IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v61y2013i5p1166-1173.html
   My bibliography  Save this article

Technical Note---Preservation of Supermodularity in Parametric Optimization Problems with Nonlattice Structures

Author

Listed:
  • Xin Chen

    (Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana--Champaign, Urbana, Illinois 61801)

  • Peng Hu

    (School of Management, Huazhong University of Science and Technology, Wuhan 430074, China)

  • Simai He

    (Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong)

Abstract

This paper establishes a new preservation property of supermodularity in a class of two-dimensional parametric optimization problems, where the constraint sets may not be lattices. This property and its extensions unify several results in the literature and provide powerful tools to analyze a variety of operations models including a two-product coordinated pricing and inventory control problem with cross-price effects that we use as an illustrative example.

Suggested Citation

  • Xin Chen & Peng Hu & Simai He, 2013. "Technical Note---Preservation of Supermodularity in Parametric Optimization Problems with Nonlattice Structures," Operations Research, INFORMS, vol. 61(5), pages 1166-1173, October.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:5:p:1166-1173
    DOI: 10.1287/opre.2013.1203
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.2013.1203
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.2013.1203?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. John K.-H Quah, 2007. "The Comparative Statics of Constrained Optimization Problems," Econometrica, Econometric Society, vol. 75(2), pages 401-431, March.
    2. Oben Ceryan & Ozge Sahin & Izak Duenyas, 2013. "Dynamic Pricing of Substitutable Products in the Presence of Capacity Flexibility," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 86-101, April.
    3. Jian Yang, 2004. "Production Control in the Face of Storable Raw Material, Random Supply, and an Outside Market," Operations Research, INFORMS, vol. 52(2), pages 293-311, April.
    4. Xiting Gong & Xiuli Chao, 2013. "Technical Note---Optimal Control Policy for Capacitated Inventory Systems with Remanufacturing," Operations Research, INFORMS, vol. 61(3), pages 603-611, June.
    5. Paul Zipkin, 2008. "On the Structure of Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 56(4), pages 937-944, August.
    6. Xiuli Chao & Hong Chen & Shaohui Zheng, 2009. "Dynamic Capacity Expansion for a Service Firm with Capacity Deterioration and Supply Uncertainty," Operations Research, INFORMS, vol. 57(1), pages 82-93, February.
    7. Xiuli Chao & Jia Chen & Shouyang Wang, 2008. "Dynamic inventory management with cash flow constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 758-768, December.
    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. Long Gao & Jim (Junmin) Shi & Michael F. Gorman & Ting Luo, 2020. "Business Analytics for Intermodal Capacity Management," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 310-329, March.
    2. Xin Chen & Daniel Zhuoyu Long & Jin Qi, 2021. "Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures," Operations Research, INFORMS, vol. 69(1), pages 1-12, January.
    3. 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.
    4. Xin Chen & Menglong Li, 2021. "Discrete Convex Analysis and Its Applications in Operations: A Survey," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1904-1926, June.

    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. Xin Chen & Daniel Zhuoyu Long & Jin Qi, 2021. "Preservation of Supermodularity in Parametric Optimization: Necessary and Sufficient Conditions on Constraint Structures," Operations Research, INFORMS, vol. 69(1), pages 1-12, January.
    2. Anyan Qi & Hyun-Soo Ahn & Amitabh Sinha, 2017. "Capacity Investment with Demand Learning," Operations Research, INFORMS, vol. 65(1), pages 145-164, February.
    3. Anyan Qi & Hyun-Soo Ahn & Amitabh Sinha, 2017. "Capacity Investment with Demand Learning," Operations Research, INFORMS, vol. 65(1), pages 145-164, February.
    4. Youyi Feng & Jianjun Xu & Shaohui Zheng, 2019. "Technical Note—Dynamic Optimal Policy for an Inventory System of Two Substitutable Products with Positive Replenishment Lead Times," Operations Research, INFORMS, vol. 67(4), pages 1027-1034, July.
    5. Xiting Gong & Xiuli Chao, 2013. "Technical Note---Optimal Control Policy for Capacitated Inventory Systems with Remanufacturing," Operations Research, INFORMS, vol. 61(3), pages 603-611, June.
    6. Saif Benjaafar & David Chen & Rowan Wang, 2017. "Managing Production-Inventory Systems with Scarce Resources," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 216-229, May.
    7. Liping Zhou & Na Geng & Zhibin Jiang & Shan Jiang, 2022. "Integrated Multiresource Capacity Planning and Multitype Patient Scheduling," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 129-149, January.
    8. Zhu, Stuart X., 2013. "Dynamic replenishment, production, and pricing decisions, in the face of supply disruption and random price-sensitive demand," International Journal of Production Economics, Elsevier, vol. 146(2), pages 612-619.
    9. Xiting Gong & Sean X. Zhou, 2013. "Optimal Production Planning with Emissions Trading," Operations Research, INFORMS, vol. 61(4), pages 908-924, August.
    10. Xin Chen & Menglong Li, 2021. "Discrete Convex Analysis and Its Applications in Operations: A Survey," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1904-1926, June.
    11. Tianxiao Chen & Xiting Gong & Qing Li & He Xu, 2021. "Multiseason production planning under export quotas," Naval Research Logistics (NRL), John Wiley & Sons, vol. 68(3), pages 279-294, April.
    12. Qing Li & Peiwen Yu, 2014. "Multimodularity and Its Applications in Three Stochastic Dynamic Inventory Problems," Manufacturing & Service Operations Management, INFORMS, vol. 16(3), pages 455-463, July.
    13. Yiting Xing & Ling Li & Zhuming Bi & Marzena Wilamowska‐Korsak & Li Zhang, 2013. "Operations Research (OR) in Service Industries: A Comprehensive Review," Systems Research and Behavioral Science, Wiley Blackwell, vol. 30(3), pages 300-353, May.
    14. Jiao Wang & Lima Zhao & Arnd Huchzermeier, 2021. "Operations‐Finance Interface in Risk Management: Research Evolution and Opportunities," Production and Operations Management, Production and Operations Management Society, vol. 30(2), pages 355-389, February.
    15. Uttiya Paul & Tarun Sabarwal, 2023. "Directional monotone comparative statics in function spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 153-169, April.
    16. Nikolai Kukushkin, 2015. "The single crossing conditions for incomplete preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 225-251, February.
    17. Barthel, Anne-Christine & Hoffmann, Eric, 2017. "Comparing optimal choices with multi-dimensional action spaces," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 45-50.
    18. Bendre, Abhijit Bhagwan & Nielsen, Lars Relund, 2013. "Inventory control in a lost-sales setting with information about supply lead times," International Journal of Production Economics, Elsevier, vol. 142(2), pages 324-331.
    19. Finn Christensen, 2019. "Comparative statics and heterogeneity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(3), pages 665-702, April.
    20. John Quah, 2016. "Supermodular Correspondences," Economics Series Working Papers 795, University of Oxford, Department of Economics.

    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:61:y:2013:i:5:p:1166-1173. 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.