The inventory lot-sizing problem with continuous time-varying demand and shortages

This study develops and analyses 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. It is shown that the procedure yields a unique optimal replenishment schedule for both increasing and decreasing demand patterns. The paper also discusses two particular cases of linear and non-linear demand trend models, and illustrates the optimal solution procedure with four numerical examples.