Online lot-sizing problems with ordering, holding and shortage costs

We study inventory management problems where demands are revealed incrementally and procurement decisions must be made before the demands are realized. There are no probabilistic distributions nor non-trivial bounds to characterize demands. We consider two cost minimization problems: (1) perishable products with lost sales and (2) durable products with backlogged demand. In both problems, costs are period dependent. These problems are analyzed by utilizing linear-fractional programming and duality theory. Structural results are proved and then developed into practical strategies.