On the inventory model with variable lead time and price-quantity discount

In this paper, we propose a mixed integer optimization approach for solving the inventory problem with variable lead time, crashing cost, and price-quantity discount. A linear programming relaxation based on piecewise linearization techniques is derived for the problem. It first converts non-linear terms into the sum of absolute terms, which are then linearized by goal programming techniques and linearization approaches. The proposed method can eliminate the complicated multiple-step solution process used in the traditional inventory models. In addition, the proposed model allows constraints to be added by the inventory decision-maker as deemed appropriate in real-world situations.