98%-Effective Lot Sizing for Series Inventory Systems with Backlogging

For deterministic series inventory systems with backlogging, we show that the continuous 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 (Roundy, R. O. 1983. 94%-Effective lot-sizing in multistage assembly systems. Technical Report 674, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York.), the best integer frequency policy provides a solution which is within 2% of the optimal.