IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v232y2014i2p393-404.html
   My bibliography  Save this article

Cooperative game analysis of retail space-exchange problems

Author

Listed:
  • Leng, Mingming
  • Parlar, Mahmut
  • Zhang, Dengfeng

Abstract

We analyze retail space-exchange problems where two or more retailers exchange their excess retail spaces to improve the utilization of their space resource. We first investigate the two-retailer space exchange problem. In order to entice both retailers with different bargaining powers to exchange their spaces, we use the generalized Nash bargaining scheme to allocate the total profit surplus between the two retailers. Next, we consider the space-exchange problem involving three or more retailers, and construct a cooperative game in characteristic function form. We show that the game is essential and superadditive, and also prove that the core is non-empty. Moreover, in order to find a unique allocation scheme that ensures the stability of the grand coalition, we propose a new approach to compute a weighted Shapley value that satisfies the core conditions and also reflects retailers’ bargaining powers. Our analysis indicates that the space exchange by more retailers can result in a higher system-wide profit surplus and thus a higher allocation to each retailer under a fair scheme.

Suggested Citation

  • Leng, Mingming & Parlar, Mahmut & Zhang, Dengfeng, 2014. "Cooperative game analysis of retail space-exchange problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 393-404.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:2:p:393-404
    DOI: 10.1016/j.ejor.2013.07.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713005948
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.07.013?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. Brueckner, Jan K, 1993. "Inter-store Externalities and Space Allocation in Shopping Centers," The Journal of Real Estate Finance and Economics, Springer, vol. 7(1), pages 5-16, July.
    2. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    3. Mahesh Nagarajan & Yehuda Bassok, 2008. "A Bargaining Framework in Supply Chains: The Assembly Problem," Management Science, INFORMS, vol. 54(8), pages 1482-1496, August.
    4. Lingxiu Dong & Panos Kouvelis & Zhongjun Tian, 2009. "Dynamic Pricing and Inventory Control of Substitute Products," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 317-339, December.
    5. Gérard P. Cachon & A. Gürhan Kök, 2007. "Category Management and Coordination in Retail Assortment Planning in the Presence of Basket Shopping Consumers," Management Science, INFORMS, vol. 53(6), pages 934-951, June.
    6. Hariga, Moncer A. & Al-Ahmari, Abdulrahman & Mohamed, Abdel-Rahman A., 2007. "A joint optimisation model for inventory replenishment, product assortment, shelf space and display area allocation decisions," European Journal of Operational Research, Elsevier, vol. 181(1), pages 239-251, August.
    7. Hansen, Pierre & Heinsbroek, Hans, 1979. "Product selection and space allocation in supermarkets," European Journal of Operational Research, Elsevier, vol. 3(6), pages 474-484, November.
    8. Irion, Jens & Lu, Jye-Chyi & Al-Khayyal, Faiz & Tsao, Yu-Chung, 2012. "A piecewise linearization framework for retail shelf space management models," European Journal of Operational Research, Elsevier, vol. 222(1), pages 122-136.
    9. Andrew Lim & Brian Rodrigues & Xingwen Zhang, 2004. "Metaheuristics with Local Search Techniques for Retail Shelf-Space Optimization," Management Science, INFORMS, vol. 50(1), pages 117-131, January.
    10. Yuxin Chen & James D. Hess & Ronald T. Wilcox & Z. John Zhang, 1999. "Accounting Profits Versus Marketing Profits: A Relevant Metric for Category Management," Marketing Science, INFORMS, vol. 18(3), pages 208-229.
    11. Evan E. Anderson & Henry N. Amato, 1974. "A Mathematical Model for Simultaneously Determining the Optimal Brand-Collection and Display-Area Allocation," Operations Research, INFORMS, vol. 22(1), pages 13-21, February.
    12. Marcel Corstjens & Peter Doyle, 1981. "A Model for Optimizing Retail Space Allocations," Management Science, INFORMS, vol. 27(7), pages 822-833, July.
    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. Masoud Rabbani & Navid Salmanzadeh-Meydani & Amir Farshbaf-Geranmayeh & Vahed Fadakar-Gabalou, 2018. "Profit maximizing through 3D shelf space allocation of 2D display orientation items with variable heights of the shelves," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 337-360, June.
    2. Zheng, Xiao-Xue & Li, Deng-Feng & Liu, Zhi & Jia, Fu & Lev, Benjamin, 2021. "Willingness-to-cede behaviour in sustainable supply chain coordination," International Journal of Production Economics, Elsevier, vol. 240(C).
    3. Erick González & Rafael Alejandro Espín & Eduardo Fernández, 2016. "Negotiation Based on Fuzzy Logic and Knowledge Engineering: Some Case Studies," Group Decision and Negotiation, Springer, vol. 25(2), pages 373-397, March.
