Optimal three-level presort loading of commercial bulk mail in the postal service industry

This study focuses on the presort loading of commercial bulk mail. Here, presort is the process by which a mailer prepares mail such that it is sorted to at least the finest extent required by the postal service provider for a claimed (discounted) price. We formulated this presort loading problem (PLP) as a special case of transportation problem with minimum quantity commitment (MQC) constraints. In addition, we developed a polynomial time optimal solution algorithm for the PLP and performed computational experiments on randomly generated problem instances under various discount structures. Results of the computational experiments show that mailers can potentially reduce their costs by sending mail less frequently, using small-sized mail trays; however, the discount structure does not affect the main results. There is some evidence that smaller cost reductions on mailing fees occur as the variation in the discount rate increases; however, the effects of discount structure are nominal compared with the gains from changing the mailing frequency. Mailing fee savings are more heavily influenced by the discount structure when MQC constraints become tighter.