Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system

We consider a two-echelon supply chain with an upstream manufacturer and a downstream retailer for a single perishable product. The manufacturer processes raw materials into finished products, which are purchased by the retailer in each replenishment cycle. The raw materials of the manufacturer are highly perishable (i.e. perishing within hours or days), and the finished goods at the retailer face demand uncertainty and obsolescence. We model the manufacturer-retailer relationship as a Stackelberg game where the retailer is the leader and decides the replenishment cycle that minimises its mismatch cost between supply and uncertain demand. The manufacturer is the follower and decides its processing rate to minimise its unit cost for finished goods. Our results show that the raw material and finished goods lifetimes, which are interrelated through the duration of the replenishment cycle, have a significant impact on supply chain costs. Although raw material spoilage cost by itself is low, we show that short raw material lifetimes have a significant impact on the costs of both parties. Additionally, we find that while high manufacturer markups increase retailer costs, they reduce the manufacturer's costs due to large production batches.