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A tractable discrete fractional programming: application to constrained assortment optimization

Author

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  • Tian Xie

    (Shanghai University of Finance and Economics)

  • Dongdong Ge

    (Shanghai University of Finance and Economics)

Abstract

In this note, we consider a discrete fractional programming in light of a decision problem where limited number of indivisible resources are allocated to several heterogeneous projects to maximize the ratio of total profit to total cost. For each project, both profit and cost are solely determined by the amount of resources allocated to it. Although the problem can be reformulated as a linear program with $$O(m^2 n)$$ O ( m 2 n ) variables and $$O(m^2 n^2)$$ O ( m 2 n 2 ) constraints, we further show that it can be efficiently solved by induction in $$O(m^3 n^2 \log mn)$$ O ( m 3 n 2 log m n ) time. In application, this method leads to an $$O(m^3 n^2 \log mn)$$ O ( m 3 n 2 log m n ) algorithm for assortment optimization problem under nested logit model with cardinality constraints (Feldman and Topaloglu, Oper Res 63: 812–822, 2015).

Suggested Citation

  • Tian Xie & Dongdong Ge, 2018. "A tractable discrete fractional programming: application to constrained assortment optimization," Journal of Combinatorial Optimization, Springer, vol. 36(2), pages 400-415, August.
  • Handle: RePEc:spr:jcomop:v:36:y:2018:i:2:d:10.1007_s10878-018-0302-x
    DOI: 10.1007/s10878-018-0302-x
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    References listed on IDEAS

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    1. James M. Davis & Guillermo Gallego & Huseyin Topaloglu, 2014. "Assortment Optimization Under Variants of the Nested Logit Model," Operations Research, INFORMS, vol. 62(2), pages 250-273, April.
    2. Jacob B. Feldman & Huseyin Topaloglu, 2015. "Capacity Constraints Across Nests in Assortment Optimization Under the Nested Logit Model," Operations Research, INFORMS, vol. 63(4), pages 812-822, August.
    3. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
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    Cited by:

    1. Rui Chen & Hai Jiang, 2020. "Capacitated assortment and price optimization under the nested logit model," Journal of Global Optimization, Springer, vol. 77(4), pages 895-918, August.

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