This thesis examines four parts of production and inventory models for buyer-supplier in the supply chain under deterministic conditions. The main objective is to find optimal lot-sizing decisions and inventory policies which derive from the classical inventory and Net Present Value (NPV) framework. Firstly, we study the production and inventory models from the classical framework to identify how to value the holding cost for buyer and supplier in the average profit or cost functions. Secondly, we propose the inventory model derived from the NPV framework to identify the incorrect model from the classical framework. It makes a clear distinction between physical inventory and opportunity costs and the supplier’s reward is identified as a lost term in the supplier’s profit function which it has been proved that the corrected supplier’s profit function does lead to a channel. Thirdly, we developed the quantity discount model derived from the NPV framework to help the supplier increase profits under constant demand. It is found that price discounts often lead to a solution very close to the joint optimal policy for buyer and supplier. Fourthly, four different VMI models are developed which derive from the NPV framework for single-supplier and single buyer under deterministic conditions. The experimental results show that the VMI+ Policy can guarantee to achieve the perfect channel coordination and gives the highest supply chain profit more than other VMI approaches and the classical framework.