IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v248y2016i2p634-645.html
   My bibliography  Save this article

A bilevel formulation of the pediatric vaccine pricing problem

Author

Listed:
  • Robbins, Matthew J.
  • Lunday, Brian J.

Abstract

We consider the characterization of optimal pricing strategies for a pediatric vaccine manufacturing firm operating in an oligopolistic market. The pediatric vaccine pricing problem (PVPP) is formulated as a bilevel mathematical program wherein the upper level models a firm that selects profit-maximizing vaccine prices while the lower level models a representative customer’s vaccine purchasing decision to satisfy a given, recommended childhood immunization schedule (RCIS) at overall minimum cost. Complicating features of the bilevel program include the bilinear nature of the upper-level objective function and the binary nature of the lower-level decision variables. We develop and test variants of three heuristics to identify the pricing scheme that will maximize a manufacturer’s profit: a Latin Hypercube Sampling (LHS) of the upper-level feasible region, an LHS enhanced by a Nelder–Meade search from each price point, and an LHS enhanced by a custom implementation of the Cyclic Coordinate Method from each price point. The practicality of the PVPP is demonstrated via application to the analysis of the 2014 United States pediatric vaccine private sector market. Testing results indicate that a robust sampling method combined with local search is the superlative solution method among those examined and, in the current market, that a manufacturer acting unilaterally has the potential to increase profit per child completing the RCIS by 35 percent (from 231.84 to 312.55 dollars) for GlaxoSmithKline, 47 percent (from 63.96 to 93.70 dollars) for Merck, and 866 percent (from 25.99 to 251.04 dollars) for Sanofi Pasteur over that obtained via current pricing mechanisms.

