In this study, we consider an assembly line operated under a base-stock policy. A product consists of two parts, and a finished product transfers to a warehouse in which demands are satisfied. Assume that demands arrive according to a Poisson process and processing times at each production line are exponentially distributed. Whenever a demand arrives, it is satisfied immediately from an inventory in the warehouse if available; otherwise, it is backlogged and satisfied later by the next product exiting from production lines. In either case, an arriving demand automatically triggers the production of a part at both production lines. These two parts will be assembled into a product that eventually transfers to the warehouse. We obtain a closed form formula of approximation for delay time or lead time distribution of a demand when a base- stock level is s. Moreover, it can be applied to the optimal base-stock level which minimizes the total inventory cost. Numerical examples are presented to show our optimal base-stock level's quality.