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The Discrete Two-Dimensional Assortment Problem

Author

Listed:
  • David W. Pentico

    (Duquesne University, Pittsburgh, Pennsylvania)

Abstract

In the two-dimensional assortment problem, a unit of product that is larger or better on two measurements or qualities may be used to substitute, at some cost, for a unit of demand that is smaller or inferior on both measurements or qualities. The problem is to determine which dimensional combinations to stock in order to minimize the combined stocking and substitution costs. Characteristics of the optimal stocking pattern are presented, and three heuristic solution procedures are compared with an optimization technique under a variety of conditions for demand and cost characteristics.

Suggested Citation

  • David W. Pentico, 1988. "The Discrete Two-Dimensional Assortment Problem," Operations Research, INFORMS, vol. 36(2), pages 324-332, April.
    • Handle: RePEc:inm:oropre:v:36:y:1988:i:2:p:324-332
    DOI: 10.1287/opre.36.2.324
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    Citations

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    Cited by:

    1. Yücel, Eda & Karaesmen, Fikri & Salman, F. Sibel & Türkay, Metin, 2009. "Optimizing product assortment under customer-driven demand substitution," European Journal of Operational Research, Elsevier, vol. 199(3), pages 759-768, December.
    2. Ghosh, Diptesh, 2003. "Neighborhood search heuristics for the uncapacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 150(1), pages 150-162, October.
    3. Narendra Agrawal & Stephen A. Smith, 2003. "Optimal retail assortments for substitutable items purchased in sets," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 793-822, October.
    4. repec:dgr:rugsom:00a54 is not listed on IDEAS
    5. Gnanendran, K. & Ho, J. K. & Sundarraj, R. P., 2003. "Stock selection heuristics for interdependent items," European Journal of Operational Research, Elsevier, vol. 145(3), pages 585-605, March.
    6. Shin, Hojung & Park, Soohoon & Lee, Euncheol & Benton, W.C., 2015. "A classification of the literature on the planning of substitutable products," European Journal of Operational Research, Elsevier, vol. 246(3), pages 686-699.
    7. Bitran, Gabriel R. & Leong, Thin-Yin., 1989. "Co-production of substitutable products," Working papers 3097-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    8. Stephen A. Smith & Narendra Agrawal, 2000. "Management of Multi-Item Retail Inventory Systems with Demand Substitution," Operations Research, INFORMS, vol. 48(1), pages 50-64, February.
    9. Pierre Hansen & Jack Brimberg & Dragan Urošević & Nenad Mladenović, 2007. "Primal-Dual Variable Neighborhood Search for the Simple Plant-Location Problem," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 552-564, November.
    10. F J Vasko & D D Newhart & K L Stott & F E Wolf, 2003. "A large-scale application of the partial coverage uncapacitated facility location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 11-20, January.
    11. Ghosh, Diptesh & Sierksma, Gerard & Goldengorin, Boris & AlMohammad, Bader F., 2000. "Equivalent instances of the simple plant location problem," Research Report 00A54, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    12. Dorothée Honhon & Vishal Gaur & Sridhar Seshadri, 2010. "Assortment Planning and Inventory Decisions Under Stockout-Based Substitution," Operations Research, INFORMS, vol. 58(5), pages 1364-1379, October.
    13. Pentico, David W., 2008. "The assortment problem: A survey," European Journal of Operational Research, Elsevier, vol. 190(2), pages 295-309, October.
    14. Freeman, Nickolas K. & Narayanan, Arunachalam & Keskin, Burcu B., 2021. "Optimal use of downward substitution in a manufacturing operation subject to uncertainty," Omega, Elsevier, vol. 103(C).
    15. Dong, Binwei & Ren, Yufei & McIntosh, Christopher, 2023. "A co-opetitive newsvendor model with product substitution and a wholesale price contract," European Journal of Operational Research, Elsevier, vol. 311(2), pages 502-514.

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