Adaptive Smoothed Functional based Algorithms for Labor Cost Optimization in Service Systems

Service systems are labor intensive with time varying workloads. The task of adapting the staffing levels to the workloads in such systems challenges while maintaining system steady-state and to comply with aggregate SLA (Service-Level Agreement) constraints, is non-trivial. We formulate this problem as a constrained parameterized Markov cost process 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 Cauchy smoothed-functional for gradient estimation for primal descent. We validate these optimization schemes on five real-life service systems and compare them with a recent algorithm, SASOC-SPSA, from [1], and a state-of-the-art optimization tool-kit OptQuest. The performance of SASOC-SF-N is found to be comparable to that of SASOCSPSA, while that of SASOC-SF-C is marginally better than SASOC-SPSA. Being an order of magnitude faster than OptQuest, our algorithms are particularly suitable for adaptive labor staffing. Also, we show that our algorithms guarantee convergence whereas OptQuest fails to find feasible solutions in †Department of Computer Science and Automation, Indian Institute of Science {hlprasu,prashanth, shalabh}@csa.iisc.ernet.in, IBM Research, Bangalore, INDIA {nirmit.desai}@in.ibm.com

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