Due to changes in the industry which have led to opportunities for new market segmentations, revenue management (RM) methods have gained in importance for liner shipping companies in the recent past. Therefore, possible market segmentations of the liner shipping market and suitable RM methods are discussed in this work. Based on a slot allocation model for container bookings, three different booking acceptance strategies are studied and compared with respect to their applicability in liner shipping and their performance regarding profit and capacity utilization. Especially, a new bid-price (BP) strategy is developed and compared to previously presented booking limit strategies. A simulation approach is used to evaluate the strategies for different scenarios. The simulation study reveals large differences in the impact the strategies can have, e.g. depending on the booking forecast quality. As the new BP strategy shows very promising results for many different realistic scenarios, it can be highly recommended for application in liner shipping.