Capacity Rationing in Stochastic Rental Systems with Advance Demand Information

Abstract

Many companies have started segmenting customers to better match their products and services to the needs of the customers. We support this development by presenting a stochastic model of a rental system with two customer classes that was motivated by the operations of one of Europe's leading logistics companies. At the company, customers can choose between premium and classic service. Under premium service, customers provide advance demand information (ADI) by reserving cars ahead of the time when they need them, and they receive a service guarantee in return. Under classic service, customers do not make a reservation and do not receive a service guarantee. Because both demand classes access a common pool of cars, the company must decide which demands to fill and which to reject. The admission decision must be made without knowing the rental duration, which is an exponentially distributed random variable. We model the system as a multiserver loss system and prove that the optimal admission policy is a threshold policy. Because computing the parameters of the policy is computationally intractable, we propose an ADI policy that can be implemented and executed with moderate effort. We analyze the performance of our ADI policy by analytically deriving upper and lower bounds on the optimal expected profit and by performing numerical experiments using data from the logistics company that motivated our research. The numerical experiments indicate that the potential benefit of using ADI is significant and that our ADI policy performs close to optimal. Finally, we extend our model to a different cost structure and to multiple ADI classes.