AbstractAfter an introductory discussion of the usefulness of the technique of dynamic programming in solving practical problems of multi-stage decision processes, the paper describes its application to inventory problems. In particular, the effect of allowing the number of decision stages to increase indefinitely is investigated, and it is shown that under certain realistic conditions this situation can be dealt with. It appears to be generally true that the average cost per period will converge, for an optimal policy, as the number of periods considered increases indefinitely, and that it is feasible to search for the policy which minimizes this long-term average cost. The paper concludes with a specific example, in which it is shown that only eight iterations were necessary to find a reasonable approximation to the optimal re-order policy.