This paper aims at designing a sustainable logistics model with a heterogeneous collaboration approach. In this regard, we worked on a logistics system by transmitting raw materials to a factory and then sending various products to consumption centers. Accordingly, three logistics layers of supply, production, and consumption were designed and the parameters of collaboration within and between the logistics layers were evaluated. After that, as novelty of our paper, the interactions of sustainability indicators with the logistics network and their effects on the collaboration were analyzed through productivity. In this paper, we use two objectives includes minimizing the supply chain costs and maximizing the productivity of the collaboration parameter affecting the sustainability indicators at different levels. Finally, the developed mathematical model is solved and validated in GAMS optimization software to analyze the performance of the proposed approach using epsilon constraint method.