A LOWER BOUND ON A CLASS OF COORDINATED INVENTORY-PRODUCTION PROBLEMS

A new lower bound is given for a class of coordinated multi-product inventory problems. This note introduces a very simple lower bound of considerable generality. It is shown that this lower bound is in fact identical to two good lower bounds reported recently. In particular, the lower bound of Roundy for the single-warehouse, N-retailer distribution problem and that of Jackson et al. for the coordinated multi-product lot sizing problem are duplicated. In each case the derivation and proof is very elementary. Alternative problems to which the bound might be applied, without making any claims at this stage of how 'good' is the bound are described.