A sustainable agro-industrial value chain is essential for sustained food security. This requires optimised planning of operations and new expansions along the value chain. In this work, a fuzzy-based multi-objective approach is developed for planning sustainable new expansions of agriculture lands. Also, the expansion and capacity of post-harvest and production facilities and operations of logistics in the agro-industrial value chain are optimised. The model is a mixed-integer linear program (MILP) which takes profit, carbon footprint, and water footprint into account during optimisation. The expansion plan is optimised based on the expected increase in the demand for a particular agro-industrial product. To illustrate the proposed model, a palm value chain case study is solved. A scenario with a projected increase in palm oil demand is considered to demonstrate the model. The results for the case study showed a distinctive difference in the expansion strategy compared to single-objective optimisation, exhibiting trade-off between profit and carbon, water footprints.