Robust optimization for integrating preventative maintenance with coal production under demand uncertainty

We consider a coal mine producing a catalog of products through multiple pieces of equipment with variable production rates over a multi-period horizon, where each product faces random demand in each period. Each piece of equipment requires Preventative Maintenance (PM) with a given duration. We study a joint PM and production problem that adaptively determines the PM starting time and the production rates for the equipment to minimize the expected total cost. We formulate a multi-period stochastic optimization model that is challenging to solve due to the complexity of adjustable binary decisions. This motivates us to propose a two-phase approach based on robust optimization to solve the problem. Phase 1 determines the binary PM decisions using a target-oriented robust optimization approach. Fixing the PM decisions, Phase 2 adaptively determines the production rates using a linear decision rule. Numerical experiments suggest that our approach outperforms some existing approaches that handle adjustable binary decisions, and performs very close to the expected value given perfect information for varying problem instances. A case study using real data from a major coal mine in China suggests that implementing our approach can potentially yield cost savings in the long run over the status quo policy.