Suggested Citation

  • Robbins, Matthew J. & Lunday, Brian J., 2016. "A bilevel formulation of the pediatric vaccine pricing problem," European Journal of Operational Research, Elsevier, vol. 248(2), pages 634-645.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:2:p:634-645
    DOI: 10.1016/j.ejor.2015.06.075
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715006293
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.06.075?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Matthew Robbins & Sheldon Jacobson & Edward Sewell, 2010. "Pricing strategies for combination pediatric vaccines and their impact on revenue: Pediarix® or Pentacel®?," Health Care Management Science, Springer, vol. 13(1), pages 54-64, March.
    2. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(2), pages 427-429, April.
    3. ,, 2004. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 20(1), pages 223-229, February.
    4. Adida, Elodie & Dey, Debabrata & Mamani, Hamed, 2013. "Operational issues and network effects in vaccine markets," European Journal of Operational Research, Elsevier, vol. 231(2), pages 414-427.
    5. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    6. Shane N. Hall & Sheldon H. Jacobson & Edward C. Sewell, 2008. "An Analysis of Pediatric Vaccine Formulary Selection Problems," Operations Research, INFORMS, vol. 56(6), pages 1348-1365, December.
    7. Zeynep Gümüş & Christodoulos Floudas, 2005. "Global optimization of mixed-integer bilevel programming problems," Computational Management Science, Springer, vol. 2(3), pages 181-212, July.
    8. Edward Sewell & Sheldon Jacobson, 2003. "Using an Integer Programming Model to Determine the Price of Combination Vaccines for Childhood Immunization," Annals of Operations Research, Springer, vol. 119(1), pages 261-284, March.
    9. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    10. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2000. "A Bilevel Model and Solution Algorithm for a Freight Tariff-Setting Problem," Transportation Science, INFORMS, vol. 34(3), pages 289-302, August.
    11. Matthew J. Robbins & Sheldon H. Jacobson & Uday V. Shanbhag & Banafsheh Behzad, 2014. "The Weighted Set Covering Game: A Vaccine Pricing Model for Pediatric Immunization," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 183-198, February.
    12. Robbins, Matthew J. & Jacobson, Sheldon H., 2011. "Pediatric vaccine procurement policy: The monopsonist's problem," Omega, Elsevier, vol. 39(6), pages 589-597, December.
    13. Banafsheh Behzad & Sheldon H. Jacobson & Matthew J. Robbins, 2015. "A symmetric capacity-constrained differentiated oligopoly model for the United States pediatric vaccine market with linear demand," IISE Transactions, Taylor & Francis Journals, vol. 47(11), pages 1252-1266, November.
    14. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2001. "A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network," Transportation Science, INFORMS, vol. 35(4), pages 345-358, November.
    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. Laura Calvet & Rocio de la Torre & Anita Goyal & Mage Marmol & Angel A. Juan, 2020. "Modern Optimization and Simulation Methods in Managerial and Business Economics: A Review," Administrative Sciences, MDPI, vol. 10(3), pages 1-23, July.
    2. Acuna, Jorge A. & Zayas-Castro, Jose L. & Feijoo, Felipe, 2022. "A bilevel Nash-in-Nash model for hospital mergers: A key to affordable care," Socio-Economic Planning Sciences, Elsevier, vol. 83(C).
    3. Çalcı, Baturay & Leibowicz, Benjamin D. & Bard, Jonathan F. & Jayadev, Gopika G., 2024. "A bilevel approach to multi-period natural gas pricing and investment in gas-consuming infrastructure," Energy, Elsevier, vol. 303(C).
    4. Lunday, Brian J. & Robbins, Matthew J., 2019. "Collaboratively-developed vaccine pricing and stable profit sharing mechanisms," Omega, Elsevier, vol. 84(C), pages 102-113.
    5. Muckstadt, John A. & Klein, Michael G. & Jackson, Peter L. & Gougelet, Robert M. & Hupert, Nathaniel, 2023. "Efficient and effective large-scale vaccine distribution," International Journal of Production Economics, Elsevier, vol. 262(C).
    6. Duijzer, Lotty Evertje & van Jaarsveld, Willem & Dekker, Rommert, 2018. "Literature review: The vaccine supply chain," European Journal of Operational Research, Elsevier, vol. 268(1), pages 174-192.
    7. Wang, Fan & Xu, Danni & Zhuo, Xiaopo & Zhang, Chao & Liu, Yaoqi, 2022. "Improving consumer welfare in vaccine market: Pricing, government subsidies and consumer awareness," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(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. Lunday, Brian J. & Robbins, Matthew J., 2019. "Collaboratively-developed vaccine pricing and stable profit sharing mechanisms," Omega, Elsevier, vol. 84(C), pages 102-113.
    2. Matthew J. Robbins & Sheldon H. Jacobson & Uday V. Shanbhag & Banafsheh Behzad, 2014. "The Weighted Set Covering Game: A Vaccine Pricing Model for Pediatric Immunization," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 183-198, February.
    3. Robbins, Matthew J. & Jacobson, Sheldon H., 2011. "Pediatric vaccine procurement policy: The monopsonist's problem," Omega, Elsevier, vol. 39(6), pages 589-597, December.
    4. Duijzer, Lotty Evertje & van Jaarsveld, Willem & Dekker, Rommert, 2018. "Literature review: The vaccine supply chain," European Journal of Operational Research, Elsevier, vol. 268(1), pages 174-192.
    5. Bo Zeng, 2020. "A Practical Scheme to Compute the Pessimistic Bilevel Optimization Problem," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1128-1142, October.
    6. Wang, Guangmin & Gao, Ziyou & Xu, Meng, 2019. "Integrating link-based discrete credit charging scheme into discrete network design problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 176-187.
    7. M. Lignola & Jacqueline Morgan, 2012. "Approximate values for mathematical programs with variational inequality constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 485-503, October.
    8. Xu, Danni & Wang, Fan & Zhuo, Xiaopo & Liu, Yaoqi, 2024. "The performance of government subsidy schemes in a competitive vaccine market considering consumers' free-riding behavior," International Journal of Production Economics, Elsevier, vol. 268(C).
    9. Martine Labbé & Alessia Violin, 2016. "Bilevel programming and price setting problems," Annals of Operations Research, Springer, vol. 240(1), pages 141-169, May.
    10. Agnieszka Kurdyś-Kujawska & Agnieszka Sompolska-Rzechuła & Joanna Pawłowska-Tyszko & Michał Soliwoda, 2021. "Crop Insurance, Land Productivity and the Environment: A Way forward to a Better Understanding," Agriculture, MDPI, vol. 11(11), pages 1-17, November.
    11. Wenfeng Chi & Yuanyuan Zhao & Wenhui Kuang & Tao Pan & Tu Ba & Jinshen Zhao & Liang Jin & Sisi Wang, 2021. "Impact of Cropland Evolution on Soil Wind Erosion in Inner Mongolia of China," Land, MDPI, vol. 10(6), pages 1-16, June.
    12. Nick Middleton & Utchang Kang, 2017. "Sand and Dust Storms: Impact Mitigation," Sustainability, MDPI, vol. 9(6), pages 1-22, June.
    13. Tarantino, Emanuele & Pavanini, Nicola & Mayordomo, Sergio, 2020. "The Impact of Alternative Forms of Bank Consolidation on Credit Supply and Financial Stability," CEPR Discussion Papers 15069, C.E.P.R. Discussion Papers.
    14. Misbah Haque & Imran Ali, 2016. "Uncertain Environment and Organizational Performance: The Mediating Role of Organizational Innovation," Asian Social Science, Canadian Center of Science and Education, vol. 12(9), pages 124-124, September.
    15. repec:spo:wpmain:info:hdl:2441/2082 is not listed on IDEAS
    16. , & ,, 2015. "Strategy-proofness and efficiency with non-quasi-linear preferences: a characterization of minimum price Walrasian rule," Theoretical Economics, Econometric Society, vol. 10(2), May.
    17. Jesus M. Carro & Alejandra Traferri, 2014. "State Dependence And Heterogeneity In Health Using A Bias‐Corrected Fixed‐Effects Estimator," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(2), pages 181-207, March.
    18. Nobuyoshi Yamori & Ayami Kobayashi, 2007. "Wealth Effect Of Public Fund Injections To Ailing Banks: Do Deferred Tax Assets And Auditing Firms Matter?," The Japanese Economic Review, Japanese Economic Association, vol. 58(4), pages 466-483, December.
    19. Vladimir Krivtsov & Brian J. D’Arcy & Alejandro Escribano Sevilla & Scott Arthur & Chris Semple, 2021. "Mitigating Polluted Runoff from Industrial Estates by SUDS Retrofits: Case Studies of Problems and Solutions Co-Designed with a Participatory Approach," Sustainability, MDPI, vol. 13(22), pages 1-24, November.
    20. Werner, Katharina & Graf Lambsdorff, Johann, 2016. "Emotional numbing and lessons learned after a violent conflict - Experimental evidence from Ambon, Indonesia," Passauer Diskussionspapiere, Volkswirtschaftliche Reihe V-74-16, University of Passau, Faculty of Business and Economics.
    21. Wong, Patricia J.Y., 2015. "Eigenvalues of a general class of boundary value problem with derivative-dependent nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 908-930.

    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:eee:ejores:v:248:y:2016:i:2:p:634-645. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.