IDEAS home Printed from https://ideas.repec.org/a/inm/ormsom/v24y2022i3p1369-1387.html

On a Variation of Two-Part Tariff Pricing of Services: A Data-Driven Approach

Author

Listed:
  • Georgia Perakis

    (MIT Sloan, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Charles Thraves

    (Department of Industrial Engineering, University of Chile, Santiago 8370456, Chile)

Abstract

Problem definition : We present a data-driven pricing problem motivated from our collaboration with a satellite service provider. In particular, we study a variant of the two-part tariff pricing scheme. The firm offers a set of data plans consisting of a bundle of data at a fixed price plus additional data at a variable price. Most literature on two-part tariff problems focuses on models that assume full information. However, little attention has been devoted to this problem from a data-driven perspective without full information. One of the main challenges when working with data comes from missing data. Methodology/results : First, we develop a new method to address the missing data problem, which comes from different sources: (i) the number of unobserved customers, (ii) customers’ willingness to pay (WTP), and (iii) demand from unobserved customers. We introduce an iteration procedure to maximize the likelihood by combining the expectation maximization algorithm with a gradient ascent method. We also formulate the pricing optimization problem as a dynamic program (DP) using a discretized set of prices. From applying Sample Average Approximation, the DP obtains a solution within 3.8% of the optimal solution of the sampled instances, on average, and within 18% with 95% confidence from the optimal solution of the exact problem. By extending the DP formulation, we show that it is better to optimize on prices rather than bundles, obtaining revenues close to optimizing jointly on both. Managerial implications : The sensitivity analysis of the problem parameters is key for decision makers to understand the risks of their pricing decisions. Indeed, assuming a higher variability of customers’ WTP induces higher revenue risks. In addition, revenues are barely (highly) sensitive to the customers’ assumed WTP variability when considering a high (low) number of unobserved customers. Finally, we extend the model to incorporate price-dependent consumption.

