46 research outputs found
Dynamic pricing under customer choice behavior for revenue management in passenger railway networks
Revenue management (RM) for passenger railway is a small but active research field with an increasing attention during the past years. However, a detailed look into existing research shows that most of the current models in theory rely on traditional RM techniques and that advanced models are rare. This thesis aims to close the gap by proposing a state-of-the-art passenger railway pricing model that covers the most important properties from practice, with a special focus on the German railway network and long-distance rail company Deutsche Bahn Fernverkehr (DB). The new model has multiple advantages over DB’s current RM system. Particularly, it uses a choice-based demand function rather than a traditional independent demand model, is formulated as a network model instead of the current leg-based approach and finally optimizes prices on a continuous level instead of controlling booking classes. Since each itinerary in the network is considered by multiple heterogeneous customer segments (e.g., differentiated by travel purpose, desired departure time) a discrete mixed multinomial logit model (MMNL) is applied to represent demand. Compared to alternative choice models such as the multinomial logit model (MNL) or the nested logit model (NL), the MMNL is significantly less considered in pricing research. Furthermore, since the resulting deterministic multi-product multi-resource dynamic pricing model under the MMNL turns out to be non- linear non-convex, an open question is still how to obtain a globally optimal solution. To narrow this gap, this thesis provides multiple approaches that make it able to derive a solution close to the global optimum. For medium-sized networks, a mixed-integer programming approach is proposed that determines an upper bound close to the global optimum of the original model (gap < 1.5%). For large-scale networks, a heuristic approach is presented that significantly decreases the solution time (by factor up to 56) and derives a good solution for an application in practice. Based on these findings, the model and heuristic are extended to fit further price constraints from railway practice and are tested in an extensive simulation study. The results show that the new pricing approach outperforms both benchmark RM policies (i.e., DB’s existing model and EMSR-b) with a revenue improvement of approx. +13-15% over DB’s existing approach under a realistic demand scenario. Finally, to prepare data for large-scale railway networks, an algorithm is presented that automatically derives a large proportion of necessary data to solve choice-based network RM models. This includes, e.g., the set of all meaningful itineraries (incl. transfers) and resources in a network, the corresponding resource consumption and product attribute values such as travel time or number of transfers. All taken together, the goal of this thesis is to give a broad picture about choice-based dynamic pricing for passenger railway networks
Assortment and Pricing Optimisation under non-conventional customer choice models
Nowadays, extensive research is being done in the area of revenue management, with applications across industries. In the center of this area lays the assortment problem, which amounts to find a subset of products to offer in order to maximise revenue, provided that customers follow a certain model of choice. Most studied models satisfy the following property: whenever the offered set is enlarged, then the probability of selecting a specific product decreases. This property is called regularity in the literature. However, customer behaviour often shows violations of this condition such as the decoy effect, where adding extra options sometimes leads to a positive effect for some products, whose probabilities of being selected increase relative to other products (e.g., including a medium size popcorn slightly cheaper than the large one, with the purpose of making the latter more attractive by comparison). We study two models of customer choice where regularity violations can be accommodated (hence the non-conventionality), and show that the assortment optimisation problem can still be solved in polynomial time.
First we analyse the Sequential Multinomial Logit (SML). Under the SML model, products are partitioned into two levels, to capture differences in attractiveness, brand awareness and, or visibility of the products in the market. When a consumer is presented with an assortment of products, she first considers products on the first level and, if none of them is purchased, products in the second level are considered. This model is a special case of the Perception-Adjusted Luce Model (PALM) recently proposed by Echenique et al.(2018). It can explain many behavioural phenomena such as the attraction, compromise, similarity effects and choice overload which cannot be explained by the Multinomial Logit (MNL) model or any discrete choice model based on random utility. We show that the concept of revenue-ordered assortment sets, which contain an optimal assortment under the MNL model, can be generalized to the SML model. More precisely, we show that all optimal assortments under the SML are revenue-ordered by level, a natural generalization of revenue-ordered assortments that contains, at most, a quadratic number of assortments. As a corollary, assortment optimization under the SML is polynomial-time solvable
Secondly, the Two-Stage Luce model (2SLM), is a discrete choice model introduced by Echenique and Saito (2018) that generalizes the standard multinomial logit model (MNL). The 2SLM does not satisfy the Independence of Irrelevant Alternatives (IIA) property nor regularity, and to model customer behaviour, each product has an intrinsic utility, and uses a dominance relation between products.
