A Vendor Buyer Supply Chain Model for Deteriorating Item with Quadratic Time Varying Demand and Pro rata Warranty Policy
The article considers a single vendor a single buyer supply chain in which the buyer sells a seasonal deteriorating product to customers over a single period of time. At the buyer's end, the demand is assumed to be quadratic in time. The vendor follows a lot for lot policy for replenishment made to the buyer and (s)he agrees to refund the customer's purchase price on a pro rata basis, if any item fails during the warranty period offered by the buyer. We derive and optimize the average expected total cost of the supply chain in order to obtain the optimal decisions of the integrated system. An algorithm is developed for finding the optimal solution of the model numerically. A numerical example is taken to demonstrate the coordination policy between the vendor and the buyer. Sensitivity analysis is carried out to investigate the effects of key parameters on the optimal decisions.