Dimensioning Large-Scale Membership Services

• Published in: Operations research Vol. 56; no. 1; pp. 173 - 187
• Main Authors: de Vericourt, Francis, Jennings, Otis B
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.01.2008; Institute for Operations Research and the Management Sciences
• Subjects: Applied sciences; Approximation; Closed systems; Computer networks; Determinism; diffusion models; Exact sciences and technology; Firm modelling; Heuristics; Information management; Information networks; limit theorems; Medical advice systems; Minimization of cost; Network servers; Open systems; Operational research and scientific management; Operational research. Management science; queues; Queuing theory; Queuing theory. Traffic theory; Reliability theory. Replacement problems; Service centers; service operations; Staffing; Steady states; stochastic model applications; Stochastic models; Studies; Technology application; Traffic; Workforce planning; United States; limit theorems; staffing; stochastic model applications; service operations; Stochastic model; Membership function; Warranty; Probabilistic approach; Health staff; queues: diffusion models; Staff management; Modeling; Limit theorem; Dimensioning; Multiserver queue; User service; Queueing system; Large scale; Repair; Queue; Service quality; Public health
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1070.0464

Motivated by workforce planning problems in health care, professional, warranty, and repair services, we propose modeling service centers that are exclusively dedicated to fixed client constituencies as closed multiserver queueing systems, a framework we refer to as membership services . We provide fluid and diffusion approximations of the number of users within the membership who are requesting service. The approximations are obtained via many-server limit theorems, where the limiting regime assumptions of each theorem correspond to a particular staffing strategy a manager might employ. Accordingly, we propose staffing rules designed to meet a certain desired performance criterion. In particular, when the objective is to minimize the staffing size subject to a constraint on the probability of delay for a service-requesting customer, we suggest staffing rules inspired by the so-called quality- and efficiency-driven (QED), or Halfin-Whitt, limiting regime. Numerical evaluations of our proposed QED scheme indicate that, although justified for large systems, the staffing rule performs well for memberships of all sizes.