Abstract: In the fiercely competitive global market, companies are more willing to entrust some business processes to external organizations to achieve benefits such as reducing costs, improving product quality, and enhancing competitiveness. A typical example of this type of outsourcing is purchasing accessories and services through global suppliers. Therefore, how to select suitable suppliers and make the best order allocation plan has become a problem worth in-depth consideration. Traditionally, supplier selection has considered standards for such things as cost, quality, and delivery time. But recently, due to the vulnerability of global supply chains in the face of unexpected and man-made disasters such as tsunamis, earthquakes, transportation accidents, and strikes, suppliers are facing various supply disruption risks, and the harm caused by these risks can immediately spread downstream in the supply chain, creating what is known as a “chain reaction”. Therefore, considering resilient suppliers has also become a key strategic decision in supplier selection and order allocation issues.
In response to the above considerations, this paper establishes a two-stage distributionally robust optimization model based on data-driven, which can flexibly solve supplier selection and order allocation problems when facing disruption risks. Firstly, we take into account the possible random disruptions that suppliers may experience, namely a decrease or loss of their production and supply capabilities, and aim to deal with them through strategies such as supplier fortifying, recovery and signing with backup suppliers. Secondly, in view of the uncertainty of disruption scenarios and the available limited historical data, three models based on stochastic programming, classical robust optimization and distributionally robust optimization with Wasserstein ambiguity set are established. Finally, using duality and linearization techniques, the three established comparative models are transformed and solved, and the corresponding results are obtained.
The numerical results indicate that adopting appropriate coping strategies can effectively alleviate the chain reaction caused by supply chain disruptions. The impact of supplier disruptions on downstream enterprises cannot be ignored. For example, after the tsunami and earthquake in Japan in 2011, suppliers of the automotive brand Toyota were unable to deliver parts in the expected quantity and speed, causing Toyota to suspend production for several days, resulting in a loss of approximately 50000 vehicles per day. Therefore, when designing the supply chain, managers should take corresponding active or passive measures to prevent or mitigate the occurrence of disruption. The model established in this paper also proves that the corresponding measures will have a positive effect on improving supply chain elasticity and reducing chain reactions between facilities.
The occurrence of supplier disruptions is irregular and uncertain, and historical data collection may be insufficient and incomplete. In order to handle such uncertainties, the distributionally robust optimization model is superior to the stochastic model and the classical robust model in terms of robustness and stability, respectively. The results of this paper also show that compared with the stochastic models, distributionally robust optimization models do not require distribution information of uncertain parameters and have the ability to cope with uncertainty in distribution information such as mean variance. The classical robust model is less stable in supplier selection results but more conservative in numerical results. Therefore, when the disruption history data is limited and the distribution information of uncertain probabilities is not completely known, it is a good choice to adopt the distributionally robust optimization method.
The risk of disruption may be related to natural disasters or specific types of events that occur through intentional or unintentional human behavior, which are less likely to occur but have a significant impact on business operations. Adopting corresponding strategies can effectively reduce the harm of supplier disruption to the economic benefits of enterprises, and with the support of reasonable mathematical models, can assist enterprises in formulating optimized decision-making plans.

Key words: supplier selection, distributionally robust, risk and uncertainty, two stage programming, supply chain resilience

摘要： 在当今全球化和高度不确定的商业环境中,设计不仅高效而且富有弹性的供应链,能够在中断情况下保证供应链的连续性是十分必要的。本文针对该问题建立了一种基于数据驱动的两阶段分布鲁棒优化模型,在面对中断风险时能够弹性的解决供应商选择和订单分配问题。首先,本文考虑了供应商可能发生的随机中断,并旨在通过供应商强化,恢复与备用供应商签约等策略来应对。其次,针对中断场景发生的不确定性和可获取的有限历史数据,建立了基于随机规划,经典鲁棒优化和具有Wasserstein非精确集的分布鲁棒优化三种方法的模型。最后,利用对偶性和线性化技术,对所建立的模型进行了转化与求解。数值结果表明:考虑弹性措施对缓解中断危害带来了显著影响;通过三种模型的对比,突出了本文所建立的分布鲁棒优化模型的性能。

关键词: 供应商选择, 分布鲁棒, 风险和不确定性, 两阶段规划, 供应链弹性