A randomized concave programming method for choice network revenue management

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.assortment optimization, randomized algorithms, network revenue management.

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

Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms -- one based on column generation and one based on random sampling -- for estimating such models from data. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms both rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25, 2021

Do Loyalty Programs Really Enhance Behavioral Loyalty? An Empirical Analysis Accounting for Self-Selecting Members

One of the pressing issues in marketing is whether loyalty programs really enhance behavioral loyalty. Loyalty program members may have a much higher share-of-wallet at the firm with the loyalty program than non-members have, but this does not necessarily imply that loyalty programs are effective. Loyal customers may select themselves to become members in order to benefit from the program. Since this implies that program membership is endogenous, we estimate models for both the membership decision (using instrumental variables) and for the effect of membership on share-of-wallet, our measure of behavioral loyalty. We use panel data from a representative sample of Dutch households who report their loyalty program memberships for all seven loyalty programs in grocery retailing as well as their expenditures at each of the 20 major supermarket chains. We find a small positive yet significant effect of loyalty program membership on share-of-wallet. This effect is seven times smaller than is suggested by a naïve model that ignores the endogeneity of program membership. The predictive validity of the proposed model is much better than for the naïve model. Our results show that creating loyalty program membership is a crucial step to enhance share-of-wallet, and we provide guidelines how to achieve this.Attraction models;Endogeneity;Grocery retailing;Loyalty programs;Tobit-II model

Assortment optimization using an attraction model in an omnichannel environment

Making assortment decisions is becoming an increasingly difficult task for many retailers worldwide as they implement omnichannel initiatives. Discrete choice modeling lies at the core of this challenge, yet existing models do not sufficiently account for the complex shopping behavior of customers in an omnichannel environment. In this paper, we introduce a discrete choice model called the multichannel attraction model (MAM). A key feature of the MAM is that it specifically accounts for both the product substitution behavior of customers within each channel and the switching behavior between channels. We formulate the corresponding assortment optimization problem as a mixed integer linear program and provide a computationally efficient heuristic method that can be readily used for obtaining high-quality solutions in large-scale omnichannel environments. We also present three different methods to estimate the MAM parameters based on aggregate sales transaction data. Finally, we describe general effects of the implementation of widely-used omnichannel initiatives on the MAM parameters, and carry out numerical experiments to explore the structure of optimal assortments, thereby gaining new insights into omnichannel assortment optimization. Our work provides the analytical framework for future studies to assess the impact of different omnichannel initiatives

An enhanced concave program relaxation for choice network revenue management

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 based on segment-level consideration sets called SDCP, we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the ?SDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.discrete-choice models, network revenue management, optimization

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