Food loss, wastage, and emissions generated from food supply chains are critical global issues. An important factor directly related to these issues is the perishability of food products. The research develops an interconnection between environmental and perishability aspects. It proposes that organizations in food supply chains must consider product characteristics such as perishability while designing their supply chains in order to pursue climate neutrality goals. This study presents a mathematical model for sustainable supplier selection and order allocation in perishable food supply chains. The model is formulated using the fuzzy-best worst method and fuzzy-multi-objective mixed-integer linear programming. A two-stage approach is followed, wherein in the first stage, fifteen sustainability focused factors for supplier selection are modelled to formulate a sustainable supplier selection index using fuzzy-best worst method. Factors such as energy and resource efficiency, environmental impact management, and social and economic sustainability factors, are considered for sustainable supplier selection. In the second stage order allocation decision is optimized by simultaneously optimizing the objectives of sustainable supplier selection, cost, environmental objectives of emissions optimization, and wastage minimization. Fuzzy modelling approach is used to incorporate uncertain nature of various modelling parameters. A weighted-goal programming approach is used to solve the multi-objective problem. The results provide us with environmentally-sustainable supplier selection and order allocation decisions along with cost efficiency and less wastage. The results show a significant improvement of 28.78% in food wastage and 28.21% in emissions, which can be achieved with only about a 6.48% increase in cost. This study provides interesting insights about how the performance of perishable supply chains changes with considerations of emissions and wastage constraints. It shows that the inclusion of perishability, wastage, and environmental objectives are key for organizations working towards climate neutrality in food supply chains.