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Service systems are labor intensive due to the large variation in the tasksrequired to address service requests from multiple customers. Aligning thestaffing levels to the forecasted workloads adaptively in such systems isnontrivial because of a large number of parameters and operational variationsleading to a huge search space. A challenging problem here is to optimize thestaffing while maintaining the system in steady-state and compliant toaggregate service level agreement (SLA) constraints. Further, because theseparameters change on a weekly basis, the optimization should not take longerthan a few hours. We formulate this problem as a constrained Markov costprocess parameterized by the (discrete) staffing levels. We propose novelsimultaneous perturbation stochastic approximation (SPSA) based SASOC (StaffAllocation using Stochastic Optimization with Constraints) algorithms forsolving the above problem. The algorithms include both first order as well assecond order methods and incorporate SPSA based gradient estimates in theprimal, with dual ascent for the Lagrange multipliers. Both the algorithms thatwe propose are online, incremental and easy to implement. Further, they involvea certain generalized smooth projection operator, which is essential to projectthe continuous-valued worker parameter tuned by SASOC algorithms onto thediscrete set. We validated our algorithms on five real-life service systems andcompared them with a state-of-the-art optimization tool-kit OptQuest. Being 25times faster than OptQuest, our algorithms are particularly suitable foradaptive labor staffing. Also, we observe that our algorithms guaranteeconvergence and find better solutions than OptQuest in many cases.

Simultaneous Perturbation Methods for Adaptive Labor Staffing in Service Systems