In this paper, we study a logistics problem arising in military transport planning. A military organization operates a large fleet of vehicles in a depot to serve the requests of various operational units. Each request has a fixed start and end time, and is served by a prescribed number of vehicles. We address the following two problems: (1) how many vehicles are at least needed to meet a given service level of requests; and (2) suppose we allow each request to shift its start time by a constant duration, can all the requests be met? A Niche genetic algorithm, together with a hybridized variant, are applied to the problem.