Staffing and routing in a two-tier call centre

This paper studies service systems with gatekeepers who diagnose a customer problem and then either refer the customer to an expert or attempt treatment. We determine the staffing levels and referral rates that minimise the sum of staffing, customer waiting, and mistreatment costs. We also compare the optimal gatekeeper system (a two-tier system) with a system staffed with only experts (a direct-access system). When waiting costs are high, a direct-access system is preferred unless the gatekeepers have a high skill level. We also show that an easily computed referral rate from a deterministic system closely approximates the optimal referral rate.