This paper considers the production/inventory model of a system in which inventory facilities are in series and between them are production/assembly units. There are inventory stocks for raw material, in-process products and end-product. External demand for an end-product is placed at the end-stock point in the system. It is assumed that uncertainty appears in external demand. Uncertainty is propagated along the production/inventory system. Modeling of the external discrete imprecise demand is based on fuzzy sets. The fuzzy model developed enables a search for the stock allocation that gives the minimum possible inventory cost of the whole serial system. The backtrack searching procedure for the most appropriate inventory stocks allocation is illustrated by an example.