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Consider base-stock control in a production-inventory system modeled as a single-server queue, GI/GI/1. The work-in-process inventory on the input side often consists of raw materials that may and as such require financing, or may deteriorate over time, which motivates us to consider an exponential holding cost function, or equivalently, the exponential moments of the GI/GI/1 model. We study the (asymptotic) optimality of the base-stock control—or “reflection control”—in this setting, and the associated interchange of limits, with respect to time and to the scaling constant.
(Joint work with Jiankui Yang and Hengqing Ye.)