Optimal internal pricing and capacity planning for service facility with finite buffer

An economic model is developed for exploring optimal internal pricing and capacity planning for service facility with finite buffer capacity. Because of the limited buffer capacity, jobs finding the system full upon their arrival would be rejected. Such rejections create a gap between the value collectively perceived by users and the actual achievement of the organizational value. This gap, called a loss externality, has never been studied before and plays an important role for designing optimal pricing scheme. In general, the underlying economic structure may involve multiple equilibria and it is unclear whether or not the system can be controlled through internal pricing. In this regard, a sufficient condition is given under which the system administrator can find two separate prices for accepted and rejected users at any demand level to be desired so that the desired demand level becomes the unique equilibrium of the system. For a short-run problem, it is shown that the optimal pricing scheme can be expressed as the sum of the congestion and the loss externalities. For a long-run problem, the optimal pricing scheme is expressed in a unified manner so that a structural relationship between the short-run problem and the long-run problem at optimality can be readily observed. A necessary and sufficient condition is also given for the marginal capacity pricing to be optimal, i.e., the optimal long-run pricing consists of the marginal cost for processing capacity and the marginal cost for buffer capacity without involving any externality at all.