A finite horizon inventory problem is encountered whenever a product is procured/ manufactured/sold for a limited time, after which it is replaced by another product performing basically the same function but differing in design/appearance/performance. The conventional methods cannot be applied for analysing the finite horizon inventory problem due to the discrete nature of the cost function. In this paper mathematical models have been developed for a case when a product is packaged in a number of container sizes and offered for a limited time. An example has been solved illustrating the method.