Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials

62 Pages Posted: 28 Aug 2018 Last revised: 22 May 2020

See all articles by Shixin Wang

Shixin Wang

New York University (NYU) - Leonard N. Stern School of Business

Xuan Wang

Hong Kong University of Science and Technology, ISOM Department

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: August 17, 2018

Abstract

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.

Keywords: Process Flexibility, Flexible Production, Profit Maximization, Robust Optimization, Worst-case Analysis

Suggested Citation

Wang, Shixin and Wang, Xuan and Zhang, Jiawei, Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials (August 17, 2018). Available at SSRN: https://ssrn.com/abstract=3233721 or http://dx.doi.org/10.2139/ssrn.3233721

Shixin Wang

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 W 4th St
Suite 9-160
New York, NY 10012
United States

Xuan Wang (Contact Author)

Hong Kong University of Science and Technology, ISOM Department ( email )

Clear Water Bay
Kowloon
Hong Kong, Not Applicable
Hong Kong
852-23585854 (Phone)

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

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