A Simple Dynamical Model of an Industrial Laboratory Incorporating Knowledge Stock

A model of an industrial laboratory is presented and analyzed. It is a highly simplified abstraction, and consists of a network with two stages in series, Research (R) and Development (D). Ideas and prototypes are incubated in the R stage, possibly patented and documented, and brought to a sufficiently stable level for transfer to teams of professional developers in the D stage. Revenue is generated from sale and licensing of patents at both stages, and the sale of products/solutions that are outputs of the D stage. The model is dynamic, evolving with time, which is discrete. In each time period the parent corporation gives the managers of the industrial laboratory a fixed, constant amount of money to invest in the two stages. The investments determine the capacities of the stages based on linear unit costs. A novel feature of the model is "knowledge stocks" for the stages, which represent the accumulated know-how from practicing research and development activities. Obsolescence and replenishment are responsible for their dynamic evolution, with replenishments owing to investments. The impact of the knowledge stocks is on the unit costs, which decrease by factors that are polynomials of the stocks. The memory in knowledge stocks make current investment decisions have long term impact on costs and profits. Three modes of profit maximizing decision-making are investigated, namely, myopic, long term average and an optimal control-based strategy that combines short and long term profits via discounting. The time evolutions are studied as nonlinear dynamical systems. For instance, we find, in the case of myopic profit maximizations, the existence of multiple equilibria and the phenomenon of entrapment in suboptimal regimes. Numerical results illustrate the main features of the model.