Service Networks with Open Routing and Procedurally Rational Customers

Problem Definition: We investigate the implications of procedurally rational customers on service networks where customers visit multiple stations but can choose the order in which to visit the stations. Academic/Practical Relevance: Self-interested customers populate various service systems. While self-interested, these customers may not be fully rational. Customers' form of reasoning and its consequences for system performance affect the planning decisions of service providers. Methodology: We study procedurally rational customers---that is, customers make decisions based on anecdotal samples of system times experienced by customers who previously visited the system and followed each possible route. Using a fluid model, we fully characterize the evolution of customer routing decisions, with customers deciding in each period based on samples from the previous period. Results: We completely specify the set of equilibrium routing profiles, where the fraction of customers choosing each route becomes stationary. In contrast with existing models of procedural rationality, we find that procedurally rational customers sometimes behave differently from fully rational customers, but not always. Equilibria can emerge under procedural rationality that differ from fully rational equilibria, in which case, system performance suffers. We also study systems in which customers make routing decisions. We find analytically that procedurally rational customers are slower to internalize price increases than fully rational customers: accordingly, the firm's optimal revenue is higher (lower) with procedurally rational customers than fully rational ones if the waiting cost is high (low). Managerial Implications: In systems in which customers make only routing decisions, procedural rationality can lead to much longer waiting times. However, the firm can avoid increased waiting times if it can choose the service rates at its stations. Furthermore, if customers make joining decisions, then a service provider should price differently depending on which form of reasoning customers use, and the firm may prefer either procedurally rational customers or fully rational ones depending on the system parameters.