| Abstract: | The calculation of reorder points when the distribution of lead-time demand is normal is quite complex, primarily because of having to bound it away from negative demand values. A number of researchers have sought feasible alternative forms of lead-time demand which can be calculated without undue difficulty. It is proposed here to assume a Poisson (daily) demand and an exponential lead time (days). If they are assumed independent their convolution is geometric, which is itself asymptotically exponential. This has a number of advantages: (1) The exponential lead time is appropriate where the lead time is often short (i.e., local source), occasionally longer (when the local sources stock out), and, infrequently, quite long. (2) The geometric lead-time demand is independent of changes of time scale. (3) Reorder points and lot sizes appear in simple closed form. (4) The exponential asymptote is sufficiently close that this further simplification is usually warranted. |
