Substitution strategy in a production-inventory system according to the higher order Markov model

Abstract

Markov models are frequently employed in a variety of real-world systems, including industrial and queuing systems. Higher order Markov model (HOM) of inventory system including remanufacture, substitution, and lost sales is developed in this study. Additionally taken into consideration are deterioration during storage, disposal, and probabilistic demand. A separate warranty period for newly created and previously manufactured goods is returned to the manufacturer. We believe that a higher order Markov model has only occasionally been applied to a production inventory system. Finding the system's steady state presents a hurdle. Another challenge is that one of the state variables depends not on its previous states but on the previous states of other variables. determines the system's requirements at its steady state 3910 regulations. Our results show increasing in the re-manufactured and deteriorated items over time. Also, inventory levels in the three warehouses. Meanwhile, an opposite conclusion in the case of manufactured, substitution, and lost sales. Substitution processes lead to increase the expected average profit.