Customer service competition in capacitated systems

We investigate a simple dynamic model of firm behavior in which firms compete by investing in capacity that is used to provide a good or service to their customers. There is a fixed total market of customers whose demands for the good or service are random and who divide their patronage between the firms in each period. Periodically, the market shares of the two firms can change based on the realized level of customer service provided in the prior period. We assume that the expected level of customer service can be expressed as a function of the (per customer) capacity of the firms' service delivery systems, and that service declines as the capacity decreases. The firms differ in their customers' willingness to defect when confronted by service failure. The primary issue we address is the firms' capacity decisions in response to customer service concerns and competitive pressure. We provide conditions under which the firms' optimal (i.e., equilibrium) capacity levels in a period are proportional to the size of their respective customer bases in that period. Further, we develop expressions for the value of a firm's customers and the implicit cost of service failure. Results for both single-period and finite-horizon problems are investigated and applied to two examples: (1) competition between Internet service providers who operate systems that we approximate by simple loss-type queueing models, and (2) competition between make-to-stock producers who operate systems that we approximate by newsvendor inventory models. For both examples, solutions are derived and interpreted.