Minimizing Net Present Value of Costs in Lot-Sizing in a Two-Echelon Inventory System

In this paper, a two-echelon supplier-manufacturer system has been studied through net present value (NPV) approach. The production rate is finite and constant in both echelons. Also it is assumed that there is a lead-time between the first echelon and it is getting to the second echelon. It is also assumed that the lot-size of manufacturer (second echelon) is m times larger than the supplier’s factors (first echelon), and the supplier can receive wares (the raw material) from the manufacturer in a cycle through several shipments, due to the point that shortage is not allowed. So, it is supposed that the supplier’s production rate is greater than manufacturer’s. The aim is to determine the optimal lot-size of each echelon such that the NPV of the total cost of system is minimized. After approximating the NPV objective function via Maclaurin expansion in both zero and non-zero lead-time cases, an exact algorithm is presented to find optimal solution of the presented model. Based on the results, the two approaches of average cost and NPV do not lead to a same result, and non-equivalency is occurred in this case.