An integrated acquisition policy for supplier selection and lot sizing considering total quantity discounts and a quality constraint

We consider a two-stage supply chain where a buyer purchases a product from multiple capacitated suppliers to satisfy a constant demand rate over a finite planning horizon. Suppliers have different perfect rates and offer total quantity discounts. The buyer selects suppliers and allocates orders to them that satisfy a minimum average quality level. A mathematical model is proposed with the objective on minimizing the total cost per time unit. The model is solved by dualizing the quality constraint. The relaxed model is solved by an efficient dynamic programming algorithm. The subgradient method is used to solve the dual problem.