Joint replacement optimization for multi-part maintenance problems

A model of multi-part asset with dependent maintenance cost is presented. The problem is to minimize the long-run average cost per time unit. To share some costs, a good policy may jointly replace multiple parts when an asset is maintained. However, it is difficult to obtain an optimal joint replacement policy in view of combinatorial explosion of the states and stochastic system dynamics. To obtain optimal policies for small problems, a novel method is built by recent developed time aggregation Markov decision approach, which leads to analytical and computational simplifications as compared with traditional Markov decision approaches. One-stage and two-stage analysis methods are developed for large problems. The upper bound of one-stage analysis method for single part problems is obtained to show the insight that it can achieve near or true optimal policy. For multi-part problems, they are proved to satisfy certain necessary optimality conditions. These conditions can significantly simplify their implementation. Numerical results show that they are more efficient and effective than other near optimal methods.