A Rationale for Fixed Charge Application

Much research effort has gone into the question of why service centers typically charge users a fixed amount that does not vary with the duration of service. One mode of imposing such charges is the allocation of fixed costs to the users. This has been studied by Zimmerman [6], Kaplan and Thompson [3], and Kaplan and Welam [4]. Another method of imposing such a charge is the use of a transfer price that is more than the marginal cost. Under conditions of known demand, Hirschleifer [2] found that marginal-cost transfer prices are optimal from the firm's viewpoint. It is therefore not clear as to why there should be a component of transfer price that does not vary with service duration. This study provides a rationale for the application of positive fixed charges to the users of a service center using opportunity costs of delay. We do not address the problem of cost allocation in which the applied fixed charge is constrained to be equal to the incurred fixed cost. This study uses concepts from queuing theory when there is a single server; the arrivals are random with a Poisson distribution; and the service time per job is also a random variable with a general distribution. Traditionally, opportunity costs of congestion are said to be incurred only when the service center is operating at nearly full capacity. In this study, we show that under conditions of uncertainty in the arrivals and the service time, congestion can occur even when the service center is operating well below capacity. It is shown that in view of these opportunity costs of delay, a fixed charge needs to be applied to achieve an optimum utilization of the service center. We compute the amount of this fixed charge and show that under very general conditions it is in the interest of the firm to reduce the usage rate from its no-charge equilibrium value by applying a fixed charge. The difference between the no-charge equilibrium usage rate and the optimal usage rate is a measure of the need for such fixed charge application. Under reasonably realistic assumptions, this study deals with how the usage rates and their differences vary with the parameters used in the model. An important finding of the sensitivity analysis in this study is that the need for restricting the usage rate by imposing the fixed charge increases when there is greater uncertainty