Food banks and food pantries play a crucial role in addressing global food insecurity by collecting and distributing food resources to vulnerable populations. However, effectively addressing diverse nutritional needs and achieving fairness under the limited availability of food resources poses a significant challenge. This study presents a solution procedure for optimising the composition of personalised food baskets delivered by food pantries to needy families. The procedure addresses three key challenges not explored in the literature: allocating discrete food packages from limited stock, accommodating individual dietary restrictions and nutritional requirements, and balancing multiple distribution objectives. We propose a multi-objective mixed-integer linear programming model that maximises the minimum nutritional coverage across all nutrients and beneficiaries, maximises the minimum food product variety, and minimises inequity in food allocation. The objectives are prioritised using relaxed lexicographic optimisation, allowing controlled trade-offs through a relaxation parameter. Applied to 25 weekly instances from El Rebost, a food pantry in Terrassa, Spain, the procedure demonstrates significant improvements over current food baskets – increasing minimum nutritional coverage by 119%, minimum product variety by 17.1%, and reducing inequity by 28% on average. Sensitivity analyses confirm the model’s robustness under varying food resource availability and across larger-scale problem instances. The framework provides food banks and food pantries with a systematic approach for designing nutritionally balanced, diverse, and equitably distributed food baskets tailored to beneficiaries’ dietary needs.