Author:
Wang Chang-Jun,Gao Zi-Jian
Abstract
<abstract>
<p>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.</p>
</abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference44 articles.
1. M. Brito, E. Laan, Inventory control with product returns: the impact of imperfect information, Eur. J. Oper. Res., 194 (2009), 85–101. https://doi.org/10.1016/j.ejor.2007.11.063
2. A. Heath, I. Manolopoulou, G. Baio, A review of methods for the analysis of the expected value of information, Med. Decis. Making, 37 (2017), 747–758. https://doi.org/10.1177/0272989X17697692
3. R. A. Howard, Information value theory, IEEE T. Syst. Man Cy., 2 (1966), 22–26. https://doi.org/10.1109/TSSC.1966.300074
4. H. Raiffa, Decision analysis: Introductory lectures on choices under uncertainty, Reading, MA: Addison-Wesley, 1968.
5. R. L. Winkler, An introduction to Bayesian inference and decision, Gainesville, FL: Probabilistic Publishing, 2003.