Service Systems with Outbound Work and Blending

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The research objective of this award is to develop new models and control mechanisms that faithfully describe contemporary service systems, such as contact centers and healthcare systems, which handle inbound and outbound work simultaneously. Special attention will be given to systems that process the two types of jobs by the same group of agents, a process referred to as "blending," in time-varying or random environments. The most significant difference between the two types of jobs is that inbound work typically arrives exogenously, so that management has no direct control on the arrival rate, whereas the arrival process of outbound work is generated by the system itself, and its arrival rate is therefore mostly controlled. The flexibility in scheduling outbound arrivals can be exploited to improve performance, and in particular, to reduce the variability associated with the arrival process of inbound work. However, outbound work also introduces new types of practical and analytical challenges that do not exist in systems that are dedicated to serving inbound work. For example, modern contact centers employ automatic dialers to generate outbound calls. In a blended service pool, it is then highly possible that all agents are busy by the time a called customer replies, so that the call is dropped. In healthcare settings, a clinic that accepts walk-ins (inbound patients) in addition to scheduled appointments (outbound patients), must take into account no-shows and late arrivals of outbound patients when making staffing and scheduling decisions. Therefore, existing results and insights that are known for systems that handle only inbound work, do not directly extend to systems that process also outbound work. Specific questions that will be addressed are: 1) How to design a system that processes the two types of jobs, e.g., when is it better to use blending, and when is it preferable to handle each type of work by a dedicated service pool. 2) How to best utilize the flexibility in face of time-dependent, or stochastic arrival rates of inbound work. 3) How to staff blended service pools so as to achieve a desired throughput rate of outbound work, subject to given service-level constraints for both inbound and outbound customers. 4) How to route customers and schedule agents in real time. If successful, this research will develop new methods and tools to design and control large service systems with outbound work and blending in non-stationary settings. Since exact analysis is prohibitively hard, novel many-server heavy-traffic limits will be proved and shown to provide effective approximations. A challenging characteristic of the asymptotic analysis is that the generation of outbound work takes place in a fast time scale, therefore requiring refined heavy-traffic analysis. This property, in addition to the non-stationarity and uncertainty regarding inbound arrival rates, presents technical complications that make limiting arguments hard to derive. Successful results will lead to new types of useful asymptotic techniques and insights which can potentially be applied in other settings as well.