Lot sizing with bounded inventory and lost sales

In production planning, there can be situations where the ability to meet customer demands is constrained by inventory capacity rather than production capacity. This situation often happens in petrochemical manufacturing, food processing, and glass manufacturing. Only a few studies can be found in the literature for this situation, and among these lost sales usually are not considered. In this paper, we consider the lot sizing problem with bounded inventory. We further consider that (1) lost sales are allowed; (2) production cost functions are non-increasing with respect to the time period; and (3) inventory capacity is non-decreasing with respect to the time period. With these considerations, we present a model as well as an algorithm which has a polynomial time complexity. An illustration is given to demonstrate both the application of our model and the algorithm.