Optimal lot-sizing and maintenance policy for a partially observable production system

• Joint development of the EMQ model of a deteriorating system and CBM.
• Consideration of both maintenance and production-related costs.
• Hidden Markov modeling of the partially observable production system.
• Development of the semi-Markov decision process and the optimization algorithm.
• Numerical studies and comparisons show an excellent performance.

In this paper, we present a joint optimization of economic manufacturing quantity (EMQ) and maintenance policy for a production facility subject to deterioration and condition monitoring (CM) at the times the production runs are completed. The production facility deterioration is described by a hidden continuous-time Markov process. CM provides partial information about the hidden state of the production facility. The objective is to develop a jointly optimal lot sizing and maintenance policy using multivariate Bayesian control approach. The posterior probability statistic is updated at each sampling epoch using Bayes’ rule. When the posterior probability crosses a control limit, the production system is stopped and full inspection is initiated, followed possibly by preventive maintenance (PM). Production will resume when all available inventory is depleted or when PM action is completed, whichever occurs later. We also assume that the production and demand rates are constant over time. The problem is formulated and solved in the semi-Markov decision process (SMDP) framework. The objective is to minimize the long-run expected average cost per unit time. The shortage and set-up costs are considered in the model along with the maintenance, inventory holding, and lost production costs. A numerical example is provided and a sensitivity analysis is performed. A comparison with the age-based maintenance policy shows an outstanding performance of the new model and the control policy proposed in this paper.