Some New Properties for Single Item Economic Lot Sizing Model with Inventory Capacity and Stockouts

This paper deals with a single item inventory capacity economic lot sizing model and sale loss. Unsatisfied demand cannot be backlogged. Although the model with time dependent bounds is a NP problem, however, when lost sale cost is non increasing, some new properties are proved in an optimal solution, the problem becomes a stockout case. A dynamic programming algorithm is developed to solve the problem in strongly polynomial with O(T 3) time. Some numerical results demonstrate that the approach proposed for stockout problem is efficient and applicable.