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Author : Laurent Alfandari
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (118 download)
Download or read book An exact method for assortment optimization under the nested logit model written by Laurent Alfandari and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Laurent Alfandari
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (13 download)
Download or read book An Exact Method for Assortment Optimization Under the Nested Logit Model written by Laurent Alfandari and published by . This book was released on 2020 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the problem of finding an optimal assortment of products maximizing the expected revenue, in which customer preferences are modeled using a Nested Logit choice model. This problem is known to be polynomially solvable in a specific case and NP-hard otherwise, with only approximation algorithms existing in the literature. For the NP-hard cases, we provide a general exact method that embeds a tailored Branch-and-Bound algorithm into a fractional programming framework. Contrary to the existing literature, in which assumptions are imposed on either the structure of nests or the combination and characteristics of products, no assumptions on the input data are imposed, and hence our approach can solve the most general problem setting. We show that the parameterized subproblem of the fractional programming scheme, which is a binary highly non-linear optimization problem, is decomposable by nests, which is a main advantage of the approach. To solve the subproblem for each nest, we propose a two-stage approach. In the first stage, we identify those products that are undoubtedly beneficial to offer, or not, which can significantly reduce the problem size. In the second stage, we design a tailored Branch-and-Bound algorithm with problem-specific upper bounds. Numerical results show that the approach is able to solve assortment instances with up to 5,000 products per nest. The most challenging instances for our approach are those in which the dissimilarity parameters of nests can be either less or greater than one.
Author : Sumit Kunnumkal
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book New Bounds for Assortment Optimization Under the Nested Logit Model written by Sumit Kunnumkal and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the assortment optimization problem under the nested logit model and obtain new bounds on the gap between the optimal expected revenue and an upper bound based on a certain continuous relaxation of the assortment problem. Our bounds can be tighter than the existing bounds in the literature and provide more insight into the key drivers of tractability for the assortment optimization problem under the nested logit model. Moreover, our bounds scale with the nest dissimilarity parameters and we recover the well-known tractability results for the assortment optimization problem under the multinomial logit model when all the nest dissimilarity parameters are equal to one. We extend our results to the cardinality constrained assortment problem where there are constraints that limit the number of products that can be offered within each nest.
Author : Danny Segev
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (13 download)
Download or read book Approximation Schemes for Capacity-Constrained Assortment Optimization Under the Nested Logit Model written by Danny Segev and published by . This book was released on 2020 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main contribution of this paper resides in proposing a novel approximate dynamic programming approach for capacitated assortment optimization under the Nested Logit model in its utmost generality. Specifically, we show that the optimal revenue can be efficiently approached within any degree of accuracy through purely combinatorial techniques, synthesizing ideas related to continuous dynamic programming, state space discretization, and sensitivity analysis of modified revenue functions. These developments allow us to devise the first fully polynomial-time approximation scheme in this context, thus resolving fundamental open questions posed in previous papers.
Author : Zhen Chen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (14 download)
Download or read book Multi-Objective Assortment Optimization written by Zhen Chen and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assortment optimization is a fundamental problem in revenue management, in which the objective usually is to select a subset of products to offer to customers in order to maximize expected revenue or profit. However, business practices often involve multiple, and potentially conflicting goals. In this work, we propose a general framework and a novel reformulation method for solving multi-objective assortment optimization problems. Specifically, we consider problems with a separable sum of multiple convex objective functions on linear combinations of choice probabilities, and we present a reformulation that effectively "linearizes" the problem. We prove that the reformulated problem is equivalent to the original problem and that it leads to a unified solution approach to multi-objective assortment optimization problems in various contexts. We show that the approach encompasses a wide range of operational objectives, such as risk, customer utility, market share, costs with economies of scale, and dualized convex constraints. We first illustrate our approach with the multinomial logit model without any constraints or with allowance for totally unimodular constraints. We further show that our framework leads to tractable solutions under the nested logit model and the Markov chain choice model. Together with large-scale numerical experiments to demonstrate the efficiency and practicality of our methods, we highlight that our work provides a powerful and flexible tool for solving multi-objective assortment problems, which arise frequently in practical revenue management settings.
