An optimization method for joint replacement decisions in maintenance

Maintenance of safety-critical assets, such as jet engines, generators, etc. is very expensive. These assets usually consist of multiple life-limited parts which are grouped in different modules, and ask for shop or on-site visits subject to part expiration or random failures. The total cost includes shop (or on-site) visit costs, asset out-of-service costs, module removal costs, part replacement costs, and part waste costs. The problem in this paper is to decide when to perform maintenance and which parts to replace each time to optimize the total cost for a fixed-length contract in discrete time units. Because decisions for parts are correlated, optimization of joint replacement decisions encounters combinatorial explosion and it is usually difficult to find the optimal or good enough solution. This paper develops a new and separable model, where the solution is obtained iteratively from several linear or quadratic problems, providing linear formulations for all coupling relations (among parts, modules and the asset). Lower bounds are provided in the mean while. Numerical results show that this method achieves the optimal costs for small problems and achieves costs within 5% beyond the lower bounds for middle or large examples. Its computational time is linear to number of parts and modules and linear to the length of time horizon as well.