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A piecewise linearization for retail shelf space allocation problem and a local search heuristic


  • Hasmukh Gajjar


  • Gajendra Adil



Retail shelf space allocation problem is well known in literature. In this paper, we make three contributions to retail shelf space allocation problem considering space elasticity (SSAPSE). First, we reformulate an existing nonlinear model for SSAPSE to an integer programming (IP) model using piecewise linearization. Second, we show that the linear programming relaxation of the proposed IP model produces tight upper bound. Third, we develop a heuristic that consistently produces near optimal solutions for randomly generated instances of problems with size (products, shelves) varying from (25, 5) to (200, 50) within a minute of CPU time. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:179:y:2010:i:1:p:149-167:10.1007/s10479-008-0455-6
    DOI: 10.1007/s10479-008-0455-6

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    References listed on IDEAS

    1. Reyes, Pedro M. & Frazier, Gregory V., 2007. "Goal programming model for grocery shelf space allocation," European Journal of Operational Research, Elsevier, vol. 181(2), pages 634-644, September.
    2. Yang, Ming-Hsien & Chen, Wen-Cher, 1999. "A study on shelf space allocation and management," International Journal of Production Economics, Elsevier, vol. 60(1), pages 309-317, April.
    3. Jonathan H. Owen & Sanjay Mehrotra, 2002. "On the Value of Binary Expansions for General Mixed-Integer Linear Programs," Operations Research, INFORMS, vol. 50(5), pages 810-819, October.
    4. Anderson, Evan E, 1979. "An Analysis of Retail Display Space: Theory and Methods," The Journal of Business, University of Chicago Press, vol. 52(1), pages 103-118, January.
    5. 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.
    6. Yang, Ming-Hsien, 2001. "An efficient algorithm to allocate shelf space," European Journal of Operational Research, Elsevier, vol. 131(1), pages 107-118, May.
    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. Alain Bultez & Philippe Naert, 1988. "SH.A.R.P.: Shelf Allocation for Retailers' Profit," Marketing Science, INFORMS, vol. 7(3), pages 211-231.
    9. Hwang, Hark & Choi, Bum & Lee, Min-Jin, 2005. "A model for shelf space allocation and inventory control considering location and inventory level effects on demand," International Journal of Production Economics, Elsevier, vol. 97(2), pages 185-195, August.
    10. 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.
    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.
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    Cited by:

    1. Teresa Bianchi-Aguiar & Elsa Silva & Luis Guimarães & Maria Antónia Carravilla & José F. Oliveira & João Günther Amaral & Jorge Liz & Sérgio Lapela, 2016. "Using Analytics to Enhance a Food Retailer’s Shelf-Space Management," Interfaces, INFORMS, vol. 46(5), pages 424-444, October.
    2. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    3. Moon, Ilkyeong & Park, Kun Soo & Hao, Jing & Kim, Dongwook, 2017. "Joint decisions on product line selection, purchasing, and pricing," European Journal of Operational Research, Elsevier, vol. 262(1), pages 207-216.
    4. 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.
    5. 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.


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