In this paper, we develop an integrated inventory model for a producer and buyer, and consider an imperfect production process having two different demands in which exponential demand for the producer and triangular demand for the buyer. The model takes into account that a partially backlogged shortage is allowed on the buyer’s part. Preservation facilities are also considered in this model for deteriorating items to reduce the deterioration rate. The production rate is assumed to be demand-dependent. This model provides a theory to reduce the deterioration rate under the effect of inflation. The total cost of the model is minimised for both crisp and fuzzy environments by using triangular fuzzy numbers and defuzzify the total cost by the centroid method. Numerical example and sensitivity analysis are also given to illustrate this proposed model.