An EPQ inventory model with Weibull distribution, dynamic time-dependent holding cost under various demand pattern using Maclaurin series approximations

In this research study we present an advanced adaption of the economic and efficient optimized production model by integrating Weibull-distributed progressive degradation, dynamic holding costs, fluctuating demand, and strong strategies for effectively managing shortages and backlogs. The economic production quantity model aims to enhance production volumes and reduce total variable costs for commodities that have a near-term expiration date yet possess a prolonged shelf life due to delayed deterioration. The model characterizes inventories with three unique demand patterns by analytically solving ordinary differential equations through Maclaurin series approximations. It specifically addresses situations when product demand varies predictably over time and accounts for the probability of defective items during production. This model has significant implications for cognitive processes in the production of consumer goods, since it provides valuable insights into efficient inventory management and production planning. The paper employs two illustrations to substantiate the utility of the established model and utilizes sensitivity analysis to propose other subjects for exploration. This work proposes an enhanced economic and efficient optimized production (EPQ) model to tackle production faults, dynamic demand patterns, Weibull-distributed deterioration-related inventory management challenges. With these components, the model tries to maximize manufacturing quantities and lower total variable costs for products with near-term expiration dates. The model analytically solves the differential equations approximating inventory levels under three different demand patterns: constant, linear, and quadratic using Maclaurin series approximations. The model also addresses the likelihood of faults in produced goods throughout the production process.