Modeling and analysis of single item multi‐period procurement lot‐sizing problem considering rejections and late deliveries

Integer linear programming approach has been used to solve a multi‐period procurement lot‐sizing problem for a single product that is procured from a single supplier considering rejections and late deliveries under all‐unit quantity discount environment. The intent of proposed model is two fold. First, we aim to establish tradeoffs among cost objectives and determine appropriate lot‐size and its timing to minimize total cost over the decision horizon considering quantity discount, economies of scale in transactions and inventory management. Second, the optimization model has been used to analyze the effect of variations in problem parameters such as rejection rate, demand, storage capacity and inventory holding cost for a multi‐period procurement lot‐sizing problem. This analysis helps the decision maker to figure out opportunities to significantly reduce cost. An illustration is included to demonstrate the effectiveness of the proposed model. The proposed approach provides flexibility to decision maker in multi‐period procurement lot‐sizing decisions through tradeoff curves and sensitivity analysis.