We consider a production line which is operated according to demands for products so as to minimize the shortage of products and the excess of inventories. In our model, the capacities of buffer storages and a warehouse are adjusted according to demands, and the blocking of each stage plays an essential role in reducing unnecessary inventories. The efficiency of the line is measured by the sum of the average shortage number of products and the average inventory number of in-process and finished products in the steady state. We propose two efficient approximate solution methods evaluating the line efficiency in terms of configuration parameters (e.g. the number of stages, the perfermances of stages, and the capacities of buffer storages and a warehouse). Of these two methods, the second method requires more tedious calculations, but is more accurate. We confirm the validity of the approaches by comparing the solutions for many example problems obtained by our methods with those obtained by computer simulation.