AbstractA new production-inventory model is developed for an item with increasing time-varying demand during a finite planning period. We assume that shortages are fully backordered, and the cost of adjusting the production rate depends on the magnitude of the change in the production rate. The objective is to find the optimal policy of adjusting the production rate in order to minimize the total system cost. A solution procedure is presented and a numerical example is provided for the special case of linearly increasing demand.