Capacity rationing in rental systems with two customer classes and batch arrivals

Service differentiation is an emerging method to improve profit and to better serve high-priority customers. Such an approach has recently been introduced by one of Europe's leading rail cargo companies. Under this approach, customers can choose between classic and premium services. Premium service is priced above classic service and premium customers receive a service guarantee which classic customers do not receive. The company has to decide under which conditions it should ration its fleet capacity to classic customers in order to increase service of premium customers. We model such a situation as a batch-arrival queuing loss system. We describe the model, solve it optimally, and derive quantities of interest such as service probabilities. We further analyze it by performing numerical experiments based on the data from the company that motivated our research. We show that the potential of capacity rationing can be substantial in situations like the one we analyzed. We also derive conditions under which rationing is especially beneficial, such as under high unit fleet holding costs or in the presence of batch arrivals compared to single arrivals.