Distributionally Robust Optimization Model for a Minimum Cost Consensus with Asymmetric Adjustment Costs Based on the Wasserstein Metric

Ziqi Wu, Kai Zhu () and Shaojian Qu
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Ziqi Wu: Alibaba, Hangzhou 311121, China
Kai Zhu: Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Shaojian Qu: School of Management Science and Technology, Nanjing University of Information Science and Technology, Nanjing 210000, China

Mathematics, 2022, vol. 10, issue 22, 1-21

Abstract: When solving the problem of the minimum cost consensus with asymmetric adjustment costs, decision makers need to face various uncertain situations (such as individual opinions and unit adjustment costs for opinion modifications in the up and down directions). However, in the existing methods for dealing with this problem, robust optimization will lead to overly conservative results, and stochastic programming needs to know the exact probability distribution. In order to overcome these shortcomings, it is essential to develop a novelty consensus model. Thus, we propose three new minimum-cost consensus models with a distributionally robust method. Uncertain parameters (individual opinions, unit adjustment costs for opinion modifications in the up and down directions, the degree of tolerance, and the range of thresholds) were investigated by modeling the three new models, respectively. In the distributionally robust method, the construction of an ambiguous set is very important. Based on the historical data information, we chose the Wasserstein ambiguous set with the Wasserstein distance in this study. Then, three new models were transformed into a second-order cone programming problem to simplify the calculations. Further, a case from the EU Trade and Animal Welfare (TAW) program policy consultation was used to verify the practicability of the proposed models. Through comparison and sensitivity analysis, the numerical results showed that the three new models fit the complex decision environment better.

Keywords: distributionally robust optimization; group decision-making; minimum cost consensus; asymmetric adjustment costs; Wasserstein distance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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