Analyzing andExtending a Bulk Mail Postage Optimization Model

Abstract: Postage is a big cost for companies and agencies that are sending large volumes of physical mail. This cost can be reduced by getting bulk discounts. Mathematical optimization is used to ensure that the lowest prices possible are found. This thesis will analyze an existing model used by a company and explain how it works. The model will also be expanded to make it applicable to new pricing models. The model is in the form of a mixed integer linear program and it is used to optimize the cost of a batch of bulk mail. The original model can handle price models where the discounts are reached by sending large volumes of letters. Not all mail delivery companies provide such discounts however. The model is then extended to allow other forms of discounts. Three extensions of the original model were implemented. The effectiveness of the extensions of the model are measured by comparing the prices attained by using the extended model and the original model. The results are discussed to assess if the implementation of the extension are worthwhile. The first extension of the model was made to allow the mixing of mail with different allowed delivery times. The problem was to ensure that the mail was not delivered slower than what was promised. By mixing the mail with different delivery times larger volumes could be attained and greater discounts were achieved which lead to better results overall. The second extension that was made was to make the model able to handle discounts based on the mean weight of the letters that are sent. The model is adjusted to work with this price model. This change did not yield a lower price than the original model in all cases. The explanation for this is that the original model is less flexible when different price models are used and therefore the extended model is more suitable to use. The last extension made was implemented to bypass an existing rule that forbids letters with too great of a weight difference to be sent together. The goal was to make the model more flexible. No conclusive improvement of the results were seen for this extension.