Author : Antoine Désir
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Capacitated Assortment Optimization written by Antoine Désir and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assortment optimization is an important problem that arises in many practical applications such as retailing and online advertising. In this problem, the goal is to select a subset of items that maximizes the expected revenue in the presence of (1) the substitution behavior of consumers specified by a choice model, and (2) a potential capacity constraint bounding the total weight of items in the assortment. The latter is a natural constraint arising in many applications. We begin by showing how challenging these two aspects are from an optimization perspective. First, we show that adding a general capacity constraint makes the problem NP-hard even for the simplest choice model, namely the multinomial logit model. Second, we show that even the unconstrained assortment optimization for the mixture of multinomial logit model is hard to approximate within any reasonable factor when the number of mixtures is not constant.In view of these hardness results, we present near-optimal algorithms for the capacity constrained assort- ment optimization problem under a large class of parametric choice models including the mixture of multinomial logit, Markov chain, nested logit and d-level nested logit choice models. In fact, we develop near-optimal algorithms for a general class of capacity constrained optimization problems whose objective function depends on a small number of linear functions. For the mixture of multinomial logit model (resp. Markov chain model), the running time of our algorithm depends exponentially on the number of segments (resp. rank of the transition matrix). Therefore, we get efficient algorithms only for the case of constant number of segments (resp. constant rank). However, in light of our hardness result, any near-optimal algorithm will have a super polynomial dependence on the number of mixtures for the mixture of multinomial logit choice model.
Author : James Mario Davis
Publisher :
ISBN 13 :
Total Pages : 424 pages
Book Rating : 4.:/5 (932 download)
Download or read book Customer Choice Models and Assortment Optimization written by James Mario Davis and published by . This book was released on 2015 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis handles a fundamental problem in retail: given an enormous variety of products which does the retailer display to its customers? This is the assortment planning problem. We solve this problem by developing algorithms that, given input parameters for products, can efficiently return the set of products that should be displayed. To develop these algorithms we use a mathematical model of how customers react to displayed items, a customer choice model. Below we consider two classic customer choice models, the Multinomial Logit model and Nested Logit model. Under each of these customer choice models we develop algorithms that solve the assortment planning problem. Additionally, we consider the constrained assortment planning problem where the retailer must display products to customers but must also satisfy operational constraints.
Author : Tien Mai
Publisher :
ISBN 13 :
Total Pages : 37 pages
Book Rating : 4.:/5 (13 download)
Download or read book An Algorithm for Assortment Optimization Under Parametric Discrete Choice Models written by Tien Mai and published by . This book was released on 2019 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work concerns the assortment optimization problem that refers to selecting a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a parametric choice model. The key challenge lies in the computational difficulty of finding the best subset solution, which often requires exhaustive search. The literature on constrained assortment optimization lacks a practically efficient method which that is general to deal with different types of parametric choice models (e.g., the multinomial logit, mixed logit or general multivariate extreme value models). In this paper, we propose a new approach that allows to address this issue. The idea is that, under a general parametric choice model, we formulate the problem into a binary nonlinear programming model, and use an iterative algorithm to find a binary solution. At each iteration, we propose a way to approximate the objective (expected revenue) by a linear function, and a polynomial-time algorithm to find a candidate solution using this approximate function. We also develop a greedy local search algorithm to further improve the solutions. We test our algorithm on instances of different sizes under various parametric choice model structures and show that our algorithm dominates existing exact and heuristic approaches in the literature, in terms of solution quality and computing cost.
Author : Ruxian Wang
Publisher :
ISBN 13 :
Total Pages : 7 pages
Book Rating : 4.:/5 (13 download)
Download or read book Capacitated Assortment and Price Optimization Under the Multinomial Logit Model written by Ruxian Wang and published by . This book was released on 2014 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an assortment and price optimization problem where a retailer chooses an assortment of competing products and determines their prices to maximize the total expected profit subject to a capacity constraint. Customers' purchase behavior follows the multinomial logit choice model with general utility functions. This paper simplifies it to a problem of finding a unique fixed point of a single-dimensional function and visualizes the assortment optimization process. An efficient algorithm to find the optimal assortment and prices is provided.
