Abstract: During the last decade, to identify and mitigate supply disruptions is a topic that receives substantial management attention. Both diversifying supply sourcing including dual-sourcing and adding a backup supplier are logic ways to manage the risk of supply disruptions. There are two options execution modes. One is N mode that pushes ordering patterns, which means that the retailer orders from the backup supplier in advance under uncertain demand circumstances, the other is Y mode, push & pull ordering patterns, which means that the retailer doesn't order from backup suppliers until he knows the demand circumstance. It's successfully proved that the model is a convex programming through two options implementation strategy adopted by the retailer, and using Karush-Kuhn-Tucker conditions, a predetermined amount of backup suppliers, the closed expressions of optimal order quantity and profit expression can also be obtained. The threshold of using a backup supplier is given. By theorems and further numerical example, it can be concluded:Optimal profits is larger than primary supplier's while primary supplier has larger order quantities under N mode, under Y mode, backup supplier's capabilities predetermined amount. The impacts of model parameters on the ordering quantity from primary supplier are a little different based on the relative size of c_e and c because of the execution of options. The capacity utilization of backup suppliers is highest when c_e<c but lowest when c_e>c under N mode, and it is in the middle level under Y mode. The retailer can obtain more profits under Y mode relative to under N mode as g, c and c_e increase, or s and γ decrease.

Key words: backup supplier, supply disruptions, capacity options contract, KKT conditions, stochastic demand