Bounds of Relative Regret Limit in p-Robust Supply Chain Network Design

This research studies the p‐robust supply chain network design with uncertain demand and cost scenarios. The optimal design integrates the supplier selection together with the facility location and capacity problem. We provide a new framework to obtain the relative regret limit, which is critical in the robust supply chain design but is assumed to be a known value in the existing literature. We obtain lower and upper bounds for relative regret limit and obtain a sequence of optimal solutions for series relative regret limits between the upper and lower bounds. An algorithm for p‐robust supply chain network design is provided. A series of numerical examples are designed to find the properties of the bottleneck scenarios. A scenario with low probability and a low optimal objective function value for the scenario has a greater chance of being a bottleneck. To focus only on the influence from the relative regret, we also introduce three separate new objective functions in p‐robust design. The proposed new theories and approaches provide a sequence of options for decision makers to reduce the marketing risks effectively in supply chain network design.