: In this Thetis, a two-echelon supplier-manufacturer system with finite production rate considering lead-time is proposed. Manufacturer supplies external demand with no shortage. It is assumed the lot size of manufacturer (second echelon) is m-factors of supplier’s (first echelon) and the supplier can supply the manufacturer’s lot-size in several shipments in a cycle of system. So, it is supposed that the production rate of supplier is greater than manufacturer’s. Planning an inventory program, joint production and interaction between the components of supply chain can enhance the customer service which leads to the component's profit in long term. Therefore, the proposed model aims to determine the optimal lot-size of each echelon such that the total cost of system is minimized. The problem studied through Average Cost and Net Present Value (non-approximated and approximated) approaches. First, the problem is studied regardless of lead-time, and the optimal value of the lot sizes and optimal number of shipments are determined through analytical relations. Then, it is shown that, through AC approach, lead-time is not affecting optimal values of decision variables. Next, the problem is studied through NPV approach and an MINLP model proposed for determining optimal values of decision variables. By approximation of MINLP objective function, via Maclaurin expansion, we found non-equivalency in problems with zero lead-time and non-zero lead-time. So, an exact algorithm is proposed to find optimal values of decision variables of approximated NPV approach. Numerical results shows that, in the problem with low to moderate lead-time, AC approach is more efficient than approximated NPV, and in the problem with considerable lead-time, approximated NPV approach has more efficiency.
