As one of the most important requirements for wireless sensor networks, prolonging network lifetime can be realized by minimizing energy consumption in cluster heads as well as sensor nodes. While most of the previous researches have focused on the energy of sensor nodes, we devote our attention to cluster heads because they are most dominant source of power consumption in the cluster-based sensor networks. Therefore, we seek to minimize energy consumption by minimizing the maximum(MINMAX) energy dissipation at each cluster heads. This work requires energy-efficient clustering of the sensor nodes while satisfying given energy constraints. In this paper, we present a constraint satisfaction modeling of cluster-based routing in a heterogeneous sensor networks because mixed integer programming cannot provide solutions to this MINMAX problem. Computational experiments show that substantial energy savings can be obtained with the MINMAX algorithm in comparison with a minimum total energy(MTE) strategy.