Managing production-inventory-maintenance systems with condition monitoring

Providing spare parts and maintenance services to customers has become an important revenue stream for equipment manufacturers. This paper studies a Production-Inventory-Maintenance (PIM) system where a manufacturer serves an installed base of machines. Each machine contains the same critical component, whose degradation behaviour is described by a Markov process and captured via condition monitoring. When the state of a component reaches a prespecified replacement threshold, the machine is considered to have failed and incurs downtime penalties until being repaired. There are a few repair servers and queueing dynamics follows the Machine Interference Problem (MIP). Component deterioration and server congestion provide advance demand information, which helps plan the production of spare parts in a make-to-stock routine. The unsatisfied requests for spare parts are fulfilled by emergency replenishments with lost-sales penalties. We formulate the production-control problem as a continuous-time Markov decision process, characterize the structure of the optimal policy, and develop an effective heuristic policy. Through numerical experiments, we reveal a number of notable differences between managing PIM systems and operating MIP systems alone: (1) Although identifying more degradation states has no value to MIP systems, PIM systems benefit substantially from such a refined state identification. (2) While MIP systems prefer more repair servers and higher repair operation efficiency, greater repair capacity may worsen the performance of PIM systems. (3) When the product of repair service rate and server number is fixed, a single server is always preferred in MIP systems. However, PIM systems could perform better with multiple less-efficient servers.