IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v20y2023i1p73-84.html
   My bibliography  Save this article

A Closed-Form EVSI Expression for a Multinomial Data-Generating Process

Author

Listed:
  • Adam Fleischhacker

    (Department of Business Administration, University of Delaware, Newark, Delaware 19716)

  • Pak-Wing Fok

    (Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716)

  • Mokshay Madiman

    (Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716)

  • Nan Wu

    (Institute for Financial Services Analytics, University of Delaware, Newark, Delaware 19716)

Abstract

This paper derives analytic expressions for the expected value of sample information (EVSI), the expected value of distribution information, and the optimal sample size when data consists of independent draws from a bounded sequence of integers. Because of the challenges of creating tractable EVSI expressions, most existing work valuing data does so in one of three ways: (1) analytically through closed-form expressions on the upper bound of the value of data, (2) calculating the expected value of data using numerical comparisons of decisions made using simulated data to optimal decisions for which the underlying data distribution is known, or (3) using variance reduction as proxy for the uncertainty reduction that accompanies more data. For the very flexible case of modeling integer-valued observations using a multinomial data-generating process with Dirichlet prior, this paper develops expressions that (1) generalize existing beta-binomial computations, (2) do not require prior knowledge of some underlying “true” distribution, and (3) can be computed prior to the collection of any sample data.

