Quality-speed trade-offs in customer-intensive services with boundedly rational customers and retrials

Abstract

We consider a system in which one server provides customer-intensive services and the service reward increases in the length of service time. However, longer service times also lead to longer waits for customers and more congestion for the system. Considering the trade-off between the service speed and service quality, in this paper, we investigate the optimal service speed and service fee from the perspectives of revenue maximization and social welfare maximization. The customers are boundedly rational and decide whether to join the system or not according to a logit model. We find that under the revenue maximization, a decrease in the degree of rationality can alleviate congestion, but harms the social welfare. If the social planner determines the service speed and price directly, we show that bounded rationality is detrimental to service managers but beneficial to customers, while social welfare remains constant. Defining the ratio between the social welfare under the revenue-optimal strategy and socially optimal strategy as the price of anarchy (PoA), which quantifies the inefficiency of the strategy of the service provider, we obtain its upper bound and lower bound and demonstrate that the PoA is decreasing when customers become more boundedly rational and the sign of customer’s actual utility is determined by both the level of customer rationality and retrial rate. Moreover, when customers are heterogeneous in terms of perceiving service, we classify customers into two classes and the revenue maximization problem is investigated through the Particle Swarm Optimization algorithm.