A dynamic lot-sizing model with quantity discount

The purpose of this article is to present a dynamic lot-sizing model with an efficient recursion to find an optimal policy when all-units quantity discounts are considered. Considering a single independent item, we obtain a minimum total cost with quantity discount which satisfies the known demand in every period. Two types of policy at period t are classified to establish a dynamic lot-sizing problem. One of the policies is that the policy has a preceding policy at period t - 1. It will develop a recursive relationship between period t and period t - 1. The other policies are regenerated at period t due to satisfying the quantity discount Icl-el. A few properties and theorems are developed to improve the computational efficiency. The number of additional items, entries and comparison items will significantly be reduced by theorems presented in this paper.