With the expansion of the study about green logistics, sustainable supply chain management (SSCM) has appeared as a new concept in current economic circumstance. This paper studies the sustainability optimization of enterprise logistics network from a strategic perspective and proposes a multiobjective sustainable logistics optimization model considering three dimensions of sustainability: economy, environment, and society. In this model, the environment factor was measured with a Life Cycle Assessment (LCA) method based on Chinese Life Cycle Database (CLCD), while for social factors, Sustainability Reporting Guidelines (GRI) are utilized to quantify the social performance. Moreover, the model was solved with an adapted version of the ε-constraint method named augment constraint algorithm (AUGMENCON) through GAMS software. The numerical experiment results of a computer manufacturer supply chain show that the proposed model is able to integrate all dimensions of sustainability and simultaneously prove the capability of AUGMENCON in providing a set of trade-off solutions for the decision makers to make different decisions under different environment and social requirements.