Disaster preparedness has been recognized as a central element in reducing the impact of disasters worldwide. The usual methods of preparedness, such as pre-positioning relief inventory in countries prone to disasters, are problematic because they require high investment in various locations, due to the uncertainty about the timing and location of the next disaster. Investing in disaster management capabilities, such as training staff, pre-negotiating customs agreements with countries prone to disasters, or harmonizing import procedures with local customs clearance procedures, has been recognized as a way to overcome this constraint. By means of system dynamics modeling, we model the delivery process of ready-to-use therapeutic food items during the immediate response phase of a disaster, and we analyze the performance of different preparedness scenarios. We find that pre-positioning inventory produces positive results for the beneficiaries, but at extremely high costs. Investing in disaster management capabilities is an interesting alternative, as it allows lead time reductions of up to 67% (18 days) compared to a scenario without preparedness, at significantly lower costs than pre-positioning inventory. We find that the best performance can be achieved when combining both preparedness strategies, allocating part of the available funding to disaster management capabilities and part to pre-positioning inventory. We analyze 2828 such combined scenarios to identify the best mix of preparedness strategies for different levels of available funding. On the basis of our findings, we provide recommendations for relief organizations on how to allocate their preparedness budget.