A constant unit purchase cost is one of the main assumptions in the classic Economic Order Quantity
model. In practice, suppliers sometimes face a known price increase. In this paper, we develop EOQ models
with a known price increase and partial backordering under two different assumptions about when
the increase will occur. We prove the concavity of the extra profit functions for both scenarios if a special
order is placed just before the price increases. A solution method is proposed and numerical examples are
presented.