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The Assortment Problem with Probabilistic Demands

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  • David W. Pentico

    (University of Pittsburgh)

Abstract

The early work done on the assortment problem assumed known demands and additive and proportional substitution cost functions for single period problems. The extension of this problem (to consider probabilistic demands and multiple periods) complicates the problem considerably. By making some assumptions about the pattern of demands and the form of a reasonable solution, the problem can be approached by using dynamic programming thus finding the shortest route through a network.

Suggested Citation

  • David W. Pentico, 1974. "The Assortment Problem with Probabilistic Demands," Management Science, INFORMS, vol. 21(3), pages 286-290, November.
    • Handle: RePEc:inm:ormnsc:v:21:y:1974:i:3:p:286-290
    DOI: 10.1287/mnsc.21.3.286
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    Citations

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    Cited by:

    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. 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.
    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. Vashkar Ghosh & Anand Paul & Lingjiong Zhu, 2022. "Stocking Under Random Demand and Product Variety: Exact Models and Heuristics," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1006-1032, March.
    5. Dorothee Honhon & Sreelata Jonnalagedda & Xiajun Amy Pan, 2012. "Optimal Algorithms for Assortment Selection Under Ranking-Based Consumer Choice Models," Manufacturing & Service Operations Management, INFORMS, vol. 14(2), pages 279-289, April.
    6. K Liu & J-A Li & Y Wu & K K Lai, 2005. "Analysis of monitoring and limiting of commercial cheating: a newsvendor model," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(7), pages 844-854, July.
    7. Dorothée Honhon & Sridhar Seshadri, 2013. "Fixed vs. Random Proportions Demand Models for the Assortment Planning Problem Under Stockout-Based Substitution," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 378-386, July.
    8. Ulrich W. Thonemann & Margaret L. Brandeau, 2000. "Optimal Commonality in Component Design," Operations Research, INFORMS, vol. 48(1), pages 1-19, February.
    9. 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.
    10. Ali Aouad & Vivek Farias & Retsef Levi, 2021. "Assortment Optimization Under Consider-Then-Choose Choice Models," Management Science, INFORMS, vol. 67(6), pages 3368-3386, June.
    11. 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.
    12. Pentico, David W., 2008. "The assortment problem: A survey," European Journal of Operational Research, Elsevier, vol. 190(2), pages 295-309, October.
    13. Liu, Ke & Li, Jing-An & Lai, Kin Keung, 2004. "Single period, single product newsvendor model with random supply shock," European Journal of Operational Research, Elsevier, vol. 158(3), pages 609-625, November.
    14. Vineet Goyal & Retsef Levi & Danny Segev, 2016. "Near-Optimal Algorithms for the Assortment Planning Problem Under Dynamic Substitution and Stochastic Demand," Operations Research, INFORMS, vol. 64(1), pages 219-235, February.
    15. Baloch, Gohram & Gzara, Fatma, 2020. "Capacity and assortment planning under one-way supplier-driven substitution for pharmacy kiosks with low drug demand," European Journal of Operational Research, Elsevier, vol. 282(1), pages 108-128.
    16. 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.
    17. 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.
    18. Yu-Hsin Lin & Hsien-Ching Chen & Chen-Yu Chien & Chih-Hung Tsai & Min-Jer Lu, 2014. "A Study of Selecting Criteria for Material Substitution under Green Environmental Consideration," International Journal of Academic Research in Business and Social Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Business and Social Sciences, vol. 4(1), pages 459-473, January.

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