: The Analysis of Characteristic Dynamics of Stock Management Structure with a First Order Supply Line Delay

Stock management is a dynamic task which is often found in managerial, physical, and biological systems. In this paper, we carry out complete parametric analysis of stock management problems with first order continuous delay aiming to obtain the range of values for different characteristic dynamics of stock. For parametric analysis, we use control theoretic approaches. We first provide the stock management structure modeled using stock-flow diagrams of system dynamics methodology. Secondly, we obtain the corresponding simplified differential equations of the stock management model. 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 paper 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.