Dynamic lot sizing with returning items and disposals

We analyze a version of the Dynamic Lot Size (DLS) model where demands can be positive and negative and disposals of excess inventory are allowed. Such problems arise naturally in several applications areas, including retailing where previously sold items are returned to the point of sale and re-enter the inventory stream (such returns can be viewed as negative demands), and in managing kits of spare parts for scheduled maintenance of aircraft (where excess spares are returned to the depot), among other applications. Both the procurement of new items and the disposal of excess inventory decisions are considered within the framework of deterministic time-varying demands, concave holding, procurement and disposal costs and a finite time horizon (disposal of excess inventory at a profit is also allowed). By analyzing the structure of optimal policies, several useful properties are derived, leading to an efficient dynamic programming algorithm. The new model is shown to be a proper generalization of the classical Dynamic Lot Sizing Model, and the computational complexity of our algorithm is compared with that of the standard algorithms for the DLS model. Both the theoretical worst-case complexity analysis and a set of computational experiments are undertaken. The proposed methodology appears to be quite adequate for dealing with realistic-sized problems.