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A randomized concave programming method for choice network revenue management

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  • Kalyan Talluri

Abstract

Models incorporating more realistic models of customer behavior, as customers choosing from an offer set, have recently become popular in assortment optimization and revenue management. The dynamic program for these models is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper we propose a new approach called SDCP to solving CDLP based on segments and their consideration sets. SDCP is a relaxation of CDLP and hence forms a looser upper bound on the dynamic program but coincides with CDLP for the case of non-overlapping segments. If the number of elements in a consideration set for a segment is not very large (SDCP) can be applied to any discrete-choice model of consumer behavior. We tighten the SDCP bound by (i) simulations, called the randomized concave programming (RCP) method, and (ii) by adding cuts to a recent compact formulation of the problem for a latent multinomial-choice model of demand (SBLP+). This latter approach turns out to be very effective, essentially obtaining CDLP value, and excellent revenue performance in simulations, even for overlapping segments. By formulating the problem as a separation problem, we give insight into why CDLP is easy for the MNL with non-overlapping considerations sets and why generalizations of MNL pose difficulties. We perform numerical simulations to determine the revenue performance of all the methods on reference data sets in the literature.

Suggested Citation

  • Kalyan Talluri, 2010. "A randomized concave programming method for choice network revenue management," Economics Working Papers 1215, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2011.
  • Handle: RePEc:upf:upfgen:1215
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    Cited by:

    1. Jacob B. Feldman & Huseyin Topaloglu, 2017. "Revenue Management Under the Markov Chain Choice Model," Operations Research, INFORMS, vol. 65(5), pages 1322-1342, October.
    2. Guillermo Gallego & Huseyin Topaloglu, 2014. "Constrained Assortment Optimization for the Nested Logit Model," Management Science, INFORMS, vol. 60(10), pages 2583-2601, October.
    3. Sumit Kunnumkal & Kalyan Talluri, 2012. "A New Compact Linear Programming Formulation for Choice Network Revenue Management," Working Papers 677, Barcelona School of Economics.
    4. Sumit Kunnumkal & Kalyan Talluri, 2012. "A new compact linear programming formulation for choice network revenue management," Economics Working Papers 1349, Department of Economics and Business, Universitat Pompeu Fabra.

    More about this item

    Keywords

    assortment optimization; randomized algorithms; network revenue management.;
    All these keywords.

    JEL classification:

    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing
    • L93 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Air Transportation
    • L83 - Industrial Organization - - Industry Studies: Services - - - Sports; Gambling; Restaurants; Recreation; Tourism

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