Given a proposed assortment S, consumers first discard all dominated products in S before using an MNL model on the remaining products. As a result, the model can capture behaviour that cannot be replicated by any discrete choice model based on random utilities. We show that the assortment problem under the 2SLM is polynomially-solvable. Moreover, we prove that the capacitated assortment optimization problem is NP-hard and present polynomial-time algorithms for the cases where (1) the dominance relation is attractiveness correlated and (2) its transitive reduction is a forest. The proofs exploit a strong connection between assortments under the 2SLM and independent sets in comparability graphs.
The third and final contribution is an in-depth study of the pricing problem under the 2SLM. We first note that changes in prices should be reflected in the dominance relation if the differences between the resulting attractiveness are large enough. This is formalised by solving the joint assortment and pricing problem under the Threshold Luce model, where one product dominates another if the ratio between their attractiveness is greater than a fixed threshold. In this setting, we show that this problem can be solved in polynomial time
A review of choice-based revenue management : theory and methods
Over the last fifteen years, the theory and practice of revenue management has experienced significant developments due to the need to incorporate customer choice behavior. In this paper, we portray these developments by reviewing the key literature on choice-based revenue management, specifically focusing on methodological publications of availability control over the years 2004–2017. For this purpose, we first state the choice-based network revenue management problem by formulating the underlying dynamic program, and structure the review according to its components and the resulting inherent challenges. In particular, we first focus on the demand modeling by giving an overview of popular choice models, discussing their properties, and describing estimation procedures relevant to choice-based revenue management. Second, we elaborate on assortment optimization, which is a fundamental component of the problem. Third, we describe recent developments on tackling the entire control problem. We also discuss the relation to dynamic pricing. Finally, we give directions for future research
The Approximability of Assortment Optimization Under Ranking Preferences
The main contribution of this paper is to provide best-possible approximability bounds for assortment planning under a general choice model, where customer choices are modeled through an arbitrary distribution over ranked lists of their preferred products, subsuming most random utility choice models of interest. From a technical perspective, we show how to relate this optimization problem to the computational task of detecting large independent sets in graphs, allowing us to argue that general ranking preferences are extremely hard to approximate with respect to various problem parameters. These findings are complemented by a number of approximation algorithms that attain essentially best-possible factors, proving that our hardness results are tight up to lower-order terms. Surprisingly, our results imply that a simple and widely studied policy, known as revenue-ordered assortments, achieves the best possible performance guarantee with respect to the price parameters
Placement Optimization of Substitutable Products
Strategic product placement can have a strong influence on customer purchase
behavior in physical stores as well as online platforms. Motivated by this, we
consider the problem of optimizing the placement of substitutable products in
designated display locations to maximize the expected revenue of the seller. We
model the customer behavior as a two-stage process: first, the customer visits
a subset of display locations according to a browsing distribution; second, the
customer chooses at most one product from the displayed products at those
locations according to a choice model. Our goal is to design a general
algorithm that can select and place the products optimally for any browsing
distribution and choice model, and we call this the Placement problem. We give
a randomized algorithm that utilizes an -approximate algorithm for
cardinality constrained assortment optimization and outputs a
-approximate solution (in expectation) for
Placement with display locations, i.e., our algorithm outputs a solution
with value at least factor of the optimal and
this is tight in the worst case. We also give algorithms with stronger
guarantees in some special cases. In particular, we give a deterministic
-approximation algorithm for the Markov choice model,
and a tight -approximation algorithm for the problem when products
have identical prices
Joint Location and Cost Planning in Maximum Capture Facility Location under Multiplicative Random Utility Maximization
We study a joint facility location and cost planning problem in a competitive
