Both random yield and uncertain demand are common occurrences in the semiconductor industry. This paper studies a decentralised supply chain comprised of a single manufacturer and a single distributor for a short life-cycle product with random yield and uncertain demand. We analyse two alternatives for doing business. One alternative is the traditional supply chain arrangement, where the distributor is fully responsible for the inventory decision whereas the manufacturer is fully responsible for the production decision. The other alternative is the vendor-managed-inventory (VMI) arrangement, where the manufacturer (vendor) is fully responsible for the entire production and inventory decisions in the supply chain. We characterise the optimal production and inventory decisions under both arrangements. We also compare the individual firms and supply chain performance under the traditional and VMI arrangements. Our results provide insights into how firms can choose the right supply chain arrangement to improve supply chain efficiency.