doi 10.1287/opre.1030.0088

Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for real-time telephone service, and another for a postponed call-back service offered with a guarantee on the maximum delay until a reply is received. Customers are sensitive to both realtime and call-back delay and their behavior is captured through a probabilistic choice model. The dynamics of the system are modelled as an M/M/N multi-class system. We rigorously justify that as the number of agents increases, the system’s load approaches its maximum processing capacity. Based on this observation, we perform an asymptotic analysis in the many-server, heavy traffic regime to find an asymptotically optimal routing rule, characterize the unique equilibrium regime of the system, approximate the system performance, and finally, propose a staffing rule that picks the minimum number of agents that satisfies a set of operational constraints on the performance of the system. Key words and phrases: Service networks, call centers, heavy traffic, service level guarantees, choice models, Nash equilibrium, Halfin-Whitt regime. Running title: Contact centers with call-back option 1 1

This thesis presents a dynamic pricing model where a seller offers two types of a generic product to a random number of customers. Customers show up sequentially. When a customer arrives, he will —depending on the prices—either purchase one unit of type 1 product or one unit of type 2 product, or will leave empty-handed. The sale ends either when the entire stock is sold out, or when the customers are exhausted. The seller’s task is to post the optimal prices for the two product types to each customer to maximize the expected total revenue. We use dynamic programming to formulate this problem, and derive the optimal policy for special cases. For general cases, we develop an algorithm to approximate the optimal policy and use numerical examples to demonstrate the efficiency of the algorithm. Finally, we apply the results to a continuous-time model where customers arrive according to a Poisson process. We develop a heuristic policy and use numerical examples to show the heuristic policy is very effective. Acknowledgments