A Higher-Order Markov Model for a Hybrid Inventory System with Probabilistic Remanufacturing Demand

This study develops a higher-order Markov model (HOM) for an inventory system with remanufacturing, substitution, and lost sales. Defective and disposed items are other factors that are considered in addition to probabilistic demand for both manufacturing and remanufacturing items. One year is the warranty period for items manufactured, and items sold return from customers to the manufacturer in increasing cumulative percentages over the months of the year. To the best our knowledge, a higher-order Markov model has rarely been used in a hybrid inventory system. The challenge is how to determine the steady state of the system with the probable demand for manufacturing and remanufacturing. We propose a new search algorithm to select the best control strategy from several strategies, and then compare it with the two-phase local search algorithm. Each state deals with (12) a probabilistic demand (policy), so the system steady state is set to (22632) policies in total for each production plan. The results showed profit maximization using the new search algorithm compared with the two-phase local search algorithm. Also, an increase in defective and returned items over time, and therefore an increase in remanufactured items. But it does not satisfy all the demand, so manufacturing increases over time due to substitution. Substitution strategy leads to increase the expected average profit.