IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v62y2014i3p512-523.html
   My bibliography  Save this article

Optimal Pricing and Inventory Control Policy with Quantity-Based Price Differentiation

Author

Listed:
  • Ye Lu

    (Department of Management Sciences, College of Business, City University of Hong Kong, Hong Kong)

  • Youhua (Frank) Chen

    (Department of Management Sciences, College of Business, City University of Hong Kong, Hong Kong)

  • Miao Song

    (Department of Industrial and Manufacturing Systems Engineering, The University of Hong Kong, Hong Kong)

  • Xiaoming Yan

    (School of Computer Science, Dongguan University of Technology, Dongguan 523808, Guangdong, China)

Abstract

A firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon. In addition to the regular unit selling price, the firm can utilize quantity discounts to increase sales. We refer to this dual-pricing strategy as quantity-based price differentiation. At the beginning of each period, the firm needs to make three decisions: replenish the inventory, set the unit selling price if the unit sales mode is deployed, and set the quantity-discount price if the quantity-sales mode is deployed (or the combination of the two modes of sales). We identify conditions under which the optimal inventory control policy and selling/pricing strategy is well structured. Remarkably, under a utility-based demand framework, these conditions can be unified by a simple regularity assumption that has long been used in the auction and mechanism design literature. Moreover, sharper structural results are yielded for the optimal selling strategy. We also examine the comparative advantage of quantity-based price differentiation with respect to model parameters. Our numerical study shows that substantial profit improvement can be gained as a result of shifting from uniform pricing to quantity-based pricing, especially when the product has a low unit ordering cost and high utility.

Suggested Citation

  • Ye Lu & Youhua (Frank) Chen & Miao Song & Xiaoming Yan, 2014. "Optimal Pricing and Inventory Control Policy with Quantity-Based Price Differentiation," Operations Research, INFORMS, vol. 62(3), pages 512-523, June.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:3:p:512-523
    DOI: 10.1287/opre.2013.1240
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2013.1240
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2013.1240?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. George E. Monahan & Nicholas C. Petruzzi & Wen Zhao, 2004. "The Dynamic Pricing Problem from a Newsvendor's Perspective," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 73-91, September.
    2. James P. Monahan, 1984. "A Quantity Discount Pricing Model to Increase Vendor Profits," Management Science, INFORMS, vol. 30(6), pages 720-726, June.
    3. Hau L. Lee & Meir J. Rosenblatt, 1986. "A Generalized Quantity Discount Pricing Model to Increase Supplier's Profits," Management Science, INFORMS, vol. 32(9), pages 1177-1185, September.
    4. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    5. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    6. Wedad Elmaghraby & P{i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
    7. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    8. Evan L. Porteus, 1971. "On the Optimality of Generalized (s, S) Policies," Management Science, INFORMS, vol. 17(7), pages 411-426, March.
    9. Qi Feng & Sirong Luo & Dan Zhang, 2014. "Dynamic Inventory–Pricing Control Under Backorder: Demand Estimation and Policy Optimization," Manufacturing & Service Operations Management, INFORMS, vol. 16(1), pages 149-160, February.
    10. Robert J. Dolan, 1987. "Quantity Discounts: Managerial Issues and Research Opportunities," Marketing Science, INFORMS, vol. 6(1), pages 1-22.
    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. Martin A. Lariviere & Evan L. Porteus, 2001. "Selling to the Newsvendor: An Analysis of Price-Only Contracts," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 293-305, May.
    13. Yuyue Song & Saibal Ray & Tamer Boyaci, 2009. "Technical Note---Optimal Dynamic Joint Inventory-Pricing Control for Multiplicative Demand with Fixed Order Costs and Lost Sales," Operations Research, INFORMS, vol. 57(1), pages 245-250, February.
    14. Nihat Altintas & Feryal Erhun & Sridhar Tayur, 2008. "Quantity Discounts Under Demand Uncertainty," Management Science, INFORMS, vol. 54(4), pages 777-792, April.
    15. Woonghee Tim Huh & Ganesh Janakiraman, 2008. "( s, S ) Optimality in Joint Inventory-Pricing Control: An Alternate Approach," Operations Research, INFORMS, vol. 56(3), pages 783-790, June.
    16. repec:inm:ormnsc:v:30:y:1984:i:12:p:1524-1539(2 is not listed on IDEAS
    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. Kyoung-Kuk Kim & Chi-Guhn Lee & Sunggyun Park, 2016. "Dynamic pricing with ‘BOGO’ promotion in revenue management," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5283-5302, September.
    2. Hong, Zhaofu & Li, Mengfan & Han, Xiaoya & He, Xuhuai, 2020. "Innovative green product diffusion through word of mouth," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    3. Ling Zhao & Jun Liu & Minghua Xiong & Anquan Zou, 2022. "Dual-Channel Retailer’s Multi-Period Inventory and Pricing Policy with the Quantity-Sales Mode," Sustainability, MDPI, vol. 14(18), pages 1-18, September.
    4. Jing Chen & Bintong Chen, 2016. "Competing with customer returns policies," International Journal of Production Research, Taylor & Francis Journals, vol. 54(7), pages 2093-2107, April.
    5. Khouja, Moutaz & Li, Yuefeng & Zhou, Jing, 2023. "Nonlinear pricing for yield management and countering strategic consumer behavior," European Journal of Operational Research, Elsevier, vol. 307(1), pages 212-232.
    6. 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.
    7. Zhaofu Hong & Hao Wang & Yeming Gong, 2019. "Green product design considering functional-product reference," Post-Print hal-02312293, HAL.
    8. Han, Xiaoya & Yu, Yugang & Hu, Guiping, 2019. "A dynamic newsvendor problem with goodwill-dependent demands and minimum commitment," Omega, Elsevier, vol. 89(C), pages 242-256.
    9. Yiwei Chen & Cong Shi, 2019. "Joint Pricing and Inventory Management with Strategic Customers," Operations Research, INFORMS, vol. 67(6), pages 1610-1627, November.
    10. Basak Altan & Pelin Atahan, 2019. "Price and Quality Decisions of a Service Provider under Heterogeneous Demand," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 33(2), pages 1-23.
    11. Hong, Zhaofu & Wang, Hao & Gong, Yeming, 2019. "Green product design considering functional-product reference," International Journal of Production Economics, Elsevier, vol. 210(C), pages 155-168.

