Two-stage stochastic programming with imperfect information update: Value evaluation and information acquisition game

Chang-Jun Wang; Zi-Jian Gao; Chang-Jun Wang; Zi-Jian Gao

doi:10.3934/math.2023224

AIMS Mathematics

2023, Volume 8, Issue 2: 4524-4550. doi: 10.3934/math.2023224

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Two-stage stochastic programming with imperfect information update: Value evaluation and information acquisition game

Chang-Jun Wang ^,,
Zi-Jian Gao

Department of Management Science, Donghua University, Shanghai, 200051, China

Received: 07 September 2022 Revised: 07 November 2022 Accepted: 23 November 2022 Published: 06 December 2022
MSC : 90C15, 90C17, 90B06, 91A80

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.
Citation: Chang-Jun Wang, Zi-Jian Gao. Two-stage stochastic programming with imperfect information update: Value evaluation and information acquisition game[J]. AIMS Mathematics, 2023, 8(2): 4524-4550. doi: 10.3934/math.2023224

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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.

References

[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 doi: 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 doi: 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 doi: 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.
[6]	R. B. Bratvold, J. E. Bickel, H. P. Lohne, Value of information in the oil and gas industry: Past, present, and future, SPE Reserv. Eval. Eng., 12 (2007), 630–638. https://doi.org/10.2118/110378-MS doi: 10.2118/110378-MS
[7]	D. Koller, N. Friedman, Probabilistic graphical models: Principles and techniques, Cambridge University Press, 2009.
[8]	E. K. Hussain, P. R. Thies, J. Hardwick, P. M. Connor, M. Abusara, Grid Island energy transition scenarios assessment through network reliability and power flow analysis, Front. Energy Res., 8 (2021), 584440. https://doi.org/10.3389/fenrg.2020.584440 doi: 10.3389/fenrg.2020.584440
[9]	Q. Wang, A. Farahat, C. Gupta, S. Zheng, Deep time series models for scarce data, Neurocomputing, 456 (2021), 504–518. https://doi.org/10.1016/j.neucom.2020.12.132 doi: 10.1016/j.neucom.2020.12.132
[10]	A. Maxhuni, P. Hernandez-Leal, L. E. Sucar, V. Osmani, E. F. Morales, O. Mayora, Stress modelling and prediction in presence of scarce data, J. Bio. Info., 63 (2016), 344–356. https://doi.org/10.1016/j.jbi.2016.08.023 doi: 10.1016/j.jbi.2016.08.023
[11]	C. J. Wang, S. T. Chen, A distributionally robust optimization for blood supply network considering disasters, Transport Res. E-Log., 134 (2020), 1–30. https://doi.org/10.1016/j.tre.2020.101840 doi: 10.1016/j.tre.2020.101840
[12]	R. A. Howard, A. E. Abbas, Foundations of decision analysis, Boston, MA: Pearson Education Limited, 2016.
[13]	K. Szaniawski, The value of perfect information, Synthese, 17 (1967), 408–424.
[14]	D. Samson, A. Wirth, J. Rickard, The value of information from multiple sources of uncertainty in decision analysis, Eur. J. Oper. Res., 39 (1989), 254–260. https://doi.org/10.1016/0377-2217(89)90163-X doi: 10.1016/0377-2217(89)90163-X
[15]	S. H. Azondékon, J. M. Martel, "Value" of additional information in multicriterion analysis under uncertainty, Eur. J. Oper. Res., 117 (1999), 45–62. https://doi.org/10.1016/S0377-2217(98)00102-7 doi: 10.1016/S0377-2217(98)00102-7
[16]	S. Ben Amor, K. Zaras, E. A. Aguayo, The value of additional information in multicriteria decision making choice problems with information imperfections, Ann. Oper. Res., 253 (2017), 61–76. https://doi.org/10.1007/s10479-016-2318-x doi: 10.1007/s10479-016-2318-x
[17]	M. E. Dakins, The value of the value of information, Hum. Ecol. Risk. Assess., 5(1999), 281–289. https://doi.org/10.1080/10807039991289437 doi: 10.1080/10807039991289437
[18]	I. Yanikoglu, B. L. Gorissen, D. den Hertog, A survey of adjustable robust optimization, Eur. J. Oper. Res., 277 (2019), 799–813. https://doi.org/10.1016/j.ejor.2018.08.031 doi: 10.1016/j.ejor.2018.08.031
[19]	G. Dutta, N. Gupta, J. Mandal, M. K. Tiwari, New decision support system for strategic planning in process industries: computational results, Comput. Ind. Eng., 124 (2018), 36–47. https://doi.org/10.1016/j.cie.2018.07.016 doi: 10.1016/j.cie.2018.07.016
[20]	S. Khalilabadi, S. H. Zegordi, E. Nikbakhsh, A multi-stage stochastic programming approach for supply chain risk mitigation via product substitution, Comput. Ind. Eng., 149 (2020), 106786. https://doi.org/10.1016/j.cie.2020.106786 doi: 10.1016/j.cie.2020.106786
[21]	J. C. López, J. Contreras, J. I. Munoz, J. Mantovani, A multi-stage stochastic non-linear model for reactive power planning under contingencies, IEEE T. Power Syst., 28 (2013), 1503–1514. https://doi.org/10.1109/TPWRS.2012.2226250 doi: 10.1109/TPWRS.2012.2226250
