- A new form of partial backorder policy (PB2) using two explicit backorder control limits and a intermediate time when dealing with shortages is introduced and parameterc analyses of various cost parameters of this policy are numerically explored. The traditional backorder policy, the lost sales policy, and a partial backorder policy using a single backorder control limit, called PB1, are special cases of PB2; hence a PB2 policy provides a unified frame work for studying different policies dealing with shortages. We provide an example where a PB2 policy produces a cost savings of 3.36% over the best of the pure backorder, the lost sales and the PB1 policies. Without the time dependent backorder cost, our PB2 policy will reduce to the PB1 policy. A cost savings of 6.63% is realized. This cost savings could be quite substantial for a firm with very large volume of business.