Author : Jacob Feldman
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Assortment Optimization Under the Multinomial Logit Model with Utility-Based Rank Cutoffs written by Jacob Feldman and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study assortment optimization problems under a natural variant of the multinomial logit model where the customers are willing to focus only on a certain number of products that provide the largest utilities. In particular, each customer has a rank cutoff, characterizing the number of products that she will focus on during the course of her choice process. Given that we offer a certain assortment of products, the choice process of a customer with rank cutoff k proceeds as follows. The customer associates random utilities with all of the products as well as the no-purchase option. She ignores all alternatives whose utilities are not within the k largest utilities. Among the remaining alternatives, the customer chooses the available alternative that provides the largest utility. Under the assumption that the~utilities follow Gumbel distributions with the same scale parameter, we provide a recursion to compute the choice probabilities. Considering the assortment optimization problem to find the revenue-maximizing assortment of products to offer, we show that the problem is NP-hard and give a polynomial-time approximation scheme. Since the customers ignore the products below their rank cutoffs in our variant of the multinomial logit model, intuitively speaking, our variant captures choosier choice behavior than the standard multinomial logit model. Accordingly, we show that the revenue-maximizing assortment under our variant includes the revenue-maximizing assortment under the standard multinomial logit model, so choosier behavior leads to larger assortments offered to maximize the expected revenue. We conduct computational experiments on both synthetic and real datasets to demonstrate that incorporating rank cutoffs can yield better predictions of customer choices and yield more profitable assortment recommendations.
Author : Clark Pixton
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (13 download)
Download or read book Branch-and-Bound Algorithms for Assortment Optimization Under Weakly Rational Choice written by Clark Pixton and published by . This book was released on 2016 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the static assortment optimization problem under weakly rational choice models, i.e. models in which adding a product to an assortment does not increase the probability of purchasing a product already in that assortment. This setting applies to most choice models studied and used in practice, such as the multinomial logit and random parameters logit models. We give a mixed-integer linear optimization formulation with an exponential number of constraints, and present two branch-and-bound algorithms for solving this optimization problem. The formulation and algorithms require only black-box access to purchase probabilities, and thus provide exact solution methods for a general class of discrete choice models, in particular those models without closed-form choice probabilities. We show that one of our algorithms is a PTAS for assortment optimization under weakly rational choice when the no-purchase probability is small, and give an approximation guarantee for the other algorithm which depends only on the prices of the products. Finally, we test the performance of our algorithms with heuristic stopping criteria, motivated by the fact that they discover the optimal solution very quickly.
Author : Knut Haase
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (129 download)
Download or read book Constrained Assortment Optimization Under the Mixed Logit Model with Design Options written by Knut Haase and published by . This book was released on 2020 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present the constrained assortment optimization problem under the mixed logit model (MXL) with design options and deterministic customer segments. The rationale is to select a subset of products of a given size and decide on the attributes of each product such that a function of market share is maximized. The customer demand is modeled by MXL. We develop a novel mixed-integer non-linear program and solve it by state-of-the-art generic solvers. To reduce variance in sample average approximation systematic numbers are applied instead of pseudo-random numbers. Our numerical results demonstrate that systematic numbers reduce computational effort by 70%. We solve instances up to 20 customer segments, 100 products each with 50 design options yielding 5,000 product-design combinations, and 500 random realizations in under two minutes. Our approach studies the impact of market position, willingness-to-pay, and bundling strategies on the optimal assortment.
Author : Aydin Alptekinoglu
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (13 download)
Download or read book The Exponomial Choice Model written by Aydin Alptekinoglu and published by . This book was released on 2015 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the use of a canonical version of a discrete choice model due to Daganzo (1979) in optimal pricing and assortment planning. In contrast to multinomial and nested logit (the prevailing choice models used for optimizing prices and assortments), this model assumes a negatively skewed distribution of consumer utilities, an assumption we motivate by conceptual arguments as well as published work. The choice probabilities in this model can be derived in closed-form as an exponomial (a linear function of exponential terms). The pricing and assortment planning insights we obtain from the Exponomial Choice (EC) model differ from the literature in two important ways. First, the EC model allows variable markups in optimal prices that increase with expected utilities. Second, when prices are exogenous, the optimal assortment may exhibit leapfrogging in prices, i.e., a product can be skipped in favor of a lower-priced one depending on the utility positions of neighboring products. These two plausible pricing and assortment patterns are ruled out by multinomial logit (and by nested logit within each nest). We provide structural results on optimal pricing for monopoly and oligopoly cases, and on the optimal assortments for both exogenous and endogenous prices. We also demonstrate how the EC model can be easily estimated--by establishing that the loglikelihood function is concave in model parameters and detailing an estimation example using real data.