Suggested Citation

  • Georgia Perakis & Charles Thraves, 2022. "On a Variation of Two-Part Tariff Pricing of Services: A Data-Driven Approach," Manufacturing & Service Operations Management, INFORMS, vol. 24(3), pages 1369-1387, May.
    • Handle: RePEc:inm:ormsom:v:24:y:2022:i:3:p:1369-1387
    DOI: 10.1287/msom.2021.1069
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/msom.2021.1069
    Download Restriction: no
    File URL: https://libkey.io/10.1287/msom.2021.1069?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. Gustavo Vulcano & Garrett van Ryzin & Richard Ratliff, 2012. "Estimating Primary Demand for Substitutable Products from Sales Transaction Data," Operations Research, INFORMS, vol. 60(2), pages 313-334, April.
    2. Richard Schmalensee, 1981. "Monopolistic Two-Part Pricing Arrangements," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 445-466, Autumn.
    3. Varian, Hal R, 1985. "Price Discrimination and Social Welfare," American Economic Review, American Economic Association, vol. 75(4), pages 870-875, September.
    4. A. Gürhan Kök & Marshall L. Fisher, 2007. "Demand Estimation and Assortment Optimization Under Substitution: Methodology and Application," Operations Research, INFORMS, vol. 55(6), pages 1001-1021, December.
    5. Gregory Dobson & Shlomo Kalish, 1988. "Positioning and Pricing a Product Line," Marketing Science, INFORMS, vol. 7(2), pages 107-125.
    6. Philipp Afèche & Opher Baron & Joseph Milner & Ricky Roet-Green, 2019. "Pricing and Prioritizing Time-Sensitive Customers with Heterogeneous Demand Rates," Operations Research, INFORMS, vol. 67(4), pages 1184-1208, July.
    7. Morvarid Rahmani & Guillaume Roels & Uday S. Karmarkar, 2017. "Collaborative Work Dynamics in Projects with Co‐Production," Production and Operations Management, Production and Operations Management Society, vol. 26(4), pages 686-703, April.
    8. Övünç Yılmaz & Pelin Pekgün & Mark Ferguson, 2017. "Would You Like to Upgrade to a Premium Room? Evaluating the Benefit of Offering Standby Upgrades," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 1-18, February.
    9. Mitchell, Bridger M, 1978. "Optimal Pricing of Local Telephone Service," American Economic Review, American Economic Association, vol. 68(4), pages 517-537, September.
    10. 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.
    11. Walter Y. Oi, 1971. "A Disneyland Dilemma: Two-Part Tariffs for a Mickey Mouse Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 85(1), pages 77-96.
    12. Oliveira, Fernando S. & Ruiz, Carlos & Conejo, Antonio J., 2013. "Contract design and supply chain coordination in the electricity industry," European Journal of Operational Research, Elsevier, vol. 227(3), pages 527-537.
    13. Kamel Jedidi & Z. John Zhang, 2002. "Augmenting Conjoint Analysis to Estimate Consumer Reservation Price," Management Science, INFORMS, vol. 48(10), pages 1350-1368, October.
    14. Yew-Kwang Ng & Mendel Weisser, 1974. "Optimal Pricing with a Budget Constraint—The Case of the Two-part Tariff," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 41(3), pages 337-345.
    15. 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.
    16. Garrett van Ryzin & Gustavo Vulcano, 2015. "A Market Discovery Algorithm to Estimate a General Class of Nonparametric Choice Models," Management Science, INFORMS, vol. 61(2), pages 281-300, February.
    17. Alberini Anna, 1995. "Optimal Designs for Discrete Choice Contingent Valuation Surveys: Single-Bound, Double-Bound, and Bivariate Models," Journal of Environmental Economics and Management, Elsevier, vol. 28(3), pages 287-306, May.
    18. Gadi Fibich & Roy Klein & Oded Koenigsberg & Eitan Muller, 2017. "Optimal Three-Part Tariff Plans," Operations Research, INFORMS, vol. 65(5), pages 1177-1189, October.
    19. Paat Rusmevichientong & Benjamin Van Roy & Peter W. Glynn, 2006. "A Nonparametric Approach to Multiproduct Pricing," Operations Research, INFORMS, vol. 54(1), pages 82-98, February.
    20. Övünç Yılmaz & Pelin Pekgün & Mark Ferguson, 2017. "Would You Like to Upgrade to a Premium Room? Evaluating the Benefit of Offering Standby Upgrades," Manufacturing & Service Operations Management, INFORMS, vol. 19(1), pages 1-18, February.
    21. S. C. Littlechild, 1975. "Common Costs, Fixed Charges, Clubs and Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(1), pages 117-124.
    22. 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.
    23. Jin‐Tan Liu & James K. Hammitt & Jung‐Der Wang & Jin‐Long Liu, 2000. "Mother's willingness to pay for her own and her child's health: a contingent valuation study in Taiwan," Health Economics, John Wiley & Sons, Ltd., vol. 9(4), pages 319-326, June.
    24. R. Canan Savaskan & Shantanu Bhattacharya & Luk N. Van Wassenhove, 2004. "Closed-Loop Supply Chain Models with Product Remanufacturing," Management Science, INFORMS, vol. 50(2), pages 239-252, February.
    25. Gérard P. Cachon & Martin A. Lariviere, 2005. "Supply Chain Coordination with Revenue-Sharing Contracts: Strengths and Limitations," Management Science, INFORMS, vol. 51(1), pages 30-44, January.
    26. Schlereth, Christian & Stepanchuk, Tanja & Skiera, Bernd, 2010. "Optimization and analysis of the profitability of tariff structures with two-part tariffs," European Journal of Operational Research, Elsevier, vol. 206(3), pages 691-701, November.
    27. Andrés Musalem & Marcelo Olivares & Eric T. Bradlow & Christian Terwiesch & Daniel Corsten, 2010. "Structural Estimation of the Effect of Out-of-Stocks," Management Science, INFORMS, vol. 56(7), pages 1180-1197, July.
    28. Martin S. Feldstein, 1972. "Equity and Efficiency in Public Sector Pricing: The Optimal Two-Part Tariff," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 86(2), pages 175-187.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhao, Ting & Chen, Zhi-Long & Liu, Xinbao, 2026. "Equipment leasing supply chain with demand uncertainty," Omega, Elsevier, vol. 138(C).

