Note on inventory models with a permissible delay in payments

This note tries to provide a patch work for the paper of Chang Dye and Chuang (published in Yugoslav Journal of Operational Research 2002, number 1, 73-84). Their paper contains an important finding of smoothly connected property that can very dramatically simplify the solution procedure of many inventory models with ramp type demand and trapezoidal type demand. Our improvement will arouse attention of the researchers and help them apply their important findings in the pending research projects.