在供应商-制造商二级供应链中，制造商作为领导者，采用一个战略供应商和一个备份供应商。有两种期权执行模式，一种是需求未知情况下提前向备份供应商订货的推式订货模式，另一种是获知需求后再向备份供应商订货的推式与拉式相结合的订货模式。证明了所建模型均为凸规划，并利用Karush-Kuhn-Tucker条件求得备份供应商的能力预定量、战略供应商订货量以及最优利润的表达式，得出了是否采用备份供应商的临界值。研究结果表明：推式模式下战略供应商的订货量较大，推拉结合模式下备份供应商的能力预定量较大，推拉结合模式下制造商的利润较大；随着战略供应商可靠性系数的增大，推式模式下首先放弃备份供应商的使用；当战略供应商的采购成本、备份供应商的期权执行成本和缺货成本较大，且残值以及可靠性系数较小时，推拉结合模式相对于完全推式的效果更加明显。
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 ce and c because of the execution of options. The capacity utilization of backup suppliers is highest when ce<c but lowest when ce>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 ce increase, or s and γ decrease.
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