Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials

The theoretical investigation of the effectiveness of limited flexibility has mainly focused on the performance metric that is based on the maximum sales in units. However, this could lead to substantial profit losses when the maximum sales metric is used to guide flexibility designs whereas the products have considerably large profit margin differences. We address this issue by introducing margin differentials into the analysis of process flexibility designs, and our results can provide useful guidelines for the evaluation and design of flexibility configurations when the products have heterogeneous margins. We adopt a robust optimization framework and study process flexibility designs from the worst-case perspective by introducing the Dual Margin Group Index (DMGI). We show that a general class of worst-case performance measures can be expressed as functions of a design's DMGIs and the given uncertainty set. Moreover, the DMGIs lead to a partial ordering that enables us to compare the worst-case performance of different designs. Applying these results, we prove that under the so-called part-wise independently symmetric uncertainty sets and a broad class of worst-case performance measures, the alternate long chain design is optimal among all long chain designs with equal number of high profit products and low profit products. Finally, we develop a heuristic based on the DMGIs to generate effective flexibility designs when products exhibit margin differentials