Dynamics of Two Classes of Continuous-Review Inventory Systems

The classes of inventory systems studied in this paper involve random, captive demand and assume continuous review of inventory and replenishment of stock in lots of size Q. The replenishment doctrine is to initiate an order for Q items whenever the sum of stock on hand and stock on order falls below a pre-determined level R. Possible examples are inventories of spare parts for maintenance, of military supplies, or of merchandising stock, so costs of purchase, of storage, and of backordenng are included in the measures of effectiveness. A general relation, between cost of back-orders and minimal-cost probability of stock-out, is derived, similar to that reported earlier [Morse, P. M. 1959. Solution of a class of discrete-time inventory problems. Opns Res. 7 67–78.] for discrete-time systems. For the first class of system studied, demands arrive at random, with a stationary probability distribution of arbitrary form, and all replenishment times are of the same length. For the second class, demand arrivals ...