Notation list.

In recent years, a relatively novel paradigm known as sustainable development has been introduced in response to concerns regarding the adverse impact of industrial activities on the environment and society. Managers in the food sector have been attempting to incorporate the principle of sustainable development in their supply chains owing to the paramount importance of social and environmental considerations in creating a competitive advantage for food products. To this end, we propose a multi-objective linear mathematical model considering the three dimensions of sustainability, i.e. economic, environmental, and social, to design a sustainable food supply chain. Given today’s volatile business environment, we employ a robust optimization model by incorporating Conditional Value-at-Risk into the configuration of two-stage stochastic programming to tackle uncertainty and take up a risk-averse strategy in supply chain design. The model aims to identify the optimal production and delivery times of the products, investigate the effects of their perishability characteristic on inventory decisions, and assess the financial and environmental advantages of transportation decisions to improve the sustainability of logistics operations. A novel version of fuzzy goal programming approach is applied to solve the proposed model. Next, the applicability of the proposed model and its solution method is verified based on computational experiments on a real-world case study of a processed food company. Lastly, conflicts between the sustainability aspects are examined, and several sensitivity analyses on risk-aversion parameters are performed to provide managerial insights for industry executives seeking to optimize their network concerning sustainability issues and well-performance under worst-case scenarios.