Dynamic Ambulance Management (DAM) is generally believed to provide means to enhance the response-time performance of emergency medical service providers. The implementation of DAM algorithms leads to additional movements of ambulance vehicles compared to the reactive paradigm, where ambulances depart from the base station when an incident is reported. In practice, proactive relocations are only acceptable when the number of additional movements is limited. Motivated by this trade-off, we study the effect of the number of relocations on the response-time performance. We formulate the relocations from one configuration to a target configuration by the Linear Bottleneck Assignment Problem, so as to provide the quickest way to transition to the target configuration. Moreover, the performance is measured by a general penalty function, assigning to each possible response time a certain penalty. We extensively validate the effectiveness of relocations for a wide variety of realistic scenarios, including a day and night scenario in a critically and realistically loaded system. The results consistently show that already a small number of relocations lead to near-optimal performance, which is important for the implementation of DAM algorithms in practice.