Priority Assignment Under Imperfect Information on Customer Type Identities

In many service systems, customers are not served in the order they arrive, but according to a priority scheme that ranks them with respect to their relative “importance.” However, it may not be an easy task to determine the importance level of customers, especially when decisions need to be made under limited information. A typical example is from health care: When triage nurses classify patients into different priority groups, they must promptly determine each patients criticality levels with only partial information on their conditions. We consider such a service system where customers are from one of two possible types. The service time and waiting cost for a customer depends on the customer’s type. Customers’ type identities are not directly available to the service provider; however, each customer provides a signal which is an imperfect indicator of the customer’s identity. The service provider uses these signals to determine priority levels for the customers with the objective of minimizing the long-run average waiting cost. In most of the paper, each customer’s signal equals the probability that the customer belongs to the type that should have a higher priority and customers incur waiting costs that are linear in time. We first show that increasing the number of priority classes decreases costs and the policy that gives the highest priority to the customer with the highest signal outperforms any finite-class priority policy. We then focus on two-class priority policies and investigate how the optimal policy changes with the system load. We also investigate the properties of “good” signals and find that signals that are larger in convex ordering are more preferable. In a simulation study, we find that when the waiting cost functions are non-decreasing, quadratic, and convex, the policy that assigns the highest priority to the customer with the highest signal performs poorly while the two-class priority policy and an extension of the generalized cμ rule perform well.