IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v60y2014i7p1792-1811.html
   My bibliography  Save this article

Optimal Multiperiod Pricing with Service Guarantees

Author

Listed:
  • Christian Borgs

    (Microsoft Research, New England Lab, Cambridge, Massachusetts 02142)

  • Ozan Candogan

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Jennifer Chayes

    (Microsoft Research, New England Lab, Cambridge, Massachusetts 02142)

  • Ilan Lobel

    (Stern School of Business, New York University, New York, New York 10012)

  • Hamid Nazerzadeh

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

Abstract

We study the multiperiod pricing problem of a service firm with capacity levels that vary over time. Customers are heterogeneous in their arrival and departure periods as well as valuations, and are fully strategic with respect to their purchasing decisions. The firm's problem is to set a sequence of prices that maximizes its revenue while guaranteeing service to all paying customers. We provide a dynamic programming based algorithm that computes the optimal sequence of prices for this problem in polynomial time. We show that due to the presence of strategic customers, available service capacity at a time period may bind the price offered at another time period. This phenomenon leads the firm to utilize the same price in multiple periods, in effect limiting the number of different prices that the service firm utilizes in optimal price policies. Also, when customers become more strategic (patient for service), the firm offers higher prices. This may lead to the underutilization of capacity, lower revenues, and reduced customer welfare. We observe that the firm can combat this problem if it has an ability, beyond posted prices, to direct customers to different service periods. This paper was accepted by Dimitris Bertsimas, optimization.

