Integrated Inspection Planning and Preventive Maintenance for a Markov Deteriorating System Under Scenario-based Demand Uncertainty

In this paper, a single-product, single-machine system under Markovian deterioration of machine condition and demand uncertainty is studied.  The objective is to find the optimal intervals for inspection and preventive maintenance activities in a condition-based maintenance planning with discrete monitoring framework. At first, a stochastic dynamic programming model whose state variable is the machine status is presented. In the first model, the demand is assumed to be deterministic and the objective is to minimize the sum of inspection, preventive maintenance, and lost sale costs. Then, in order to take the demand uncertainty into account, the extended model is formulated as a scenario-based two-stage stochastic programming one. In the second model, selecting the best inspection plan and finding the appropriate intervals for preventive maintenance are considered as the first and second stage decisions, respectively. Analyzing an illustrative example to study the effect of demand uncertainty in the problem shows thatthe total average cost is a non-decreasing function of machine state and demand. Moreover, if the machine state is worsened or the demand is increased, the number of inspections increase and the preventive maintenance should be executed at the same time or earlier. Finally, when the unit lost sale cost is greater than a certain amount, ignoring the demand uncertainty is not costly.