A New Recursive Dynamic Lot-Sizing Model with Multi-Level Discount

The optimal solution of dynamic lot-sizing problem with multi-level discount is solved by integer programming model in the past papers. However, a complex computation and a large computer memory are generated. Due to the complexity and the big computer memory, the heuristic approaches and the variable neighborhood algorithm are usually adopted in the large-scale multi-level lot-sizing problem. This paper develops a model with a recursive relation between the adjacent periods, and to obtain an optimal solution when multi-level discount is considered. Four types of the feasible policies in the Dynamic Lot-Sizing model with multi-level discount are classified to develop the recursive relations. A few properties, theorems and algorithms are developed to show the recursion between the adjacent periods. The number of addition items will significantly be reduced. The recursive algorithm can significantly decrease the computational entries, comparison entries and computer memory and improve the computation efficiency.