Suggested Citation

  • Christian Borgs & Ozan Candogan & Jennifer Chayes & Ilan Lobel & Hamid Nazerzadeh, 2014. "Optimal Multiperiod Pricing with Service Guarantees," Management Science, INFORMS, vol. 60(7), pages 1792-1811, July.
    • Handle: RePEc:inm:ormnsc:v:60:y:2014:i:7:p:1792-1811
    DOI: 10.1287/mnsc.2013.1839
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.2013.1839
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.2013.1839?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. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    2. Youyi Feng & Guillermo Gallego, 1995. "Optimal Starting Times for End-of-Season Sales and Optimal Stopping Times for Promotional Fares," Management Science, INFORMS, vol. 41(8), pages 1371-1391, August.
    3. Qian Liu & Garrett J. van Ryzin, 2008. "Strategic Capacity Rationing to Induce Early Purchases," Management Science, INFORMS, vol. 54(6), pages 1115-1131, June.
    4. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
    5. Xuanming Su, 2007. "Intertemporal Pricing with Strategic Customer Behavior," Management Science, INFORMS, vol. 53(5), pages 726-741, May.
    6. Dimitris Bertsimas & Aurélie Thiele, 2006. "A Robust Optimization Approach to Inventory Theory," Operations Research, INFORMS, vol. 54(1), pages 150-168, February.
    7. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
    8. Kalyan Talluri & Garrett van Ryzin, 2004. "Revenue Management Under a General Discrete Choice Model of Consumer Behavior," Management Science, INFORMS, vol. 50(1), pages 15-33, January.
    9. Dasu, Sriram & Tong, Chunyang, 2010. "Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes," European Journal of Operational Research, Elsevier, vol. 204(3), pages 662-671, August.
    10. Wang, Ruqu, 1993. "Auctions versus Posted-Price Selling," American Economic Review, American Economic Association, vol. 83(4), pages 838-851, September.
    11. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
    12. Yossi Aviv & Yuri Levin & Mikhail Nediak, 2009. "Counteracting Strategic Consumer Behavior in Dynamic Pricing Systems," International Series in Operations Research & Management Science, in: Christopher S. Tang & Serguei Netessine (ed.), Consumer-Driven Demand and Operations Management Models, edition 1, chapter 0, pages 323-352, Springer.
    13. David Besanko & Wayne L. Winston, 1990. "Optimal Price Skimming by a Monopolist Facing Rational Consumers," Management Science, INFORMS, vol. 36(5), pages 555-567, May.
    14. Yossi Aviv & Amit Pazgal, 2008. "Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 339-359, December.
    15. Wedad Elmaghraby & Altan Gülcü & P{i}nar Keskinocak, 2008. "Designing Optimal Preannounced Markdowns in the Presence of Rational Customers with Multiunit Demands," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 126-148, June.
    16. Nancy L. Stokey, 1981. "Rational Expectations and Durable Goods Pricing," Bell Journal of Economics, The RAND Corporation, vol. 12(1), pages 112-128, Spring.
    17. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
    18. Lazear, Edward P, 1986. "Retail Pricing and Clearance Sales," American Economic Review, American Economic Association, vol. 76(1), pages 14-32, March.
    19. Xuanming Su & Fuqiang Zhang, 2009. "On the Value of Commitment and Availability Guarantees When Selling to Strategic Consumers," Management Science, INFORMS, vol. 55(5), pages 713-726, May.
    20. Coase, Ronald H, 1972. "Durability and Monopoly," Journal of Law and Economics, University of Chicago Press, vol. 15(1), pages 143-149, April.
    21. Hyun-soo Ahn & Mehmet Gümüş & Philip Kaminsky, 2007. "Pricing and Manufacturing Decisions When Demand Is a Function of Prices in Multiple Periods," Operations Research, INFORMS, vol. 55(6), pages 1039-1057, December.
    22. Mallesh M. Pai & Rakesh Vohra, 2013. "Optimal Dynamic Auctions and Simple Index Rules," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 682-697, November.
    23. Nancy L. Stokey, 1979. "Intertemporal Price Discrimination," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 93(3), pages 355-371.
    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. Lin, Xuxun & Wang, Haiyan, 2022. "Dynamic pricing for online information services considering service duration and quality level," Omega, Elsevier, vol. 109(C).
    2. Andre P. Calmon & Florin D. Ciocan & Gonzalo Romero, 2021. "Revenue Management with Repeated Customer Interactions," Management Science, INFORMS, vol. 67(5), pages 2944-2963, May.
    3. Omar Besbes & Ilan Lobel, 2015. "Intertemporal Price Discrimination: Structure and Computation of Optimal Policies," Management Science, INFORMS, vol. 61(1), pages 92-110, January.
    4. Jiang, Yuanchun & Liu, Yezheng & Shang, Jennifer & Yildirim, Pinar & Zhang, Qingfu, 2018. "Optimizing online recurring promotions for dual-channel retailers: Segmented markets with multiple objectives," European Journal of Operational Research, Elsevier, vol. 267(2), pages 612-627.
    5. Negin Golrezaei & Hamid Nazerzadeh & Ramandeep Randhawa, 2020. "Dynamic Pricing for Heterogeneous Time-Sensitive Customers," Manufacturing & Service Operations Management, INFORMS, vol. 22(3), pages 562-581, May.
    6. Yanzhe (Murray) Lei & Stefanus Jasin, 2020. "Real-Time Dynamic Pricing for Revenue Management with Reusable Resources, Advance Reservation, and Deterministic Service Time Requirements," Operations Research, INFORMS, vol. 68(3), pages 676-685, May.
    7. Yiwei Chen & Vivek F. Farias, 2018. "Robust Dynamic Pricing with Strategic Customers," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1119-1142, November.
    8. Zubair Khalid & Ghulam Abbas & Muhammad Awais & Thamer Alquthami & Muhammad Babar Rasheed, 2020. "A Novel Load Scheduling Mechanism Using Artificial Neural Network Based Customer Profiles in Smart Grid," Energies, MDPI, vol. 13(5), pages 1-23, February.
    9. Yuan Deng & Jieming Mao & Balasubramanian Sivan & Kangning Wang, 2021. "Optimal Pricing Schemes for an Impatient Buyer," Papers 2106.02149, arXiv.org, revised Feb 2023.
    10. Yiwei Chen & Vivek F. Farias & Nikolaos Trichakis, 2019. "On the Efficacy of Static Prices for Revenue Management in the Face of Strategic Customers," Management Science, INFORMS, vol. 65(12), pages 5535-5555, December.
    11. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    12. Ilan Lobel & Jigar Patel & Gustavo Vulcano & Jiawei Zhang, 2016. "Optimizing Product Launches in the Presence of Strategic Consumers," Management Science, INFORMS, vol. 62(6), pages 1778-1799, June.
    13. Vibhanshu Abhishek & Mustafa Dogan & Alexandre Jacquillat, 2021. "Strategic Timing and Dynamic Pricing for Online Resource Allocation," Management Science, INFORMS, vol. 67(8), pages 4880-4907, August.
    14. Hossein Jahandideh & Julie Ward Drew & Filippo Balestrieri & Kevin McCardle, 2020. "Individualized Pricing for a Cloud Provider Hosting Interactive Applications," Service Science, INFORMS, vol. 12(4), pages 130-147, December.
    15. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    16. Egan, Malcolm & Jakob, Michal, 2016. "Market mechanism design for profitable on-demand transport services," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 178-195.
    17. Yiwei Chen & Cong Shi, 2019. "Joint Pricing and Inventory Management with Strategic Customers," Operations Research, INFORMS, vol. 67(6), pages 1610-1627, November.
    18. Alex Gershkov & Benny Moldovanu & Philipp Strack, 2018. "Revenue-Maximizing Mechanisms with Strategic Customers and Unknown, Markovian Demand," Management Science, INFORMS, vol. 64(5), pages 2031-2046, May.
    19. Yiwei Chen & Ming Hu, 2020. "Pricing and Matching with Forward-Looking Buyers and Sellers," Manufacturing & Service Operations Management, INFORMS, vol. 22(4), pages 717-734, July.

