This paper addresses the performance evaluation and optimization of a production-distribution system composed of a warehouse supplied by a manufacturing plant with finite capacity. Customer orders arrive randomly with random order size. Transportation time from plant to warehouse is fixed. We propose an analytical approach that uses only the first two moments of random variables to evaluate the inventory cost and demand fill rate. A gradient-based method is then proposed to minimize the average total inventory cost subject to fill rate requirement. Numerical comparisons with simulation show that the analytical approach is very efficient.