Adaptive Smoothed Functional Algorithms for Optimal Staffing Levels in Service Systems

Service systems are people-centric. The service providers employ a large workforce to service many clients, aiming to meet the service-level agreements (SLAs) and deliver a satisfactory client experience. A challenge is that the volumes of service requests change dynamically and the types of such requests are unique to each client. The task of adapting the staffing levels to the workloads in such systems while complying with aggregate SLA constraints is nontrivial. We formulate this problem as a constrained parametrized Markov process with a discrete parameter and propose two multi-timescale smoothed functional (SF)-based stochastic optimization SASOC (staff allocation using stochastic optimization with constraints) algorithms--SASOC-SF-N and SASOC-SF-C--for its solution. Whereas SASOC-SF-N uses a Gaussian-based smoothed functional approach, SASOC-SF-C uses the Cauchy smoothed functional algorithm for primal descent. Further, all SASOC algorithms incorporate a generalized projection operator that extends the system to a continuous setting with suitably defined transition probabilities. We validate these optimization schemes on five real-life service systems and compare their performance with a previous SASOC algorithm and the commercial optimization software OptQuest. Our algorithms are observed to be 25 times faster than OptQuest and have proven convergence guarantees to the optimal staffing levels, whereas OptQuest fails to find feasible solutions in some cases even under a reasonably high threshold on the number of search iterations. From the optimization experiments, we observe that our algorithms find better solutions than OptQuest in many cases, and among our algorithms, SASOC-SF-C performs marginally better than SASOC-SF-N.