A Replenishment Model for Radioactive Nuclide Generators

The nuclide generator is a radioactive element of long half life which is used to produce a short-lived daughter, or decay product, useful in medical diagnosis. This paper discusses the inventory problem for such exponentially decaying substances. Methods are proposed for finding the optimizing replenishment size when the reorder point, replenishment cost function, and other parameters are given. The reorder point is determined by certain medical requirements which give rise to a rather complicated model. A simple method is presented for finding close bounds on the required solution.