market under random utility maximization (RUM) models. The objective is to
locate new facilities and make decisions on the costs (or budgets) to spend on
the new facilities, aiming to maximize an expected captured customer demand,
assuming that customers choose a facility among all available facilities
according to a RUM model. We examine two RUM frameworks in the discrete choice
literature, namely, the additive and multiplicative RUM. While the former has
been widely used in facility location problems, we are the first to explore the
latter in the context. We numerically show that the two RUM frameworks can well
approximate each other in the context of the cost optimization problem. In
addition, we show that, under the additive RUM framework, the resultant cost
optimization problem becomes highly non-convex and may have several local
optima. In contrast, the use of the multiplicative RUM brings several
advantages to the competitive facility location problem. For instance, the cost
optimization problem under the multiplicative RUM can be solved efficiently by
a general convex optimization solver or can be reformulated as a conic
quadratic program and handled by a conic solver available in some off-the-shelf
solvers such as CPLEX or GUROBI. Furthermore, we consider a joint location and
cost optimization problem under the multiplicative RUM and propose three
approaches to solve the problem, namely, an equivalent conic reformulation, a
multi-cut outer-approximation algorithm, and a local search heuristic. We
provide numerical experiments based on synthetic instances of various sizes to
evaluate the performances of the proposed algorithms in solving the cost
optimization, and the joint location and cost optimization problems
Robust Dynamic Assortment Optimization in the Presence of Outlier Customers
We consider the dynamic assortment optimization problem under the multinomial
logit model (MNL) with unknown utility parameters. The main question
investigated in this paper is model mis-specification under the
-contamination model, which is a fundamental model in robust
statistics and machine learning. In particular, throughout a selling horizon of
length , we assume that customers make purchases according to a well
specified underlying multinomial logit choice model in a
()-fraction of the time periods, and make arbitrary purchasing
decisions instead in the remaining -fraction of the time periods.
In this model, we develop a new robust online assortment optimization policy
via an active elimination strategy. We establish both upper and lower bounds on
the regret, and show that our policy is optimal up to logarithmic factor in T
when the assortment capacity is constant. Furthermore, we develop a fully
adaptive policy that does not require any prior knowledge of the contamination
parameter . Our simulation study shows that our policy outperforms
the existing policies based on upper confidence bounds (UCB) and Thompson
sampling.Comment: 27 pages, 1 figur
Display Optimization for Vertically Differentiated Locations Under Multinomial Logit Preferences
We introduce a new optimization model, dubbed the display optimization problem, that captures a common aspect of choice behavior, known as the framing bias. In this setting, the objective is to optimize how distinct items (corresponding to products, web links, ads, etc.) are being displayed to a heterogeneous audience, whose choice preferences are influenced by the relative locations of items. Once items are assigned to vertically differentiated locations, customers consider a subset of the items displayed in the most favorable locations, before picking an alternative through Multinomial Logit choice probabilities. The main contribution of this paper is to derive a polynomial-time approximation scheme for the display optimization problem. Our algorithm is based on an approximate dynamic programming formulation that exploits various structural properties to derive a compact state space representation of provably near-optimal item-to-position assignment decisions. As a by-product, our results improve on existing constant-factor approximations for closely-related models, and apply to general distributions over consideration sets. We develop the notion of approximate assortments, that may be of independent interest and applicable in additional revenue management settings. Lastly, we conduct extensive numerical studies to validate the proposed modeling approach and algorithm. Experiments on a public hotel booking data set demonstrate the superior predictive accuracy of our choice model vis-a-vis the Multinomial Logit choice model with location bias, proposed in earlier literature. In synthetic computational experiments, our approximation scheme dominates various benchmarks, including natural heuristics -- greedy methods, local-search, priority rules -- as well as state-of-the-art algorithms developed for closely-related models
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