Cluster scheduling is a crucial issue in cluster-tree Wireless Sensor Networks (WSNs). The paper presents a methodology that provides a Time Division Cluster Scheduling (TDCS) mechanism based on the shortest path problem. The objective is to meet all the flows' deadlines defined by the maximum number of crossed periods for each flow to reach its destination assuming one collision domain. Formulating the problem as the shortest path problem gives us a light exact algorithm suitable to the scarce properties of WSNs especially related to memory, power consumption and processors. Our polynomial algorithm leads to the minimization of the energy consumption and, consequently, the lifetime of the network is maximized by setting the TDCS period as long as possible. Since each cluster is active only once during the period, the given flow may span over several periods when there are flows with an opposite direction. The scheduling tool enables the system designers to efficiently configure all the required parameters of the IEEE 802.15.4/ZigBee beacon-enabled cluster-tree WSNs in the network configuration time.