Author : Chenhao Wang
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book When Advertising Meets Assortment Planning written by Chenhao Wang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although assortment optimization has been extensively studied, not much is known about how it is affected by advertising. In this paper, we address this gap by considering a novel joint advertising and assortment optimization problem. To capture the effect of advertising in the context of assortment planning, we assume that one can increase the preference weight of a product by advertising it, and the degree of improvement is decided by the effectiveness of advertising, which could be product-specific, and the amount of advertising efforts allocated to that product. Given budget constraints on advertising, our objective is to find a solution, which is composed of an advertising strategy and an assortment of products, that maximizes the expected revenue. We analyze the structural properties of this problem and derive effective solutions under different settings. If there is no capacity constraint on the number of products displayed to consumers, we show that revenue-ordered assortments still maintain optimality, and we leverage this result to derive an optimal solution. For the cardinality constrained case, it is difficult to solve the optimization problem directly; therefore, we show by relaxation that a near-optimal solution can be found efficiently.
Author : Hai Jiang
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (13 download)
Download or read book Multiproduct Price Optimization Under the Multilevel Nested Logit Model written by Hai Jiang and published by . This book was released on 2014 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the multiproduct price optimization problem under the multilevel nested logit model, which includes the multinomial logit and the two-level nested logit models as special cases. When the price sensitivities are identical within each primary nest, that is, within each nest at level 1, we prove that the profit function is concave with respect to the market share variables. We proceed to show that the markup, defined as price minus cost, is constant across products within each primary nest, and that the adjusted markup, defined as price minus cost minus the reciprocal of the product between the scale parameter of the root nest and the price-sensitivity parameter of the primary nest, is constant across primary nests at optimality. This allows us to reduce this multidimensional pricing problem to an equivalent single-variable maximization problem involving a unimodal function. Based on these findings, we investigate the oligopolistic game and characterize the Nash equilibrium. We also develop a dimension reduction technique which can simplify price optimization problems with flexible price-sensitivity structures.
Author : Yicheng Bai
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book Assortment and Price Optimization Under an Endogenous Context-Dependent Multinomial Logit Model written by Yicheng Bai and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by empirical evidence that the utility of each product depends on the assortment of products offered along with it, we propose an endogenous context-dependent multinomial logit model (Context-MNL) under which the utility of each product depends on both the product's intrinsic value and the deviation of the intrinsic value from the expected maximum utility among all the products in the offered assortment. Under the Context-MNL model, an assortment provides a context in which customers evaluate the utility of each product. Our model generalizes the standard multinomial logit model and allows the utility of each product to depend on the offered assortment. The model is parsimonious, requires only one parameter more than the standard multinomial logit model, captures the assortment-dependent effect endogenously, and does~not require the decision-maker to determine in advance the relevant attributes of the assortment that might affect the product utility. The Context-MNL model also admits tractable maximum likelihood estimation and is operationally tractable, with efficient solution methods for solving assortment and price optimization problems. Our numerical study, which is based on data from Expedia, shows that compared to the standard multinomial logit model, the Context-MNL model substantially improves out-of-sample goodness of fit and prediction accuracy.
Author : Shuting Shen
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models written by Shuting Shen and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assortment optimization has received active explorations in the past few decades due to its practical importance. Despite the extensive literature dealing with optimization algorithms and latent score estimation, uncertainty quantification for the optimal assortment still needs to be explored and is of great practical significance. Instead of estimating and recovering the complete optimal offer set, decision-makers may only be interested in testing whether a given property holds true for the optimal assortment, such as whether they should include several products of interest in the optimal set, or how many categories of products the optimal set should include. This paper proposes a novel inferential framework for testing such properties. We consider the widely adopted multinomial logit (MNL) model, where we assume that each customer will purchase an item within the offered products with a probability proportional to the underlying preference score associated with the product. We reduce inferring a general optimal assortment property to quantifying the uncertainty associated with the sign change point detection of the marginal revenue gaps. We show the asymptotic normality of the marginal revenue gap estimator, and construct a maximum statistic via the gap estimators to detect the sign change point. By approximating the distribution of the maximum statistic with multiplier bootstrap techniques, we propose a valid testing procedure. We also conduct numerical experiments to assess the performance of our method.
