Abstract In this paper, we extend Teng, J.T., Chang, H.J., Dye, C.Y., Hung, C.H. [2002. An optimal replenishment policy for deteriorating items with time-varying demand and partial backlogging. Operations Research Letters 30(6), 387–393.] and Hou, K.L. [2006. An inventory model for deteriorating items with stock-dependent consumption rate and shortages under inflation and time discounting. European Journal of Operational Research 168(2), 463–474.] by considering an inventory lot-size model under inflation for deteriorating items with stock-dependent consumption rate when shortages are partial backlogging. The proposed model allows for (1) partial backlogging, (2) time-varying replenishment cycles, and (3) time-varying shortage intervals. Consequently, the proposed model is in a general framework that includes numerous previous models as special cases. We then prove that the optimal replenishment schedule exists uniquely, and provide a good estimate for finding the optimal replenishment number. Furthermore, we briefly discuss some special cases of the proposed model related to previous models. Finally, numerical examples to illustrate the solution process and some managerial implications are provided.