98%-effective lot sizing for series inventory systems with backlogging

For deterministic series inventory systems with backlogging, we show that the continous relaxation of the best integer frequency policies is a lower bound on all feasible policies. The problem with backlogging can be reduced, in O(n) time, to an equivalent problem without backlogging. Therefore, based on the result of R. O. Roundy, the best integer frequency policy provides a solution which is within 2% of the optimal.