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Supply chains (SC) in an attempt to be more competitive, are adopting new management paradigm. Among these paradigms there are four that deserve particular mention because of their importance to better SC performance: lean, agile, resilient and green. The main objective of this paper is to propose a conceptual model for a lean, agile, resilience and green SC, with the purpose of improving their operational, economic and environmental performance. In this attempt a set of SC management practices, which were named LARG practices, and several performance measures are suggested. This model is based in the literature review about the four SC management paradigms and also SC performance measurement. Among the suggested LARG practices the ones influencing more the SC performance are the just in time and also the supplier relationships. Also the SC performance measures with more LARG practices influencing them are the inventory levels and the time, that is, the SC's operational performance is the most affected.