    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. Negin Golrezaei & Hamid Nazerzadeh & Ramandeep Randhawa, 2020. "Dynamic Pricing for Heterogeneous Time-Sensitive Customers," Manufacturing & Service Operations Management, INFORMS, vol. 22(3), pages 562-581, May.
    2. Ken Moon & Kostas Bimpikis & Haim Mendelson, 2018. "Randomized Markdowns and Online Monitoring," Management Science, INFORMS, vol. 64(3), pages 1271-1290, March.
    3. Xuanming Su, 2007. "Intertemporal Pricing with Strategic Customer Behavior," Management Science, INFORMS, vol. 53(5), pages 726-741, May.
    4. Adam J. Mersereau & Dan Zhang, 2012. "Markdown Pricing with Unknown Fraction of Strategic Customers," Manufacturing & Service Operations Management, INFORMS, vol. 14(3), pages 355-370, July.
    5. Mantin, Benny & Gillen, David, 2011. "The hidden information content of price movements," European Journal of Operational Research, Elsevier, vol. 211(2), pages 385-393, June.
    6. Dasu, Sriram & Tong, Chunyang, 2010. "Dynamic pricing when consumers are strategic: Analysis of posted and contingent pricing schemes," European Journal of Operational Research, Elsevier, vol. 204(3), pages 662-671, August.
    7. Dror Hermel & Benny Mantin, 2018. "Selling to strategic consumers: on the benefits of consumers’ valuation uncertainty and abundant inventory," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 17(3), pages 146-165, June.
    8. Vincent Mak & Amnon Rapoport & Eyran J. Gisches & Jiaojie Han, 2014. "Purchasing Scarce Products Under Dynamic Pricing: An Experimental Investigation," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 425-438, July.
    9. Yossi Aviv & Mike Mingcheng Wei & Fuqiang Zhang, 2019. "Responsive Pricing of Fashion Products: The Effects of Demand Learning and Strategic Consumer Behavior," Management Science, INFORMS, vol. 65(7), pages 2982-3000, July.
    10. Kuo, Chia-Wei & Huang, Kwei-Long, 2012. "Dynamic pricing of limited inventories for multi-generation products," European Journal of Operational Research, Elsevier, vol. 217(2), pages 394-403.
    11. Seungjin Whang, 2015. "Demand Uncertainty and the Bayesian Effect in Markdown Pricing with Strategic Customers," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 66-77, January.
    12. Wu, Meng & Ran, Yun & Zhu, Stuart X., 2022. "Optimal pricing strategy: How to sell to strategic consumers?," International Journal of Production Economics, Elsevier, vol. 244(C).
    13. Dror Hermel & Benny Mantin & Yossi Aviv, 2022. "Can coupons counteract strategic consumer behavior?," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 21(3), pages 262-273, June.
    14. Mustafa O. Kabul & Ali K. Parlaktürk, 2019. "The Value of Commitments When Selling to Strategic Consumers: A Supply Chain Perspective," Management Science, INFORMS, vol. 65(10), pages 4754-4770, October.
    15. Namin, Aidin & Soysal, Gonca P. & Ratchford, Brian T., 2022. "Alleviating demand uncertainty for seasonal goods: An analysis of attribute-based markdown policy for fashion retailers," Journal of Business Research, Elsevier, vol. 145(C), pages 671-681.
    16. Wedad Elmaghraby & Altan Gülcü & P{i}nar Keskinocak, 2008. "Designing Optimal Preannounced Markdowns in the Presence of Rational Customers with Multiunit Demands," Manufacturing & Service Operations Management, INFORMS, vol. 10(1), pages 126-148, June.
    17. Yanan Song & Xiaobo Zhao, 2017. "A newsvendor problem with boundedly rational strategic customers," International Journal of Production Research, Taylor & Francis Journals, vol. 55(1), pages 228-243, January.
    18. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    19. Song, Yanan & Zhao, Xiaobo, 2016. "Strategic customer behavior facing possible stockout: An experimental study," International Journal of Production Economics, Elsevier, vol. 180(C), pages 57-67.
    20. Vibhanshu Abhishek & Mustafa Dogan & Alexandre Jacquillat, 2021. "Strategic Timing and Dynamic Pricing for Online Resource Allocation," Management Science, INFORMS, vol. 67(8), pages 4880-4907, August.

    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:ormnsc:v:60:y:2014:i:7:p:1792-1811. 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.