On the risk-averse optimization of service level in a supply chain under disruption risks

The worst-case optimization of service level in the presence of supply chain disruption risks is considered for the two different service levels measures: the expected worst-case demand fulfillment rate and the expected worst-case order fulfillment rate. The optimization problem is formulated as a joint selection of suppliers and stochastic scheduling of customer orders under random disruptions of supplies. The suppliers are located in different geographic regions and the supplies are subject to random local and regional disruptions. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional service-at-risk as a worst-case service level measure. The risk-averse solutions that optimize the worst-case performance of a supply chain are compared for the two service level measures. In addition, to demonstrate the impact on the cost in the process of optimizing the worst-case service level, a joint optimization of expected cost and conditional service-at-risk using a weighted-sum approach is considered and illustrated with numerical examples. The findings indicate that the worst-case order fulfillment rate shows a higher service performance than the worst-case demand fulfillment rate. Maximization of the expected worst-case fraction of fulfilled customer orders better mitigates the impact of disruption risks. The supply portfolio is more diversified and the expected worst-case fraction of fulfilled orders is greater for most confidence levels. Finally, the results clearly show that worst-case service level is in opposition to cost.