@article{Wang2023, 
author = {Chang-Jun Wang and Zi-Jian Gao},
title = {Two-stage stochastic programming with imperfect information update: Value evaluation and information acquisition game},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {4524-4550},
keywords = {robust optimization, two-stage stochastic programming, expected value of imperfect information, costly information acquisition game, two-stage production and shipment},
url = {https://www.sciopen.com/article/10.3934/math.2023224},
doi = {10.3934/math.2023224},
abstract = {We focus on the two-stage stochastic programming (SP) with information update, and study how to evaluate and acquire information, especially when the information is imperfect. The scarce-data setting in which the probabilistic interdependent relationship within the updating process is unavailable, and thus, the classic Bayes' theorem is inapplicable. To address this issue, a robust approach is proposed to identify the worst probabilistic relationship of information update within the two-stage SP, and the robust Expected Value of Imperfect Information (EVII) is evaluated by developing a scenario-based max-min-min model with the bi-level structure. Three ways are developed to find the optimal solution for different settings. Furthermore, we study a costly information acquisition game between a two-stage SP decision-maker and an exogenous information provider. A linear compensation contract is designed to realize the global optimum. Finally, the proposed approach is applied to address a two-stage production and shipment problem to validate the effectiveness of our work. This paper enriches the interactions between uncertain optimization and information management and enables decision-makers to evaluate and manage imperfect information in a scarce-data setting.}
}