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This research formulates a multi-objective problem (MOP) for supply chain network (SCN) design by incorporating the issues of social relationship, carbon emissions, and supply chain risks such as disruption and opportunism. The proposed MOP includes three conflicting objectives: maximization of total profit, minimization of supply disruption and opportunism risks, and minimization of carbon emission considering a number of supply chain constraints. Furthermore, this research analyses the effect of social relationship levels between different tiers of SCN on the profitability, risk, and emission over the time. In this regard, we focus on responding to the following questions. (1) How does the evolving social relationship affect the objectives of the supply chain (SC)? (2) How do the upstream firms' relationships affect the relationships of downstream firms, and how these relationships influence the objectives of the SC? (3) How does the supply disruption risk interact with the opportunism risk through supply chain relationships, and how these risks affect the objectives of the SC? (4) How do these three conflicting objectives trade-off? A Pareto-based multiobjective evolutionary algorithm-non-dominated sorting genetic algorithm-II (NSGA-II) has been employed to solve the presented problem. In order to improve the quality of solutions, tuning parameters of the NSGA-II are modulated using Taguchi approach. An illustrative example is presented to manifest the capability of the model and the algorithm. The results obtained evince the robust performance of the proposed MOP.

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