Agri-food sector performance strongly impacts global economy, which means that developing optimisation models to support the decision-making process in agri-food supply chains (AFSC) is necessary. These models should contemplate AFSC’s inherent characteristics and sources of uncertainty to provide applicable and accurate solutions. To the best of our knowledge, there are no conceptual frameworks available to design AFSC through mathematical programming modelling while considering their inherent characteristics and sources of uncertainty, nor any there literature reviews that address such characteristics and uncertainty sources in existing AFSC design models. This paper aims to fill these gaps in the literature by proposing such a conceptual framework and state of the art. The framework can be used as a guide tool for both developing and analysing models based on mathematical programming to design AFSC. The implementation of the framework into the state of the art validates its. Finally, some literature gaps and future research lines were identified.