A collaborative strategy for a three echelon supply chain with ramp type demand, deterioration and inflation

A supply chain system has been investigated in which a single manufacturer procures raw materials from a single supplier, processes them to produce finished products, and then delivers the products to a single retailer. The customer’s demand rate is assumed to be time-sensitive in nature (ramp type) that allows two-phase variation in the demand and production rate. Our adoption of ramp type demand reflects a real market demand for a newly launched product. Shortages are allowed with partial backlogging of demand (only for the retailer), i.e. the rest represent lost sales. The effects of inflation of the cost parameters and deterioration are also considered separately. We show that the total cost function is convex. Using this convexity, a simple algorithm is presented to determine the optimal order quantity and optimal cycle time for the total cost function. The results are discussed with numerical examples and particular cases of the model discussed briefly. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.