It is argued in this paper that conventional inventory control theory in the form that it is implemented and widely used today, is largely the product of an era when most businesses operated with primitive mechanical calculators rather than computers. The methods devised at the time reflect the fact that calculations had to be undertaken by hand and therefore could be neither complicated nor burdensome. There was, as a consequence, an extensive reliance on analytical methods. This enabled the development and use of tables and nomographs to simplify and streamline the associated calculations. In recent years we have witnessed changes of revolutionary proportions with the development and widespread penetration of cheap, powerful computational technologies into most aspects of business activity. The proposition put forward and elaborated in this paper is that it is timely to review current practices in inventory control, and determine whether the new technologies provide opportunities for approaches possessing a greater reliance on numerical methods in place of those with an analytical orientation. As a consequence new possibilities for periodic review order-up-to and reorder level inventory systems are explored together with adaptations which allow for growth and seasonal effects in demand. A common feature of the proposed approaches is that they largely bypass the statistical forecasting methods commonly used in conjunction with computerised inventory control systems. Furthermore, they provide a mechanism for coping with problems of uncertainty without recourse to formal probability theory. It is argued that, as a consequence, they are better suited for use in most business settings where those delegated to control inventories usually lack the formal mathematical skills and knowledge to fully understand and to make effective use of the classical methods.