Hunger occurs in all locations around the globe, from developing to developed countries. In fact, there were over 37 million food insecure individuals (those without access to consistent nutritious food) in the United States in 2018, and this number increased in recent years due to the COVID pandemic. In many countries, food banks are used to consolidate food donations from individuals or government agencies and then provide that food to local partner agencies (such as food pantries and soup kitchens), who distribute it to food insecure individuals. As nonprofit humanitarian organizations, food banks strive to achieve geographic equity in their food distribution, so one area (or county) is not favored over others. However, food banks also want to maximize food distribution with their limited budgets. This equitable distribution versus cost balancing act is made even more challenging since food banks experience extreme variability in both the supply (donations) of food and partner agencies' capacity to deliver food to the food insecure. Our paper focuses on how mobile pantry programs, additional food bank storage capacity, and improved partner agency capacity can be utilized to address this supply and distribution capacity variability while considering food expiration times. Mobile pantry programs allow food banks to distribute food directly to the food insecure by sending their own trucks and employees to locations where food is most needed. Although all three of these approaches can be helpful, our results show that mobile pantries are a more effective approach to achieve high equity levels. This is especially true in the case of produce with relatively short expiration times. We also find that utilizing mobile pantry programs can increase equitable partner agency distribution considerably, because even small amounts of mobile pantry distribution in under-served areas allow for more equitable partner agency distribution in areas with available partner agency distribution capacity. Our research is based on data from our partner food bank, but our modeling and extensive sensitivity analysis should be applicable to many food banks with a similar collection and distribution structure.