A note for "On an inventory model for deteriorating items and time-varying demand"

In this technical note we discuss a paper of Benkherouf and Balkhi recently published in Mathematical Methods of Operations Research. They established the model for deteriorating items with increasing demand and proved the uniqueness for the solution of the system of first partial derivatives. However, there are some questionable results in their procedure to verify the existence of the solution. The purpose of this note is threefold: First, we prove that their theorem cannot be verified under their assumption. Second, we find that the example set by them does not satisfy their assumed condition. Third, we point out the logic problem in their verification procedure.