Dynamic Production Inventory Systems with Deterioration: Nonlinear Modelling and Game-Theoretic Extensions

Source abstract

This study develops and analyses a nonlinear production inventory model for non-instantaneous deteriorating items under time-dependent production and demand rates. The model is further extended into a differential game setting to capture strategic interactions between production and demand agents. Analytical solutions are derived for the deterministic model, while the game-theoretic system is solved numerically using a forward–backward sweep method. Cost functionals and optimal cycle time are studied. The results demonstrate that incorporating dynamic controls and strategic interactions significantly improves modelling realism and decision-making efficiency.