    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. Qi Feng & Sirong Luo & J. George Shanthikumar, 2020. "Integrating Dynamic Pricing with Inventory Decisions Under Lost Sales," Management Science, INFORMS, vol. 66(5), pages 2232-2247, May.
    2. Sirong Luo & Jianrong Wang, 2017. "A technical note on the dynamic nonstationary inventory-pricing control model with lost sale," International Journal of Production Research, Taylor & Francis Journals, vol. 55(19), pages 5816-5825, October.
    3. Wen Chen & Adam J. Fleischhacker & Michael N. Katehakis, 2015. "Dynamic pricing in a dual‐market environment," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(7), pages 531-549, October.
    4. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    5. Yiwei Chen & Cong Shi, 2019. "Joint Pricing and Inventory Management with Strategic Customers," Operations Research, INFORMS, vol. 67(6), pages 1610-1627, November.
    6. 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.
    7. Wang, Huihui & Yu, Yimin & Zhang, Wei & Hua, Zhongsheng, 2019. "Procurement strategies for lost-sales inventory systems with all-units discounts," European Journal of Operational Research, Elsevier, vol. 272(2), pages 539-548.
    8. Nihat Altintas & Feryal Erhun & Sridhar Tayur, 2008. "Quantity Discounts Under Demand Uncertainty," Management Science, INFORMS, vol. 54(4), pages 777-792, April.
    9. Abhishek Chakraborty, 2021. "A surcharge pricing policy for supply chain coordination under the just-in-time (JIT) environment in the presence of backordering," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1049-1076, December.
    10. Guillermo Gallego & Michael Z. F. Li & Yan Liu, 2020. "Dynamic Nonlinear Pricing of Inventories over Finite Sales Horizons," Operations Research, INFORMS, vol. 68(3), pages 655-670, May.
    11. Hong Chen & Zhan Zhang, 2014. "Technical Note—Joint Inventory and Pricing Control with General Additive Demand," Operations Research, INFORMS, vol. 62(6), pages 1335-1343, December.
    12. 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.
    13. Fernando Bernstein & Yang Li & Kevin Shang, 2016. "A Simple Heuristic for Joint Inventory and Pricing Models with Lead Time and Backorders," Management Science, INFORMS, vol. 62(8), pages 2358-2373, August.
    14. Yongbo Xiao, 2018. "Dynamic pricing and replenishment: Optimality, bounds, and asymptotics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 3-25, February.
    15. Xiong‐zhi Wang & Guo‐qing Wang, 2019. "Integrating dynamic pricing and inventory control for fresh‐agri product under consumer choice," Australian Economic Papers, Wiley Blackwell, vol. 58(1), pages 96-111, March.
    16. Wang, Qinan & Chay, Yiowmin & Wu, Zhang, 2011. "Streamlining inventory flows with time discounts to improve the profits of a decentralized supply chain," International Journal of Production Economics, Elsevier, vol. 132(2), pages 230-239, August.
    17. Krishnan S. Anand & Ravi Aron, 2003. "Group Buying on the Web: A Comparison of Price-Discovery Mechanisms," Management Science, INFORMS, vol. 49(11), pages 1546-1562, November.
    18. M. Güler & Taner Bilgiç & Refik Güllü, 2015. "Joint pricing and inventory control for additive demand models with reference effects," Annals of Operations Research, Springer, vol. 226(1), pages 255-276, March.
    19. Xin Chen & Zhan Pang & Limeng Pan, 2014. "Coordinating Inventory Control and Pricing Strategies for Perishable Products," Operations Research, INFORMS, vol. 62(2), pages 284-300, April.
    20. Xu, Xiaolin & Cai, Xiaoqiang & Chen, Youhua, 2011. "Unimodality of price-setting newsvendor's objective function with multiplicative demand and its applications," International Journal of Production Economics, Elsevier, vol. 133(2), pages 653-661, 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:oropre:v:62:y:2014:i:3:p:512-523. 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.