IDEAS home Printed from https://ideas.repec.org/a/bla/popmgt/v28y2019i4p847-877.html
   My bibliography  Save this article

Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs

Author

Listed:
  • Peng Hu
  • Ye Lu
  • Miao Song

Abstract

This study considers a periodic‐review joint pricing and inventory control problem for a single product, where production incurs a fixed cost plus a convex or concave variable cost. Our objective is to maximize the expected discounted profit over the entire planning horizon. We fully characterize the optimal policy for the single‐period problem. As the optimal policy for the multi‐period problem is too complicated to be implemented in practice, we develop well‐structured heuristic policies, and establish worst‐case performance bounds on the profit gap between the heuristic policies and the optimal policies. Numerical studies show that our heuristic policies perform extremely well. To further reveal the structural properties of the optimal policies, we also introduce two new concepts named κ‐convexity and sym‐κ‐convexity, provide the associated preservation results, and then characterize the optimal policies.

Suggested Citation

  • Peng Hu & Ye Lu & Miao Song, 2019. "Joint Pricing and Inventory Control with Fixed and Convex/Concave Variable Production Costs," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 847-877, April.
    • Handle: RePEc:bla:popmgt:v:28:y:2019:i:4:p:847-877
    DOI: 10.1111/poms.12950
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/poms.12950
    Download Restriction: no
    File URL: https://libkey.io/10.1111/poms.12950?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. Qing Li & Xiaoli Wu & Ki Ling Cheung, 2009. "Optimal Policies for Inventory Systems with Separate Delivery-Request and Order-Quantity Decisions," Operations Research, INFORMS, vol. 57(3), pages 626-636, June.
    2. Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
    3. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    4. Ye Lu & Miao Song & Yi Yang, 2018. "Approximation Approaches for Inventory Systems with General Production/Ordering Cost Structures," Production and Operations Management, Production and Operations Management Society, vol. 27(3), pages 417-432, March.
    5. Ye Lu & Miao Song & Yi Yang, 2016. "Joint Inventory and Pricing Coordination with Incomplete Demand Information," Production and Operations Management, Production and Operations Management Society, vol. 25(4), pages 701-718, April.
    6. Evan L. Porteus, 1971. "On the Optimality of Generalized (s, S) Policies," Management Science, INFORMS, vol. 17(7), pages 411-426, March.
    7. 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.
    8. Yi Yang & Youhua (Frank) Chen & Yun Zhou, 2014. "Coordinating Inventory Control and Pricing Strategies Under Batch Ordering," Operations Research, INFORMS, vol. 62(1), pages 25-37, February.
    9. Mordechai Henig & Yigal Gerchak & Ricardo Ernst & David F. Pyke, 1997. "An Inventory Model Embedded in Designing a Supply Contract," Management Science, INFORMS, vol. 43(2), pages 184-189, February.
    10. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    11. M. Güler & Taner Bi̇lgi̇ç & Refi̇k Güllü, 2014. "Joint inventory and pricing decisions with reference effects," IISE Transactions, Taylor & Francis Journals, vol. 46(4), pages 330-343.
    12. Xiuli Chao & Paul H. Zipkin, 2008. "Optimal Policy for a Periodic-Review Inventory System Under a Supply Capacity Contract," Operations Research, INFORMS, vol. 56(1), pages 59-68, February.
    13. Güler, M. Güray & Bilgiç, Taner & Güllü, Refik, 2014. "Joint inventory and pricing decisions when customers are delay sensitive," International Journal of Production Economics, Elsevier, vol. 157(C), pages 302-312.
    14. Ozgun Caliskan-Demirag & Youhua (Frank) Chen & Yi Yang, 2012. "Ordering Policies for Periodic-Review Inventory Systems with Quantity-Dependent Fixed Costs," Operations Research, INFORMS, vol. 60(4), pages 785-796, August.
    15. Chen Shaoxiang, 2004. "The Infinite Horizon Periodic Review Problem with Setup Costs and Capacity Constraints: A Partial Characterization of the Optimal Policy," Operations Research, INFORMS, vol. 52(3), pages 409-421, June.
    16. Xin Chen & Peng Hu & Stephen Shum & Yuhan Zhang, 2016. "Dynamic Stochastic Inventory Management with Reference Price Effects," Operations Research, INFORMS, vol. 64(6), pages 1529-1536, December.
    17. Qing Li & Shaohui Zheng, 2006. "Joint Inventory Replenishment and Pricing Control for Systems with Uncertain Yield and Demand," Operations Research, INFORMS, vol. 54(4), pages 696-705, August.
    18. L. Joseph Thomas, 1974. "Technical Note—Price and Production Decisions with Random Demand," Operations Research, INFORMS, vol. 22(3), pages 513-518, June.
    19. Ju‐Liang Zhang & Jian Chen & Chung‐Yee Lee, 2012. "Coordinated pricing and inventory control problems with capacity constraints and fixed ordering cost," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 376-383, August.
    20. Evan L. Porteus, 1972. "The Optimality of Generalized (s, S) Policies under Uniform Demand Densities," Management Science, INFORMS, vol. 18(11), pages 644-646, July.
    21. Youhua (Frank) Chen & Saibal Ray & Yuyue Song, 2006. "Optimal pricing and inventory control policy in periodic‐review systems with fixed ordering cost and lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(2), pages 117-136, March.
    22. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    23. Gallego, Guillermo & Scheller-Wolf, Alan, 2000. "Capacitated inventory problems with fixed order costs: Some optimal policy structure," European Journal of Operational Research, Elsevier, vol. 126(3), pages 603-613, 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. 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.
    2. 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.
    3. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    4. Li, Mengmeng & Mizuno, Shinji, 2022. "Dynamic pricing and inventory management of a dual-channel supply chain under different power structures," European Journal of Operational Research, Elsevier, vol. 303(1), pages 273-285.
    5. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    6. Bai, Tian & Wu, Meng & Zhu, Stuart X., 2019. "Pricing and ordering by a loss averse newsvendor with reference dependence," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 343-365.
    7. 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.
    8. 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.
    9. Ling Zhao & Anquan Zou & Pin Zhou, 2023. "E‐retailer's dynamic inventory and pricing policy with price‐protection services," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 44(1), pages 490-501, January.
    10. 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—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.

