In this paper, an attempt is made to characterize the preservation technology for deteriorating items to reduce the deterioration rate. This model assumes a single producer and single supplier and formulates a production model with a time varying rate of deterioration rate. Here production and demand are treated as a fuzzy variables and total cost is minimized for both the crisp and fuzzy model. Shortage is allowed on the supplier’s part, which is partially backlogged. A solution procedure is presented to determine an optimal replenishment cycle and total cost per unit time, which is a convex function of preservation technology cost. Results have been validated with relevant example. In a way, the proposed model provides a unique theory to reduce the deterioration rate for the production model.

This study develops an integrated production inventory model from the perspectives of vendor, supplier and buyer. The demand rate is time dependent for the vendor and supplier and buyer assumes the stock dependent demand rate. As per the demand, supplier uses two warehouses (rented and owned) for the storage of excess quantities. Shortages are allowed at the buyer’s part only and the unfulfilled demand is partially backlogged. The effect of imperfect production processes on lot sizing is also considered. This complete model is studied under the effect of inflation. The objective is to minimize the total cost for the system. A solution procedure is developed to find a near optimal solution for the model. A numerical example along with sensitivity analysis is given to illustrate the model.