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The Assortment Problem with Nonlinear Cost Functions

Author

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  • David W. Pentico

    (John J. Kane Hospital, Pittsburgh, Pennsylvania)

Abstract

The early work done on the assortment problem assumed a linear production cost and a substitution cost based only on the difference in value of the item used and the item required. The research reported in this paper extends the analysis by considering concave production cost functions and substitution cost functions that add either a unit fixed cost or a unit-independent fixed charge to the previously considered “scrap” cost. The form of an optimal stocking policy is developed for each case and horizon theorems are proved to aid in the computations. Algorithms for finding optimal policies are described.

Suggested Citation

  • David W. Pentico, 1976. "The Assortment Problem with Nonlinear Cost Functions," Operations Research, INFORMS, vol. 24(6), pages 1129-1142, December.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:6:p:1129-1142
    DOI: 10.1287/opre.24.6.1129
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    Citations

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    Cited by:

    1. C. Arbib & F. Marinelli, 2009. "Exact and Asymptotically Exact Solutions for a Class of Assortment Problems," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 13-25, February.
    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. 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.
    4. Holthaus, Oliver, 2003. "On the best number of different standard lengths to stock for one-dimensional assortment problems," International Journal of Production Economics, Elsevier, vol. 83(3), pages 233-246, March.
    5. 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.
    6. Brun, Alessandro & Capra, Eugenio & Miragliotta, Giovanni, 2009. "VRP revisited: The impact of behavioural costs in balancing standardisation and variety," International Journal of Production Economics, Elsevier, vol. 117(1), pages 16-29, January.
    7. repec:dgr:rugsom:00a54 is not listed on IDEAS
    8. 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.
    9. Ulrich W. Thonemann & Margaret L. Brandeau, 2000. "Optimal Commonality in Component Design," Operations Research, INFORMS, vol. 48(1), pages 1-19, February.
    10. 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.
    11. 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.
    12. 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).
    13. 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.
    14. Pentico, David W., 2008. "The assortment problem: A survey," European Journal of Operational Research, Elsevier, vol. 190(2), pages 295-309, October.
    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. Jans, Raf & Degraeve, Zeger & Schepens, Luc, 2008. "Analysis of an industrial component commonality problem," European Journal of Operational Research, Elsevier, vol. 186(2), pages 801-811, April.
    17. 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.
    18. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.

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