The Basic Model of the Production and Shipment Policy for the Single-vendor Single-buyer when Demand Rate is Linearly Decreasing with Time

A basic model for a supply chain in which a vendor supplies a product to a buyer is considered. The vendor manufactures the product at a finite rate and periodically ships the output to the buyer. The buyer then consumes the product at a linearly decreasing time-varying rate. Costs are attached to manufacturing batch set up, the delivery of a shipment and stockholding at the vendor and buyer. The objective is to determine the shipment policy which minimises the total cost, assuming the vendor and buyer collaborate and find a way of sharing the consequent benefits. How the optimal shipment policy may be derived when the shipments size and shipments intervalare identical is shown. These procedures are illustrated with numerical examples.