A Production Inventory Model for Fractionally Time-Dependent Demand Rate with Weibull Deterioration and Partially Backlogged Items

This article presents a report on a creation stock model that the point is to foster an ideal creation and stock procedure that boosts the general benefit while thinking about the impact of expansion on the decaying things over the long haul. The exponential demand rate is thought to accurately reflect real-world demand fluctuations over time. The model gives a manager’s realistic representation of the production and inventory system by considering these aspects, allowing them to make informed decisions. To enhance the creation and stock strategy, a numerical structure is created, consolidating different expense parts, for example, holding cost, arrangement cost, creation cost, and lack cost. The goal is to find the ideal creation amount and reorder point that limit the all-out cost and expand the general benefit. The proposed model's analytical results show a complex connection between the optimal production quantity, reorder point, and other relevant parameters. According to the findings, production inventory models must consider both the exponential demand rate and the inflation rate of deteriorating goods. The proposed model offers a pragmatic methodology for upgrading the creation and stock choices, at last improving the productivity and functional effectiveness of organizations managing crumbling things within the sight of expansion. This paper has followed an analytical approach to diminish the entire inventory cost. Finally, a sensitivity analysis was performed to study the effect of changes of different parameters of the model on the optimal policy. Moreover, in order to approve the determined models, we have clarified mathematical models and examined affectability.