Backup agreements with penalty scheme under supply disruptions

This article considers a supply chain for a single product involving one retailer and two independent suppliers, when the main supplier might fail to supply the products, the backup supplier can always supply the products at a higher price. The retailer could use the backup supplier as a regular provider or a stand-by source by reserving some products at the supplier. A backup agreement with penalty scheme is constructed between the retailer and the backup supplier to mitigate the supply disruptions and the demand uncertainty. The expected profit functions and the optimal decisions of the two players are derived through a sequential optimisation process. Then, the sensitivity of two players' expected profits to various input factors is examined through numerical examples. The impacts of the disruption probability and the demand uncertainty on the backup agreement are also investigated, which could provide guideline for how to use each sourcing method.