Analysis of an Inventory Model for Time-Dependent Linear Demand Rate Three Levels of Production With Shortage

Abstract

Objective: The objective of this study is to investigate the continuous-production inventory problem for a single product at a three-level facing a constant deterioration rate. It is anticipated that the customer will make renewal arrangements in accordance with the established and extensively utilized order-up-to policy, and may place orders from two providers with differing prices and levels of consistency. Theoretical Framework: In this study demand is a linear function of time, and the deterioration rate is persistent. In this model, the shortage is allowed, and partial backlogging. It is expected that the backlog rate is influenced by how long it takes to get the next replenishment. It involves aspects from various areas of scientific knowledge to understand the different perceptions contained in the scientific literature on the phenomenon of Industry 4.0. Method: The algorithms for this model have been developed in Mathematica Software 9.0. We examine the effects of several difficulty criteria on the best options regarding manufacturing time and replenishment at the store using analytical analysis. Results and Discussion: Thus, our model offers a novel management insight that aids in achieving the ideal profit level for a production system or business. In reality, we obtain a promising outcome from the numerical case. To compare various solutions, we also carry out very comprehensive numerical experiments. Research Implications: This research aims to detect the best course of action for reducing overall inventory costs and increasing overall income. We also verified that the total cost and commonly optimal time used to interrupt geometric production systems could be analyzed with a constant production model. This approach is particularly relevant for organizations seeking to improve operational efficiency and customer satisfaction through better risk management. Originality/Value: This study contributes to our understanding of how and with whom to collaborate by highlighting the relationships among inventory management, innovation performance, and logistics performance. The value of the study is the contribution it makes to the literature on the cost analysis issues. Therefore, the article can be of benefit to the scientific community with an interest in the study of the subject.