Pricing and Capacity Sizing of a Service Facility: Customer Abandonment Effects

This paper studies the effect of customer abandonment in the economic optimization of a service facility. Specifically, we consider how to jointly set the price and service capacity in order to maximize the steady-state expected profit, when the system is subject to customer abandonment and the price is paid only by customers that eventually receive service. We do this under the assumption that there is a high rate of prospective customer arrivals. Our analysis reveals that the economically optimal operating regime is consistent with the standard heavy traffic regime. Furthermore, we derive the following economical insight: when the capacity cost is sufficiently high, it can be advantageous for the system manager to “underinvest” in capacity and “take advantage of the abandonments” to trim congestion. Lastly, we show the loss in profit when customer abandonments are ignored is on the order of the square-root of the demand rate.