An integrated equal-lots policy for shipping a vendor's final production batch to a single buyer under linearly decreasing demand

This paper considers a supply chain in which a vendor supplies a product to a buyer. The vendor is about to manufacture the final batch of the product at a finite rate and then periodically ship the output to the buyer. The buyer then consumes the product at a linearly decreasing demand rate. Most previous work on this topic has been based on the assumption of fixed demand rate. Costs are attached to the manufacturing batch set-up, the delivery of a shipment, and stockholding at the vendor and buyer. The objective is to determine the number of shipments and sizes of those shipments which minimise the total cost-assuming the vendor and buyer collaborate and find a way of sharing the consequent benefits. We show how the optimal policy may be derived when the shipments size are identical. We illustrate this policy with numerical examples.