    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. Boxiao Chen & Xiuli Chao, 2020. "Dynamic Inventory Control with Stockout Substitution and Demand Learning," Management Science, INFORMS, vol. 66(11), pages 5108-5127, November.
    2. Aditya Jain & Nils Rudi & Tong Wang, 2015. "Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need," Operations Research, INFORMS, vol. 63(1), pages 134-150, February.
    3. Garrett van Ryzin & Gustavo Vulcano, 2015. "A Market Discovery Algorithm to Estimate a General Class of Nonparametric Choice Models," Management Science, INFORMS, vol. 61(2), pages 281-300, February.
    4. Winston Chang & Lawrence Southwick, 1987. "On the pricing and benefit structure of a private club or public utility," Public Choice, Springer, vol. 55(3), pages 227-244, October.
    5. Georgia Perakis & Melvyn Sim & Qinshen Tang & Peng Xiong, 2023. "Robust Pricing and Production with Information Partitioning and Adaptation," Management Science, INFORMS, vol. 69(3), pages 1398-1419, March.
    6. Joonkyum Lee & Vishal Gaur & Suresh Muthulingam & Gary F. Swisher, 2016. "Stockout-Based Substitution and Inventory Planning in Textbook Retailing," Manufacturing & Service Operations Management, INFORMS, vol. 18(1), pages 104-121, February.
    7. Roger Sherman & Michael Visscher, 1982. "Rate-of-Return Regulation and Two-Part Tariffs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 97(1), pages 27-42.
    8. Severin Borenstein & Lucas W. Davis, 2012. "The Equity and Efficiency of Two-Part Tariffs in U.S. Natural Gas Markets," Journal of Law and Economics, University of Chicago Press, vol. 55(1), pages 75-128.
    9. Ningyuan Chen & Ming Hu, 2023. "Frontiers in Service Science: Data-Driven Revenue Management: The Interplay of Data, Model, and Decisions," Service Science, INFORMS, vol. 15(2), pages 79-91, June.
    10. Sara Hsu & David Kiefer, 2005. "Perfect Price Discrimination is not So Perfect," Working Paper Series, Department of Economics, University of Utah 2005_04, University of Utah, Department of Economics.
    11. Oliver, Matthew E., 2019. "Pricing flexibility under rate-of-return regulation: Effects on network infrastructure investment," Economic Modelling, Elsevier, vol. 78(C), pages 150-161.
    12. Omar Besbes & Omar Mouchtaki, 2023. "How Big Should Your Data Really Be? Data-Driven Newsvendor: Learning One Sample at a Time," Management Science, INFORMS, vol. 69(10), pages 5848-5865, October.
    13. Boxiao Chen & Cong Shi, 2025. "Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems with Demand Learning," Operations Research, INFORMS, vol. 73(4), pages 1723-1743, July.
    14. Daniel Steeneck & Fredrik Eng-Larsson & Francisco Jauffred, 2022. "Estimating Lost Sales for Substitutable Products with Uncertain On-Shelf Availability," Manufacturing & Service Operations Management, INFORMS, vol. 24(3), pages 1578-1594, May.
    15. De Borger, Bruno, 2001. "Discrete choice models and optimal two-part tariffs in the presence of externalities: optimal taxation of cars," Regional Science and Urban Economics, Elsevier, vol. 31(4), pages 471-504, July.
    16. Kairen Zhang & Xiangyu Gao & Zhanyue Wang & Sean X. Zhou, 2025. "Sampling-Based Approximation for Series Inventory Systems," Management Science, INFORMS, vol. 71(10), pages 8200-8217, October.
    17. Ricard Gil & Evsen Korkmaz & Ozge Sahin, 2020. "Can free-shipping hurt online retailers?," Quantitative Marketing and Economics (QME), Springer, vol. 18(3), pages 305-342, September.
    18. Yi-Chun Akchen & Felipe Caro, 2026. "On Size Substitution and Its Role in Assortment and Inventory Planning," Manufacturing & Service Operations Management, INFORMS, vol. 28(2), pages 624-642, March.
    19. Ricard Gil & Evsen Korkmaz & Ozge Sahin, 0. "Can free-shipping hurt online retailers?," Quantitative Marketing and Economics (QME), Springer, vol. 0, pages 1-38.
    20. Yin, Xiangkang, 2004. "Two-part tariff competition in duopoly," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 799-820, June.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:ormsom:v:24:y:2022:i:3:p:1369-1387. 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.