A Markovian production-inventory system with consideration of random quality disruption

Abstract

In this paper, we develop a stochastic model for an imperfect production-inventory system that faces random quality disruption and has limited time for production. In each time planning horizon, the inventory level is affected by product quality disruption. When the production system switches to the 'out-of-control' state from the 'in-control' state, it starts producing some defective products along with defect-free products, and this switching time is stochastic. The process of the inventory levels at the start of the time horizon is expressed by using a finite and continuous state continuous-time Markov process. We construct mathematical expressions of the transition probability, the steady-state probability, and the long-run average cost. Through a numerical experiment, the near-optimal solution is achieved. The outcome shows that under the situation of production time constraint, the integration of safety stock in an interruption prone production-inventory system, assists in improving the average cost function. The results also show that the optimal safety stock is large when the defect percentage, or the production switching rate, or the shortage cost is very high. Conversely, the small safety stock is desirable when the inventory holding cost or the rework cost is high.

Analysis of a discrete-time Markov process with a bounded continuous state space by the Fredholm integral equation of the second kind

“…To the best of our knowledge, there is currently no mathematical approach that uses the Fredholm integral equation of the second kind to study the steady state of a general discrete-time Markov process with a bounded continuous state space. Recently, Karim and Nakade [11] show such an application in a special case of an economic production quantity (EPQ) model. They derive the expression of the steady-state distribution by using Fredholm integral equations.…”

Markov Chain and Inventory Management of Manufacturing Companies in Nigeria

“…Afrinaldi (2020) employed the Markov chain in determining the number quantity of supplies required, re-order level or safety inventory level. Karim and Nakade (2020) also used the Markov chain to ensure equitable and effective distribution of inventory management and supplies. Lotfi, Mardani and Weber (2021) noted that determining the optimal quantity of supplies needed, reorder levels and safety inventory level are significant in inventory management by using a stochastic optimization model to lend support in inventory management decision-making and effective inventory management to prevent disruptions in the supply chain cycles.…”