Abstract-In wireless sensor networks (WSNs), the field information (e.g., temperature, humidity, airflow) is acquired via several battery-equipped wireless sensors and is relayed towards a sink node. As the size of the WSNs increases, it becomes inefficient (in terms of power consumption) to gather all information in a single sink. To tackle this problem, one can increase the number of sinks. The set of sensor nodes sending data to sink k is called commodity k. In this paper, we formulate the lexicographically optimal commodity lifetime routing problem. A stepwise centralized algorithm, called the lexicographically optimal commodity lifetime (LOCL) algorithm, is proposed which can obtain the optimal routing solution and lead to lexicographical fairness among commodity lifetimes. We then show that under certain assumptions, the lexicographical optimality among commodity lifetimes can be achieved by providing lexicographical optimality among node lifetimes. This motivates us to propose our second algorithm, called the lexicographically optimal node lifetime (LONL) algorithm, which suitable for practical implementation. Simulation results show that our proposed LOCL and LONL algorithms increase the normalized commodity and node lifetimes compared to the maximum lifetime with multiple sinks (MLMS) [1] and lexicographical max-min fair (LMM) [2] routing algorithms.