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Service systems are people-centric. The service providers employ a large work force to service many clients, aiming to meet the 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 (Service-Level Agreement) constraints, is non-trivial. 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 algorithms: SASOC-SF-N and SASOC-SF-C, respectively, for its solution. While SASOC-SF-N uses Gaussian based smoothed-functional, SASOC-SF-C uses the Cauchy smoothed-functional algorithm for primal descent. Further, all SASOC algorithms incorporate a generalized projection operator (L.A. et al. [2012],[Bhatnagar et al., 2012, Chapter 9]) 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 recent algorithm, SASOC-SPSA, from Prashanth et al. [2011], and a 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 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.

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Service systems are labor intensive. Further, the workload tends to vary greatly with time. Adapting the staffing levels to the workloads in such systems is nontrivial due to a large number of parameters and operational variations, but crucial for business objectives such as minimal labor inventory. One of the central challenges is to optimize the staffing while maintaining system steadystate and compliance to aggregate SLA constraints. We formulate this problem as a parametrized constrained Markov process and propose a novel stochastic optimization algorithm for solving it. Our algorithm is a multi-timescale stochastic approximation scheme that incorporates a SPSA based algorithm for 'primal descent' and couples it with a 'dual ascent' scheme for the Lagrange multipliers. We validate this optimization scheme on five real-life service systems and compare it with a state-of-the-art optimization tool-kit OptQuest. Being two orders of magnitude faster than OptQuest, our scheme is particularly suitable for adaptive labor staffing. Also, we observe that it guarantees convergence and finds better solutions than OptQuest in many cases.

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