In the Japanese automobile and electrical industries it is often necessary to consider the production ordering systems as multi-stage production inventory systems. Previous analyses of production ordering systems have left untouched the variations in the production ordering quantities and inventory at each stage, in spite of the fact that the amplification phenomena of these variations are critical in a multi-stage production inventory system. Generally, we are able to classify the multi-stage production ordering systems into two types, i.e. the push-type and the pull-type. This paper discusses the following subjects concerning the push-type and multi-stage production ordering system based on forecasting: (1) the effects of demand fluctuations and forecast errors on the amplification of production order variations and inventory variations in terms of a basic production ordering model, and (2) the same effects in a modified production ordering model which is able to decrease both the variations in the production ordering quantities and in the inventory at each stage.