Structured buffer-allocation problems

We study the effect of changing buffer sizes in serial lines with general blocking, a mechanism that incorporates limited intermediate finished goods inventory at each stage, as well as limited intermediate raw material inventory. This model includes ordinary manufacturing, communication, and kanban blocking as special cases. We present conditions under which increasing buffer sizes or re-allocating buffer capacity increases throughput, and in some cases characterize optimal allocations. Our comparisons hold pathwise; they depend on structural properties of a line but not its service time distributions. The key to our analysis is formulating the model as a generalized semi-Markov process (GSMP). We show that a serial line with general blocking possesses various structural properties from which pathwise comparisons follow directly, making a detailed case-by-case analysis unnecessary These results help illustrate the power of GSMPs as a modeling framework.