    4. Liu, Zhi & Zheng, Xiao-Xue & Li, Deng-Feng & Liao, Chen-Nan & Sheu, Jiuh-Biing, 2021. "A novel cooperative game-based method to coordinate a sustainable supply chain under psychological uncertainty in fairness concerns," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 147(C).
    5. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(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. Bianchi-Aguiar, Teresa & Hübner, Alexander & Carravilla, Maria Antónia & Oliveira, José Fernando, 2021. "Retail shelf space planning problems: A comprehensive review and classification framework," European Journal of Operational Research, Elsevier, vol. 289(1), pages 1-16.
    2. Flamand, Tulay & Ghoniem, Ahmed & Haouari, Mohamed & Maddah, Bacel, 2018. "Integrated assortment planning and store-wide shelf space allocation: An optimization-based approach," Omega, Elsevier, vol. 81(C), pages 134-149.
    3. Hübner, Alexander & Schaal, Kai, 2017. "A shelf-space optimization model when demand is stochastic and space-elastic," Omega, Elsevier, vol. 68(C), pages 139-154.
    4. Kim, Gwang & Moon, Ilkyeong, 2021. "Integrated planning for product selection, shelf-space allocation, and replenishment decision with elasticity and positioning effects," Journal of Retailing and Consumer Services, Elsevier, vol. 58(C).
    5. Irion, Jens & Lu, Jye-Chyi & Al-Khayyal, Faiz & Tsao, Yu-Chung, 2012. "A piecewise linearization framework for retail shelf space management models," European Journal of Operational Research, Elsevier, vol. 222(1), pages 122-136.
    6. Alexander Hübner & Kai Schaal, 2017. "Effect of replenishment and backroom on retail shelf-space planning," Business Research, Springer;German Academic Association for Business Research, vol. 10(1), pages 123-156, June.
    7. Hasmukh Gajjar & Gajendra Adil, 2010. "A piecewise linearization for retail shelf space allocation problem and a local search heuristic," Annals of Operations Research, Springer, vol. 179(1), pages 149-167, September.
    8. Schaal, Kai & Hübner, Alexander, 2018. "When does cross-space elasticity matter in shelf-space planning? A decision analytics approach," Omega, Elsevier, vol. 80(C), pages 135-152.
    9. Hansen, Jared M. & Raut, Sumit & Swami, Sanjeev, 2010. "Retail Shelf Allocation: A Comparative Analysis of Heuristic and Meta-Heuristic Approaches," Journal of Retailing, Elsevier, vol. 86(1), pages 94-105.
    10. Gecili, Hakan & Parikh, Pratik J., 2022. "Joint shelf design and shelf space allocation problem for retailers," Omega, Elsevier, vol. 111(C).
    11. Kuo, Chia-Wei & Yang, Shu-Jung Sunny, 2013. "The role of store brand positioning for appropriating supply chain profit under shelf space allocation," European Journal of Operational Research, Elsevier, vol. 231(1), pages 88-97.
    12. Tsao, Yu-Chung & Lu, Jye-Chyi & An, Na & Al-Khayyal, Faiz & Lu, Richard W. & Han, Guanghua, 2014. "Retailer shelf-space management with trade allowance: A Stackelberg game between retailer and manufacturers," International Journal of Production Economics, Elsevier, vol. 148(C), pages 133-144.
    13. Ge, Jiwen & Honhon, Dorothee & Fransoo, Jan C. & Zhao, Lei, 2020. "Manufacturer competition in the nanostore retail channel," European Journal of Operational Research, Elsevier, vol. 286(1), pages 360-374.
    14. Alexander Hübner & Fabian Schäfer & Kai N. Schaal, 2020. "Maximizing Profit via Assortment and Shelf‐Space Optimization for Two‐Dimensional Shelves," Production and Operations Management, Production and Operations Management Society, vol. 29(3), pages 547-570, March.
    15. Chen, Yajing & Wu, Zhimin & Wang, Yunlong, 2024. "Omnichannel product selection and shelf space planning optimization," Omega, Elsevier, vol. 127(C).
    16. J Irion & J-C Lu & F A Al-Khayyal & Y-C Tsao, 2011. "A hierarchical decomposition approach to retail shelf space management and assortment decisions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(10), pages 1861-1870, October.
    17. Robert Russell & Timothy Urban, 2010. "The location and allocation of products and product families on retail shelves," Annals of Operations Research, Springer, vol. 179(1), pages 131-147, September.
    18. Zhao, Ju & Zhou, Yong-Wu & Wahab, M.I.M., 2016. "Joint optimization models for shelf display and inventory control considering the impact of spatial relationship on demand," European Journal of Operational Research, Elsevier, vol. 255(3), pages 797-808.
    19. Hübner, Alexander & Schaal, Kai, 2017. "An integrated assortment and shelf-space optimization model with demand substitution and space-elasticity effects," European Journal of Operational Research, Elsevier, vol. 261(1), pages 302-316.
    20. Hübner, Alexander H. & Kuhn, Heinrich, 2012. "Retail category management: State-of-the-art review of quantitative research and software applications in assortment and shelf space management," Omega, Elsevier, vol. 40(2), pages 199-209, April.

    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:232:y:2014:i:2:p:393-404. 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.