Compensation and Staffing to Trade Off Speed and Quality in Large Service Systems

Abstract

Most common queueing models used for service system design assume the servers work at fixed (possibly heterogeneous) rates. However, real-life service systems are staffed by people, and people may change their service speed in response to their compensation incentives. The delicacy is that the resulting employee service rate affects the staffing, but also the staffing affects the resulting employee service rate. Our objective in this paper is to find a joint staffing and compensation policy that induces optimal service system performance.We do this under the assumption that there is a trade-off between service speed and quality, and employees are paid based on both. The employees each selfishly choose their own service speed in order to maximize their own expected utility, which can have both a monetary and a non-monetary component. We characterize the symmetric equilibrium service speed in large systems under a simple linear staffing and compensation policy. We show that there is a limiting first best policy within that class. The important insight is that in the large system limit the problem decouples into one where the system manager first jointly determines the staffing and service speed, and second uses the compensation to achieve that desired service speed. We further show the conditions under which a critically loaded, efficiency-driven, quality-driven, or mixed regime — in which there is simultaneous customer abandonment and server idling — emerges under a first-best policy.