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Resource scheduling and routing tree construction in WiMAX mesh centralized scheduling are not defined in the standard and thus are subject to extensive research. In this paper, we consider routing and scheduling in a WiMAX-based mesh network. We assume that nodes are not necessarily stationary, but rather mobile with a mobility that may yield to frequent topology changes (e.g., failure of existing links and creation of new transmission links). We model the joint routing and scheduling as an optimization problem whose objective is either to determine a minimum length schedule by maximizing spectrum spatial reuse or maximizing the network lifetime by routing around the less stable RF-links, while satisfying a set of (uplink/downlink) end-to-end demands. While solving the problem with the two objectives, we study the tradeoffs between these two objectives. We show that minimizing the schedule length forces the joint routing and scheduling problem to generate a routing tree and feasible transmission groups which favor higher spectrum spatial reuse (and hence higher system throughput), irrespective of the robustness of the selected transmission links. In addition, we show that maximizing the network stability or lifetime yields the selection of different routing trees and slot assignments which do not necessarily result in shorter schedule length. We perform numerical experiences where we compare the performances of our proposed models with respect to the network stability and resource spatial reuse.