AbstractIn this study, we develop and analyse an optimal solution procedure for the inventory lot-sizing problem with a general class of time-varying demand functions. The objective of the procedure is to determine the optimal replenishment schedule over a finite planning horizon during which shortages are allowed and are completely backordered. We show that the procedure yields a unique optimal replenishment schedule for both increasing and decreasing demand patterns. We also discuss two particular cases of linear and non-linear demand trend models, and we illustrate the optimal solution procedure with four numerical examples.