A Mathematical Model for the Implementation of New Technologies in Shipbuilding: Dynamics Analysis and Efficiency Assessment

Abstract

This article presents a comprehensive mathematical model describing the process of implementing innovative technologies in the shipbuilding industry. While diffusion models are widely studied, there is a lack of deterministic dynamic models that integrate financial, technical, and human capital factors specifically for capital-intensive industries like shipbuilding. The model focuses on the key parameters determining the speed and success of technology diffusion: economic efficiency, investment level, adaptation costs, and personnel qualifications. Based on the apparatus of differential equations and methods of multi-criteria optimization, a system has been constructed that allows for a quantitative assessment of the impact of control actions (e.g., the volume of state subsidies or the intensity of retraining programs) on the pace of technological modernization of a shipbuilding enterprise. The stability of the model is analyzed, and critical conditions under which the implementation becomes self-sustaining are determined. The main contributions include: the derivation of an analytical critical success condition; a numerical demonstration of scenarios leading to success, stagnation, or failure; practical recommendations for structuring investments. The results can be used to formulate technological development strategies for shipbuilding holdings and to substantiate state support programs for the industry.