693 research outputs found
Dynamic Assortment Optimization with Changing Contextual Information
In this paper, we study the dynamic assortment optimization problem under a
finite selling season of length . At each time period, the seller offers an
arriving customer an assortment of substitutable products under a cardinality
constraint, and the customer makes the purchase among offered products
according to a discrete choice model. Most existing work associates each
product with a real-valued fixed mean utility and assumes a multinomial logit
choice (MNL) model. In many practical applications, feature/contexutal
information of products is readily available. In this paper, we incorporate the
feature information by assuming a linear relationship between the mean utility
and the feature. In addition, we allow the feature information of products to
change over time so that the underlying choice model can also be
non-stationary. To solve the dynamic assortment optimization under this
changing contextual MNL model, we need to simultaneously learn the underlying
unknown coefficient and makes the decision on the assortment. To this end, we
develop an upper confidence bound (UCB) based policy and establish the regret
bound on the order of , where is the dimension of
the feature and suppresses logarithmic dependence. We further
established the lower bound where is the cardinality
constraint of an offered assortment, which is usually small. When is a
constant, our policy is optimal up to logarithmic factors. In the exploitation
phase of the UCB algorithm, we need to solve a combinatorial optimization for
assortment optimization based on the learned information. We further develop an
approximation algorithm and an efficient greedy heuristic. The effectiveness of
the proposed policy is further demonstrated by our numerical studies.Comment: 4 pages, 4 figures. Minor revision and polishing of presentatio
Static Pricing Problems under Mixed Multinomial Logit Demand
Price differentiation is a common strategy for many transport operators. In
this paper, we study a static multiproduct price optimization problem with
demand given by a continuous mixed multinomial logit model. To solve this new
problem, we design an efficient iterative optimization algorithm that
asymptotically converges to the optimal solution. To this end, a linear
optimization (LO) problem is formulated, based on the trust-region approach, to
find a "good" feasible solution and approximate the problem from below. Another
LO problem is designed using piecewise linear relaxations to approximate the
optimization problem from above. Then, we develop a new branching method to
tighten the optimality gap. Numerical experiments show the effectiveness of our
method on a published, non-trivial, parking choice model
- …