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Operations Seminar

Wednesday September 18, 2013


9:30AM - 10:45AM



Achal Bassamboo, Northwestern


Title: Using Newsvendor Models to Design Service Systems with Arrival Rate Uncertainty

The newsvendor model is a classic OM tool that aids in capacity selection when dealing with uncertainties in matching supply with demand. However, this model is typically static with the uncertain demand arriving all at once, and does not seem to offer much insight into managing queueing systems, such as telephone call-centers, in which customers arrive dynamically with different service requirements. In this talk, we study the capacity-planning problem in a queueing system with uncertain arrival rate in which the objective is to choose a staffing level that minimizes the sum of capacity costs and abandonment/waiting time costs. We show that under a large market (or high volume) approximation, this optimization problem reduces to a newsvendor problem, and the capacity it prescribes performs remarkably well. In particular, the gap between the performance of the optimal staffing level and that of our proposed prescription is provably independent of the ¿size¿ of the system, i.e., it remains bounded as the system size (demand volume) increases. This stands in contrast to the more conventional theory that applies when arrival rates are known, and commonly used rules-of-thumb predicated on it. Specifically, in that setting the difference between the optimal performance and that of the newsvendor prescription diverges at a rate proportional to square-root of the size of the system. One manifestation of this is the celebrated square root safety staffing principle that dates back to work of Erlang, which augments solutions of the deterministic analysis with additional servers of order square root the volume of demand. In our work, we establish that this type of prescription is needed only when arrival rates are suitably ¿predictable.¿

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Patricia Bryan

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