Suggested Citation

  • Adam Fleischhacker & Pak-Wing Fok & Mokshay Madiman & Nan Wu, 2023. "A Closed-Form EVSI Expression for a Multinomial Data-Generating Process," Decision Analysis, INFORMS, vol. 20(1), pages 73-84, March.
    • Handle: RePEc:inm:ordeca:v:20:y:2023:i:1:p:73-84
    DOI: 10.1287/deca.2022.0462
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.2022.0462
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.2022.0462?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Li Chen & Erica L. Plambeck, 2008. "Dynamic Inventory Management with Learning About the Demand Distribution and Substitution Probability," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 236-256, May.
    2. Mark Strong & Jeremy E. Oakley & Alan Brennan & Penny Breeze, 2015. "Estimating the Expected Value of Sample Information Using the Probabilistic Sensitivity Analysis Sample," Medical Decision Making, , vol. 35(5), pages 570-583, July.
    3. Ronald W. Hilton, 1981. "The Determinants of Information Value: Synthesizing Some General Results," Management Science, INFORMS, vol. 27(1), pages 57-64, January.
    4. Hawre Jalal & Fernando Alarid-Escudero, 2018. "A Gaussian Approximation Approach for Value of Information Analysis," Medical Decision Making, , vol. 38(2), pages 174-188, February.
    5. Marshall Fisher & Kumar Rajaram & Ananth Raman, 2001. "Optimizing Inventory Replenishment of Retail Fashion Products," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 230-241, November.
    6. Gary D. Eppen & Ananth. V. Iyer, 1997. "Improved Fashion Buying with Bayesian Updates," Operations Research, INFORMS, vol. 45(6), pages 805-819, December.
    7. Yigal Gerchak & David Mossman, 1992. "On the Effect of Demand Randomness on Inventories and Costs," Operations Research, INFORMS, vol. 40(4), pages 804-807, August.
    8. Satoshi Morita & Peter F. Thall & Peter Müller, 2008. "Determining the Effective Sample Size of a Parametric Prior," Biometrics, The International Biometric Society, vol. 64(2), pages 595-602, June.
    9. Woonghee Tim Huh & Retsef Levi & Paat Rusmevichientong & James B. Orlin, 2011. "Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator," Operations Research, INFORMS, vol. 59(4), pages 929-941, August.
    10. Jinfeng Yue & Bintong Chen & Min-Chiang Wang, 2006. "Expected Value of Distribution Information for the Newsvendor Problem," Operations Research, INFORMS, vol. 54(6), pages 1128-1136, December.
    11. Yelland, Phillip M., 2009. "Bayesian forecasting for low-count time series using state-space models: An empirical evaluation for inventory management," International Journal of Production Economics, Elsevier, vol. 118(1), pages 95-103, March.
    12. Zhiyuan Wang & Zhiqiang (Eric) Zheng & Wei Jiang & Shaojie Tang, 2021. "Blockchain‐Enabled Data Sharing in Supply Chains: Model, Operationalization, and Tutorial," Production and Operations Management, Production and Operations Management Society, vol. 30(7), pages 1965-1985, July.
    13. Retsef Levi & Georgia Perakis & Joline Uichanco, 2015. "The Data-Driven Newsvendor Problem: New Bounds and Insights," Operations Research, INFORMS, vol. 63(6), pages 1294-1306, December.
    14. Christopher Jackson & Anne Presanis & Stefano Conti & Daniela De Angelis, 2019. "Value of Information: Sensitivity Analysis and Research Design in Bayesian Evidence Synthesis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1436-1449, October.
    15. Gregory A. Godfrey & Warren B. Powell, 2001. "An Adaptive, Distribution-Free Algorithm for the Newsvendor Problem with Censored Demands, with Applications to Inventory and Distribution," Management Science, INFORMS, vol. 47(8), pages 1101-1112, August.
    16. Joseph M. Milner & Panos Kouvelis, 2005. "Order Quantity and Timing Flexibility in Supply Chains: The Role of Demand Characteristics," Management Science, INFORMS, vol. 51(6), pages 970-985, June.
    17. A. E. Ades & G. Lu & K. Claxton, 2004. "Expected Value of Sample Information Calculations in Medical Decision Modeling," Medical Decision Making, , vol. 24(2), pages 207-227, March.
    18. Soroush Saghafian & Brian Tomlin, 2016. "The Newsvendor under Demand Ambiguity: Combining Data with Moment and Tail Information," Operations Research, INFORMS, vol. 64(1), pages 167-185, February.
    19. Debarun Bhattacharjya & Jo Eidsvik & Tapan Mukerji, 2013. "The Value of Information in Portfolio Problems with Dependent Projects," Decision Analysis, INFORMS, vol. 10(4), pages 341-351, December.
    20. Retsef Levi & Robin O. Roundy & David B. Shmoys, 2007. "Provably Near-Optimal Sampling-Based Policies for Stochastic Inventory Control Models," Mathematics of Operations Research, INFORMS, vol. 32(4), pages 821-839, November.
    21. Abraham Mehrez, 1985. "Technical Note—The Effect of Risk Aversion on the Expected Value of Perfect Information," Operations Research, INFORMS, vol. 33(2), pages 455-458, April.
    22. Kwak, Jin Kyung & Gavirneni, Srinagesh, 2011. "Retailer policy, uncertainty reduction, and supply chain performance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 271-278, August.
    23. J. Eric Bickel, 2008. "The Relationship Between Perfect and Imperfect Information in a Two-Action Risk-Sensitive Problem," Decision Analysis, INFORMS, vol. 5(3), pages 116-128, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gah-Yi Ban & Jérémie Gallien & Adam J. Mersereau, 2019. "Dynamic Procurement of New Products with Covariate Information: The Residual Tree Method," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 798-815, October.
    2. Cong Shi & Weidong Chen & Izak Duenyas, 2016. "Technical Note—Nonparametric Data-Driven Algorithms for Multiproduct Inventory Systems with Censored Demand," Operations Research, INFORMS, vol. 64(2), pages 362-370, April.
    3. Boxiao Chen & Xiuli Chao & Cong Shi, 2021. "Nonparametric Learning Algorithms for Joint Pricing and Inventory Control with Lost Sales and Censored Demand," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 726-756, May.
    4. Boxiao Chen & Xiuli Chao, 2020. "Dynamic Inventory Control with Stockout Substitution and Demand Learning," Management Science, INFORMS, vol. 66(11), pages 5108-5127, November.
    5. Hao Yuan & Qi Luo & Cong Shi, 2021. "Marrying Stochastic Gradient Descent with Bandits: Learning Algorithms for Inventory Systems with Fixed Costs," Management Science, INFORMS, vol. 67(10), pages 6089-6115, October.
    6. Erkip, Nesim Kohen, 2023. "Can accessing much data reshape the theory? Inventory theory under the challenge of data-driven systems," European Journal of Operational Research, Elsevier, vol. 308(3), pages 949-959.
    7. Gah-Yi Ban, 2020. "Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring," Operations Research, INFORMS, vol. 68(2), pages 309-326, March.
    8. Boxiao Chen & David Simchi-Levi & Yining Wang & Yuan Zhou, 2022. "Dynamic Pricing and Inventory Control with Fixed Ordering Cost and Incomplete Demand Information," Management Science, INFORMS, vol. 68(8), pages 5684-5703, August.
    9. Soroush Saghafian & Brian Tomlin, 2016. "The Newsvendor under Demand Ambiguity: Combining Data with Moment and Tail Information," Operations Research, INFORMS, vol. 64(1), pages 167-185, February.
    10. Woonghee Tim Huh & Paat Rusmevichientong, 2014. "Online Sequential Optimization with Biased Gradients: Theory and Applications to Censored Demand," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 150-159, February.
    11. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    12. Woonghee Tim Huh & Paat Rusmevichientong, 2009. "A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand," Mathematics of Operations Research, INFORMS, vol. 34(1), pages 103-123, February.
    13. Ali E. Abbas & N. Onur Bakır & Georgia-Ann Klutke & Zhengwei Sun, 2013. "Effects of Risk Aversion on the Value of Information in Two-Action Decision Problems," Decision Analysis, INFORMS, vol. 10(3), pages 257-275, September.
    14. Anyan Qi & Hyun-Soo Ahn & Amitabh Sinha, 2017. "Capacity Investment with Demand Learning," Operations Research, INFORMS, vol. 65(1), pages 145-164, February.
    15. Georgia Perakis & Guillaume Roels, 2010. "Robust Controls for Network Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 12(1), pages 56-76, November.
    16. Lin An & Andrew A. Li & Benjamin Moseley & R. Ravi, 2023. "The Nonstationary Newsvendor with (and without) Predictions," Papers 2305.07993, arXiv.org, revised Oct 2023.
    17. Philippe Delquié, 2008. "The Value of Information and Intensity of Preference," Decision Analysis, INFORMS, vol. 5(3), pages 129-139, September.
    18. Rui Wang & Xiao Yan & Chuanjin Zhu, 2023. "Solving a Distribution-Free Multi-Period Newsvendor Problem With Advance Purchase Discount via an Online Ordering Solution," SAGE Open, , vol. 13(2), pages 21582440231, June.
    19. Debarun Bhattacharjya & Léa A. Deleris, 2014. "The Value of Information in Some Variations of the Stopping Problem," Decision Analysis, INFORMS, vol. 11(3), pages 189-203, September.
    20. Jiri Chod & Mihalis G. Markakis & Nikolaos Trichakis, 2021. "On the Learning Benefits of Resource Flexibility," Management Science, INFORMS, vol. 67(10), pages 6513-6528, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ordeca:v:20:y:2023:i:1:p:73-84. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.