Shutdown Maintenance Scheduling using Two-Stage Stochastic Programming with Endogenous Uncertainty

We introduce the problem of maintenance scheduling across two consecutive maintenance plans which require plant shutdown. Due to budget, resource, and time limitations, maintenance of some components needs to be postponed from the first shutdown to the second with the risk of costly failures in between. We minimise the total expected cost of maintenance and scheduling by developing a two-stage stochastic programming model. The first stage determines which components should be postponed, whereas the second stage determines whether these components undergo maintenance in the second shutdown based on the occurrence of a failure event. The probability of failure depends on the first-stage decision leading to a stochastic problem with endogenous uncertainty. We solve the model for randomly generated instances with a limited number of components to illustrate the complexity of the problem. We propose a strategy for the early detection of infeasible solutions and demonstrate its effectiveness through numerical results.