Developing a weighted reward criterion for the Markov-based decision of road maintenance

Reward criterion is an important decision factor in a Markov-based road maintenance optimization model. At present, average reward criterion or discounted reward criterion is widely used to optimize life cycle costs of road maintenance. However, the former one cannot reflect the time value of life cycle costs whereas the latter one tends to neglect the costs accumulated in the later periods over the decision horizon. In this regard, a weighted reward criterion is developed for the Markov-based road maintenance optimization model. It measures the trade-off of the average reward and the discounted reward by setting the weights of two rewards. In addition, the existence of the optimal plan under the weighted reward criterion is proven by two numerical examples under two scenarios with and without considering the inflation on maintenance costs. Finally, comparison is conducted between the proposed criterion and the average reward criterion/the discounted reward criterion to check the impacts of discount rates and inflation rates on the optimal plan.