Background. The study of control and maintenance of production inventories of deteriorating items with and without shortages has grown in its importance recently. The effect of deterioration is very important in many inventory systems. Deterioration is defined as decay or damage such that the item cannot be used for its original purpose. Methods: In this article order level inventory models have been developed for deteriorating items with linear demand and Weibull deterioration. In developing the model we have assumed that the production rate and the demand rate are time dependent. The unit production cost is inversely proportional to demand. Inventory-production system has two parameters Weibull deterioration. Results and conclusions: Two models have been developed considering without shortage cases and with shortage case where the shortages are completely backlogged. The objective of the model is to develop an optimal policy that minimizes the total average cost. Sensitivity analysis has been carried out to show the effect of changes in the parameter on the optimum total average cost.