Stochastic modelling and analysis of a deteriorating serial production–inventory network

This study focuses on the stochastic modelling and analysis of a serial production network consisting of two manufacturing stations operating under a make-to-stock inventory policy. The outcome is a single type of product and every manufacturing station includes a machine and an output buffer. Both machines are gradually deteriorating during their operation. Deterioration results in a reduced production rate. Continuous-time Markov chain was used to model all the possible states the network transits over time due to the occurrence of certain events, such as client arrival, deterioration failure, production or repair completion. The structure of the Markov chain was thoroughly studied providing useful information, supporting the effort of numerical solving to determine the steady-state probabilities enabling the calculation of useful performance metrics like equipment availability, down time, idle time, utilisation and average inventory. Through a series of numerical experiments, the behaviour of the serial production network was examined while alternating its parameters. Interesting conclusions emerged regarding the factors affecting the operation of such production systems subjected to gradual deterioration.