A joint economic lot size model for raw material ordering, manufacturing setup, and finished goods delivering

In this research we consider a single-manufacturer single-buyer supply chain problem where the manufacturer orders raw materials from its supplier, then using its manufacturing processes converts the raw materials to finished goods, and finally delivers the finished goods to its customer. The manufacturer produces the product in batches at a finite rate and periodically delivers the finished goods at a fixed lot size to its customer, who has a constant demand rate. An integrated inventory control model, making joint economic lot sizes of manufacturer's raw material ordering, production batch, and buyer's ordering, is developed to minimize the mean total cost per unit time of the raw materials ordering and holding, manufacturer's setup and finished goods holding, the buyer's ordering, and inventory holding. Numerical examples are also setup to illustrate that jointly considering the inventory costs above results in less mean total cost than that of considering them separately.