    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. Ozgun Caliskan-Demirag & Youhua Chen & Yi Yang, 2013. "Production-inventory control policy under warm/cold state-dependent fixed costs and stochastic demand: partial characterization and heuristics," Annals of Operations Research, Springer, vol. 208(1), pages 531-556, September.
    2. Awi Federgruen & Zhe Liu & Lijian Lu, 2020. "Synthesis and Generalization of Structural Results in Inventory Management: A Generalized Convexity Property," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 547-575, May.
    3. Nan Yang & Renyu Zhang, 2022. "Dynamic pricing and inventory management in the presence of online reviews," Production and Operations Management, Production and Operations Management Society, vol. 31(8), pages 3180-3197, August.
    4. Gurkan, M. Edib & Tunc, Huseyin & Tarim, S. Armagan, 2022. "The joint stochastic lot sizing and pricing problem," Omega, Elsevier, vol. 108(C).
    5. Li, Yang & Liu, Feng, 2021. "Joint inventory and pricing control with lagged price responses," International Journal of Production Economics, Elsevier, vol. 241(C).
    6. Nan Yang & Renyu Zhang, 2022. "Comparative Statics Analysis of An Inventory Management Model with Dynamic Pricing, Market Environment Fluctuation, and Delayed Differentiation," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 341-357, January.
    7. 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—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    8. Ozgun Caliskan-Demirag & Youhua (Frank) Chen & Yi Yang, 2012. "Ordering Policies for Periodic-Review Inventory Systems with Quantity-Dependent Fixed Costs," Operations Research, INFORMS, vol. 60(4), pages 785-796, August.
    9. 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.
    10. Xiting Gong & Youhua (Frank) Chen & Quan Yuan, 2022. "Coordinating Inventory and Pricing Decisions Under Total Minimum Commitment Contracts," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 511-528, February.
    11. Li, Mengmeng & Mizuno, Shinji, 2022. "Dynamic pricing and inventory management of a dual-channel supply chain under different power structures," European Journal of Operational Research, Elsevier, vol. 303(1), pages 273-285.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Li‐Ming Chen & Amar Sapra, 2013. "Joint inventory and pricing decisions for perishable products with two‐period lifetime," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(5), pages 343-366, August.
    18. Gan, Xianghua & Sethi, Suresh P. & Xu, Liang, 2019. "Simultaneous Optimization of Contingent and Advance Purchase Orders with Fixed Ordering Costs," Omega, Elsevier, vol. 89(C), pages 227-241.
    19. Saif Benjaafar & David Chen & Yimin Yu, 2018. "Optimal policies for inventory systems with concave ordering costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(4), pages 291-302, June.
    20. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2011. "Average Cost Single-Stage Inventory Models: An Analysis Using a Vanishing Discount Approach," Operations Research, INFORMS, vol. 59(1), pages 143-155, February.

    More about this item

    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:bla:popmgt:v:28:y:2019:i:4:p:847-877. 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: Wiley Content Delivery (email available below). General contact details of provider: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1937-5956 .

    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.