Emergency response systems should respond to disasters in a timely and cost-effective manner. One of the most complicated tasks facing managers is debris management. During post-disaster operations, response teams must make road network connections between supplier nodes and demand (population) nodes in order to protect human health and safety. The effectiveness of response operations depends on positioning of relief supplies in anticipation of new clearance equipment requests at new locations, as well as with relocation of clearance equipment items to rebalance the use of items post disaster. To solve this problem, a novel dynamic post-disaster debris clearance problem is introduced—one that features non-myopic positioning of clearance equipment items based on a queuing formulation that is compatible with the maximum-weighted flow problem under incomplete information proposed by Çelik et al., (2015). By including a clearance equipment positioning strategy, we improve the strategy of the stochastic debris clearance problem, with a new framework on dynamically optimizing the post-disaster debris clearance strategy with limited observable information about the disaster-relief resources located on the road network. The proposed dynamic debris clearance approach sets out to satisfy the need for debris clearance and relief services by using the connection between the demand nodes and the supplier nodes in a case where information on the disaster region is only partially observable. An empirical study of Hurricane Harvey in the City of Houston was performed to obtain concepts into the impacts of dynamic programming model and parameters in order to supply the needed relief via a positioning strategy for clearance equipment items.