Multi-product pricing:A discrete choice model based on Markov Chain Choice Model combined with reservation prices

Finding the optimal selling prices for an assortment of multiple, substitutable products is a problem that occurs daily in many industries. To solve this problem, a new customer choice model is proposed, based on the Markov Chain Choice Model combined with reservation prices. A discrete version of the model is proposed and it is solved to optimality. This discrete model is instrumental in a simulation procedure to estimate the optimal reservation prices in the original continuous model. Important benefits of the proposed model are that the model is intuitive and close to reality, because it includes both the customers' willingness to pay and substitution behavior explicitly, and it can handle any type of correlation between products.</p

On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization

Motivated by the classic exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the general customer choice model based on random utility called multi-attempt model, in which a customer may consider several substitutes before finally deciding to not purchase anything. We show that the approximation error of multi-attempt model decreases exponentially in the number of attempts. However, despite its strong theoretical performance, the empirical performance of multi-attempt model is not satisfactory. This motivates us to construct a modification of multi-attempt model called re-scaled multi-attempt model. We show that re-scaled 2-attempt model is exact when the underlying true choice model is Multinomial Logit (MNL); if, however, the underlying true choice model is not MNL, we show numerically that the approximation quality of re-scaled 2-attempt model is very close to that of Markov chain model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use off-the-shelf solvers, or borrow existing algorithms from literature, to solve a general assortment optimization problem with a variety of real-world constraints.http://deepblue.lib.umich.edu/bitstream/2027.42/122455/1/1322_Ahn.pd

Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue $\pi$ and then choosing all products with revenue at least $\pi$. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. (2014). An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition. We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.Comment: Minor changes following referees' comment

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

Assortment Optimization under the Decision Forest Model

We study the problem of finding the optimal assortment that maximizes expected revenue under the decision forest model, a recently proposed nonparametric choice model that is capable of representing any discrete choice model and in particular, can be used to represent non-rational customer behavior. This problem is of practical importance because it allows a firm to tailor its product offerings to profitably exploit deviations from rational customer behavior, but at the same time is challenging due to the extremely general nature of the decision forest model. We approach this problem from a mixed-integer optimization perspective and propose two different formulations. We theoretically compare the two formulations in strength, and analyze when they are integral in the special case of a single tree. We further propose a methodology for solving the two formulations at a large-scale based on Benders decomposition, and show that the Benders subproblem can be solved efficiently by primal dual greedy algorithms when the master solution is fractional for one of the formulations, and in closed form when the master solution is binary for both formulations. Using synthetically generated instances, we demonstrate the practical tractability of our formulations and our Benders decomposition approach, and their edge over heuristic approaches. In a case study based on a real-world transaction data, we demonstrate that our proposed approach can factor the behavioral anomalies observed in consumer choice into assortment decision and create higher revenue

Approximation algorithms for dynamic assortment optimization models

We consider the single-period joint assortment and inventory planning problem with stochastic demand and dynamic substitution across products, motivated by applications in highly differentiated markets, such as online retailing and airlines. This class of problems is known to be notoriously hard to deal with from a computational standpoint. In fact, prior to the present paper, only a handful of modeling approaches were shown to admit provably good algorithms, at the cost of strong restrictions on customers’ choice outcomes. Our main contribution is to provide the first efficient algorithms with provable performance guarantees for a broad class of dynamic assortment optimization models. Under general rank-based choice models, our approximation algorithm is best possible with respect to the price parameters, up to lower-order terms. In particular, we obtain a constant-factor approximation under horizontal differentiation, where product prices are uniform. In more structured settings, where the customers’ ranking behavior is motivated by price and quality cues, we derive improved guarantees through tailor-made algorithms. In extensive computational experiments, our approach dominates existing heuristics in terms of revenue performance, as well as in terms of speed, given the myopic nature of our methods. From a technical perspective, we introduce a number of novel algorithmic ideas of independent interest, and unravel hidden relations to submodular maximization

Three Essays on Modeling Consumer Behavior and Its Operations Management Implications.

Traditionally, models used in operations management have considered the firm side of the problem by making simplifying assumptions on demand or market. In practice, however, consumers or agents in the market actively make decisions or choices based on self interest. This dissertation aims to analyze how insights and results from traditional models are affected when we account for such active decision making by consumers or the market. In Chapter II, we study how the customers' decision of joining the queue to receive a service varies by the individual incentive as well as the firm's capacity decision, which also depends on the firm’s selfishness. By considering three customer types: individual, collective, and social, and two firm types: profit maximizing and welfare maximizing, we are able to disentangle the effects of selfishness of the customers and the firm, and the interactions between these two in equilibrium. Among other results, we find that there can be a ``benefit of selfishness'' to consumers and the system, in contrast to the price of anarchy literature. In Chapter III, we discuss the customers' redemption behavior of loyalty points and its impact on the seller's pricing and inventory rationing strategy. We model the customer choice between cash or loyalty points by characterizing consumers in three dimensions: the reservation price, the point balance, and their perceived valuation of points. Applying this choice model into the seller's dynamic pricing model, we characterize the seller's optimal strategy that specifies the optimal price, the control of reward sales (black-out), and the redemption points. In Chapter IV, we study the customers’ substitution behavior when their preferred product is not available, and the seller's assortment optimization problem. Motivated by the exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the random utility customer choice model called rescaled multi-attempt model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use an off-the-shelf solver to solve a general assortment optimization problem with a variety of real-world constraints.PhDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133387/1/hakjin_1.pd