Staffing, Routing, and Payment to Trade off Speed and Quality in Large Service Systems

• 成果类型: Article
• 署名作者: Zhan, Dongyuan; Ward, Amy R.
• 署名单位: University of London; University College London; University of Chicago
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2018.1838
• 发表日期: 2019
• 页码: 1738-1751
• 关键词: queuing-systems; call center; moral hazard; capacity; time; uncertainty; management; RESOLUTION; accuracy; centers

摘要

Most common queueing models used for service-system design assume that 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 incentives. The delicacy is that the resulting service speed is jointly affected by staffing, routing, and payment decisions. Our objective in this paper is to find a joint staffing, routing, and payment 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 that employees are paid based on both. The employees selfishly choose their own service speed to maximize their own expected utility (which depends on the staffing through their busy time). The endogenous service-rate assumption leads to a centralized control problem in which the system manager jointly optimizes over the staffing, routing, and service rate. By solving the centralized control problem under fluid scaling, we find four different economically optimal operating regimes: critically loaded, efficiency driven, quality driven, and intentional idling (in which there is simultaneous customer abandonment and server idling). Then we show that a simple piece-rate payment scheme can be used to solve the associated decentralized control problem under fluid scaling.