Abstract
Based on uncertainty theory, this paper mainly studies the uncertainties and the information value in the two-stage uncertain programming with recourse. We first define three fundamental concepts and investigate their theoretical properties, based on which we present two optimal indices, i.e., EVPI and VUS. Then, we introduce a method to calculate the expected value of the second-stage objective function involving discrete uncertain variables. Due to the complexity of calculation, the upper bound and lower bound for the two indices are studied, respectively. Finally, two examples are given to illustrate these concepts clearly. The results obtained in this paper can provide theoretical basis for studying uncertainties and information value in decision-making process under uncertain systems.
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Birge JR, Louveaux F (2011) Introduction to stochastic programming. Springer, Berlin
Dantzig GB (1955) Linear programming under uncertainty. Manag Sci 1(3–4):197–206
Eckermann S, Karnon J, Willan AR (2010) The value of value of information: best informing research design and prioritization using current methods. Pharmacoeconomics 28(9):699
Eckermann S, Willan AR (2007) Expected value of information and decision making in HTA. Health Econ 16(2):195
Fan Y et al (2015) Planning water resources allocation under multiple uncertainties through a generalized fuzzy two-stage stochastic programming method. IEEE Trans Fuzzy Syst 23(5):1488–1504
Hoomans T, Fenwick EA, Palmer S, Claxton K (2009) Value of information and value of implementation: application of an analytic framework to inform resource allocation decisions in metastatic hormone-refractory prostate cancer. Value Health 12(2):315–324
Leovey H, Romisch W (2015) Quasi-Monte Carlo methods for linear two-stage stochastic programming problems. Math Program 151(1):315–345
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009a) Theory and practice of uncertain programming. Springer, Berlin
Liu B (2009b) Some research problems in uncertainty theory. J Uncertain Syst 3:3–10
Liu B (2010a) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2010b) Uncertain risk analysis and uncertain reliability analysis. J Uncertain Syst 4(4):163–170
Liu B (2013) Polyrectangular theorem and independence of uncertain vectors. J Uncertain Anal Appl, 1, Article 9
Liu B, Chen XW (2015) Uncertain multiobjective programming and uncer- 340 tain goal programming. J Uncertain Anal Appl, 3, Article 10
Liu B, Yao K (2015) Uncertain multilevel programming: algorithm and applications. Comput Ind Eng 89:235–240
Parisio A, Jones CN (2015) A two-stage stochastic programming approach to employee scheduling in retail outlets with uncertain demand. Omega 53:97–103
Romeijnders W, Stougie L, Vlerk MHVD (2014) Approximation in two-stage stochastic integer programming. Surv Oper Res Manag Sci 19(1):17–33
Shapiro A, Dentcheva D (2014) Lectures on stochastic programming: mod- eling and theory, Siam
Sheng Y, Yao K (2014) Some formulas of variance of uncertain random variable. J Uncertain Anal Appl 2, Article 12
Wang Z, Guo J, Zheng M, Wang Y (2015) Uncertain multiobjective traveling salesman problem. Eur J Oper Res 241(2):478–489
Wolf C, Fabian CI, Koberstein A, Suhl L (2014) Applying oracles of on-demand accuracy in two-stage stochastic programming-a computational study. Eur J Oper Res 239(2):437–448
Zhang B, Peng J (2013) Uncertain programming model for uncertain optimal assignment problem. Appl Math Model 37(9):6458–6468
Zheng M, Yi Y, Wang Z, Liao T (2017a) Relations among efficient solutions in uncertain multiobjective programming. Fuzzy Optim Decis Mak, doi:10.1007/s10700-016-9252-x, to be published
Zheng M, Yi Y, Wang Z, Liao T (2016) Efficient solution concepts andtheir application in uncertain multiobjective programming. Appl SoftComputing, doi:10.1016/j.asoc.2016.07.021, to be published
Zheng M, Yi Y, Wang Z, Chen JF (2017b) Study on two-stage uncertain programming based on uncertainty theory. J Intell Manuf 28(3):633–642
Acknowledgements
The author gratefully acknowledges the financial support provided by State Key Laboratory Development Program of China (Grant No. 9140C890302) and National Natural Science Foundation of China (Grant Nos.61502523, 61502521).
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Zheng, M., Yi, Y., Wang, X. et al. The information value and the uncertainties in two-stage uncertain programming with recourse. Soft Comput 22, 5791–5801 (2018). https://doi.org/10.1007/s00500-017-2662-z
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DOI: https://doi.org/10.1007/s00500-017-2662-z