[22]	D. Bhattacharjya, J. Eidsvik, T. Mukerji, The value of information in portfolio problems with dependent projects, Decis. Anal., 10 (2013), 341–351. https://doi.org/10.1287/deca.2013.0277 doi: 10.1287/deca.2013.0277
[23]	C. M. Lee, A Bayesian approach to determine the value of information in the newsboy problem, Int. J. Prod. Econ., 112 (2008), 391–402. https://doi.org/10.1016/j.ijpe.2007.04.005 doi: 10.1016/j.ijpe.2007.04.005
[24]	S. Santos, A. Gaspar, D. J. Schiozer, Value of information in reservoir development projects: Technical indicators to prioritize uncertainties and information sources, J. Petrol. Sci. Eng., 157(2017), 1179–1191. https://doi.org/10.1016/j.petrol.2017.08.028 doi: 10.1016/j.petrol.2017.08.028
[25]	S. Ben Amor, J. M. Martel, Multiple criteria analysis in the context of information imperfections: Processing of additional information, Oper. Res., 5 (2005), 395–417. https://doi.org/10.1007/BF02941128 doi: 10.1007/BF02941128
[26]	J. Bernardo, A. Smith, Bayesian theory, 2 Eds., Wiley & Sons, New York, 2000.
[27]	S. J. Armstrong, Combining forecasts principles of forecasting: A handbook for researchers and practitioners, Kluwer Academic Publishers, Norwell, MA, 2001,417–439.
[28]	R. L. Winkler, Y. Grushka-Cockayne, K. C. Lichtendahl, V. Jose, Probability forecasts and their combination: A research perspective, Decis. Anal., 16 (2019), 239–260. https://doi.org/10.1287/deca.2019.0391 doi: 10.1287/deca.2019.0391
[29]	D. P. Morton, E. Popova, A Bayesian stochastic programming approach to an employee scheduling problem, IIE Trans., 36 (2004), 155–167. https://doi.org/10.1080/07408170490245450 doi: 10.1080/07408170490245450
[30]	O. Dowson, D. P. Morton, B. K. Pagnoncelli, Partially observable multistage stochastic programming, Oper. Res. Lett., 48 (2020), 505–512. https://doi.org/10.1016/j.orl.2020.06.005 doi: 10.1016/j.orl.2020.06.005
[31]	O. Compte, P. Jehiel, Auctions and information acquisition: sealed bid or dynamic formats? Rand. J. Econ., 38 (2007), 355–372. https://doi.org/10.2307/25046310 doi: 10.2307/25046310
[32]	P. Miettinen, Information acquisition during a Dutch auction, J. Econ. Theory, 148 (2013), 1213–1225. https://doi.org/10.1016/j.jet.2012.09.018 doi: 10.1016/j.jet.2012.09.018
[33]	E. M. Azevedo, D. M. Pennock, W. Bo, E. G. Weyl, Channel auctions, Manage Sci., 66 (2020), 2075–2082. https://doi.org/10.1287/mnsc.2019.3487 doi: 10.1287/mnsc.2019.3487
[34]	N. Golrezaei, H. Nazerzadeh, Auctions with dynamic costly information acquisition, Oper. Res., 65 (2017), 130–144. https://doi.org/10.1007/s00199-007-0301-0 doi: 10.1007/s00199-007-0301-0
[35]	Q. Fu, K. Zhu, Endogenous information acquisition in supply chain management, Eur. J. Oper. Res., 201 (2010), 454–462. https://doi.org/10.1016/j.ejor.2009.03.019 doi: 10.1016/j.ejor.2009.03.019
[36]	G. Li, H. Zheng, S. P. Sethi, X. Guan, Inducing downstream information sharing via manufacturer information acquisition and retailer subsidy, Decision Sci., 51 (2020), 691–719. https://doi.org/10.1111/deci.12340 doi: 10.1111/deci.12340
[37]	Q. Fu, Y. Li, K. Zhu, Costly information acquisition under horizontal competition, Oper. Res. Lett., 46 (2018), 418–423. https://doi.org/10.1016/j.orl.2018.05.003 doi: 10.1016/j.orl.2018.05.003
[38]	H. Cao, X. Guan, T. Fan, L. Zhou, The acquisition of quality information in a supply chain with voluntary vs. mandatory disclosure, Prod. Oper. Manag., 29 (2020), 595–616. https://doi.org/10.1111/poms.13130 doi: 10.1111/poms.13130
[39]	Y. Song, T. Fan, Y. Tang, F. Zou, Quality information acquisition and ordering decisions with risk aversion, Int. J. Prod. Res., 59 (2021), 6864–6880. https://doi.org/10.1080/00207543.2020.1828640 doi: 10.1080/00207543.2020.1828640
[40]	A. Madansky, Inequalities for stochastic linear programming problems, Manage. Sci., 6 (1960), 197–204. https://doi.org/10.1287/mnsc.6.2.197 doi: 10.1287/mnsc.6.2.197
[41]	M. A. Stulman, Some aspects of the distributional properties of the expected value of perfect information (EVPI), J. Oper. Res. Soc., 33 (1982), 827–836. https://doi.org/10.1057/jors.1982.178 doi: 10.1057/jors.1982.178
[42]	D. Bertsimas, M. Sim, The price of robustness, Oper. Res., 52 (2004), 35–53. https://doi.org/10.1287/opre.1030.0065 doi: 10.1287/opre.1030.0065
[43]	B. Colson, P. Marcotte, G. Savard, An overview of bilevel optimization, Ann. Oper. Res., 153 (2007), 235–256. https://doi.org/10.1007/s10479-007-0176-2 doi: 10.1007/s10479-007-0176-2
[44]	A. Ben-Tal, L. E. Ghaoui, A. Nemirovski, Robust optimization, Princeton, NJ: Princeton University Press, 2009, 28–60.

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