AbstractThis paper presents a mathematical model developed for optimization of single-item multi-stage production-inventory systems. The demands are assumed to occur randomly at the same rate whereas processing and setup times are different, each following exponential distributions with different means. The model assumes a "one-for-one ordering" inventory policy and that on total system cost expression comprising setup, holding and penalty costs is obtained for optimization. As a special case, single stage, cost expressions become the same as those obtained by Baker. Computational results for two stages are given. Implications of aggregating the two stages into an equivalent simple stage are discussed.