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Joern Meissner, Arne K Strauss, Kalyan Talluri
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| Abstract |
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The network choice revenue management problem models customers as choosing from an offer set, and
the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting
dynamic program for the firm is intractable and approximated by a deterministic linear program
called the CDLP which has an exponential number of columns. However, under the choice-set paradigm
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, starting
with a concave program formulation called SDCP that is based on segment-level consideration sets, we
add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In
addition we propose a natural direct tightening of the SDCP called ESDCPK, and compare the performance
of both methods on the benchmark data sets in the literature. In our computational testing on the
benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken
by column generation. For a large network our 2PC procedure runs under 70 seconds to come within
0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network
with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC
runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP
when segment consideration sets overlap and the consideration sets themselves are relatively small. |
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| Keywords |
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Bid Prices, Yield Management, Heuristics, Discrete-Choice, Network Revenue Management
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| Status |
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Forthcoming in Production and Operations Management (POM). |
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| Download |
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www.meiss.com/download/RM-Meissner-Strauss-Talluri.pdf
(241 kb) |
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| Reference |
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BibTeX,
Plain Text |
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