An efficient heuristic for a partially observable Markov decision process of machine replacement

There is, so far, only limited practical experience applying solution schemes for real-life partially observable Markov decision processes (POMDP's). In this work we address the special-case POMDP associated with the famous machine-replacement problem. The machine deteriorates down a series of states according to known transition probabilities. A state is identified by a probability of producing a defective item. Only a sample of the produced items is observable at each stage, in which it is to be decided whether to replace the machine or not. We suggest a very simple heuristic decision-rule that can easily handle replacement-type problems of large size and which is based on the Howard solution of the fully observable version of the problem. By a simulation experimental design we compare the performance of this heuristic relative to the generic POMDP solution algorithm which has been proposed by Lovejoy.