Sustainability in supply chains (SC) is a topic that has been widely discussed recently and, similarly to the quest to develop green SCs, it does not contemplate the integration of economic and social dimensions of sustainable SC management (SSCM). This article proposes a conceptual framework to provide key factors that act as a valuable tool to further develop quantitative models of location, inventory and transportation (LIT) problems in SSCs. The objectives of this paper are to: (i) review the literature by focusing on conceptual frameworks for sustainable SC; (ii) map and construct the conceptual framework blocks by describing each element and dimension; and (iii) validate the conceptual framework. The conceptual framework comprises five main blocks: SC structures, sustainable inputs, quantitative models, inventory policies and sustainability objectives. These five blocks are then formed by different dimensions and elements, which are described in this paper and validated in a mining case study. The results show that no previous studies propose a reference conceptual framework to model a sustainable LIT problem in a CLSC context, which is the main novelty of this paper. Finally, the conceptual framework is validated and applied as a diagnostic tool in two copper mining companies.