Decision-making models based on optimization and differential equations

Decision-making systems are fundamental in management, influencing organizational efficiency, resource allocation, and strategic outcomes. Traditional qualitative approaches often fail to capture the dynamic interactions and uncertainties inherent in complex systems. This paper presents a mathematical modelling framework for decision-making systems using differential equations and optimization techniques. The model represents the temporal evolution of multiple decision variables, incorporating both internal interactions and external stimuli. Numerical simulations, performed via Runge-Kutta methods, demonstrate the dynamic behaviour of the system under various scenarios. Results highlight the stability, sensitivity, and effectiveness of different decision strategies, providing insights for practical management applications and strategic planning.

Keywords: Decision-making systems, mathematical modelling, differential equations, optimization, numerical simulation