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 ...
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.
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