Prescriptive analytics for a multi-shift staffing problem

Motivated by the work with an industry partner, this paper proposes and examines novel data-driven approaches to solve a certain type of capacity-sizing problem, which we term the multi-shift staffing problem (MSSP). In our MSSP, a company has to staff multiple shifts for each workday in the presence of uncertain arrival rates that vary throughout the day and patient “customers” that do not abandon the queue while waiting for a service, but who must be served by some pre-defined time. Drawing on established methods in both capacity management and prescriptive analytics, we propose to use fluid and stationary approximations of the demand arrival process to apply tailored prescriptive analytics approaches to determine staffing levels for multiple interrelated shifts. The prescriptive analytics approaches rely on machine learning techniques that incorporate a detailed representation of the non-stationary structure of arrivals and leverage extensive auxiliary data. In particular, we adapt established prescriptive analytics approaches—weighted sample average approximation and kernelized empirical risk minimization—and propose a new optimization prediction approach to solving the multi-shift staffing problem. Using a case study that is based on extensive data from our project partner, the maintenance service provider, we demonstrate the applicability of these approaches, highlight their benefits over traditional “estimate then optimize” approaches, and shed light on their structural properties and performance drivers.