Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Assortment Optimization Under A Single Transition Model
Download Assortment Optimization Under A Single Transition Model full books in PDF, epub, and Kindle. Read online Assortment Optimization Under A Single Transition Model ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Assortment Optimization Under a Single Transition Model by : Kameng Nip
Download or read book Assortment Optimization Under a Single Transition Model written by Kameng Nip and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider a new customer choice model which we call the single transition choice model. In this model, there is a universe of products and customers arrive at each product with a certain probability. If the arrived product is unavailable, then the seller can recommend a subset of available products to the customer and the customer will purchase one of the recommended products or choose not to purchase with certain transition probabilities. The distinguishing features of the model are that the seller can control which products to recommend depending on the arrived product and that each customer either purchases a product or leaves the market after one transition.We study the assortment optimization problem under this model. Particularly, we show that this problem is NP-Hard even if the customer can transition from each product to at most two products. Despite the complexity of the problem, we provide polynomial time algorithms or approximation algorithms for several special cases, such as when the customer can only transition from each product to at most a given number of products and the size of each recommended set is at most a given number. We also provide a tight worst-case performance bound for revenue-ordered assortments. In addition, we propose a compact mixed integer program formulation for this problem, which is efficient for problems of moderate size. Finally, we conduct numerical experiments to demonstrate the effectiveness of the proposed algorithms.
Book Synopsis Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model by : Shukai Li
Download or read book Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model written by Shukai Li and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study a dynamic assortment selection problem where arriving customers make purchase decisions among offered products from a universe of $N$ products under a Markov-chain-based choice (MCBC) model. The retailer observes only the assortment and the customer's single choice per period. Given limited display capacity, resource constraints, and no a priori knowledge of problem parameters, the retailer's objective is to sequentially learn the choice model and optimize cumulative revenues over a selling horizon of length $T$. We develop an explore-then-exploit learning algorithm that balances the trade-off between exploration and exploitation. The algorithm can simultaneously estimate the arrival and transition probabilities in the MCBC model by solving linear equations and determining the near-optimal assortment based on these estimates. Furthermore, compared to existing heuristic estimation methods that suffer from inconsistency and a large computational burden, our consistent estimators enjoy superior computational times.
Book Synopsis Capacity Constrained Assortment Optimization Under the Markov Chain Based Choice Model by : Antoine Désir
Download or read book Capacity Constrained Assortment Optimization Under the Markov Chain Based Choice Model written by Antoine Désir and published by . This book was released on 2015 with total page 33 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 such settings, the goal is to select a subset of items to offer from a universe of substitutable items in order to maximize expected revenue when consumers exhibit a random substitution behavior. We consider a capacity constrained assortment optimization problem under the Markov Chain based choice model, recently considered by Blanchet et al. (2013). In this model, the substitution behavior of customers is modeled through transitions in a Markov chain. Capacity constraints arise naturally in many applications to model real-life constraints such as shelf space or budget limitations. We show that the capacity constrained problem is APX-hard even for the special case when all items have unit weights and uniform prices, i.e., it is NP-hard to obtain an approximation ratio better than some given constant. We present constant factor approximations for both the cardinality and capacity constrained assortment optimization problem for the general Markov chain model. Our algorithm is based on a "local-ratio" paradigm that allows us to transform a non-linear revenue function into a linear function. The local-ratio based algorithmic paradigm also provides interesting insights towards the optimal stopping problem as well as other assortment optimization problems.
Book Synopsis Robust Assortment Optimization Under the Markov Chain Model by : Antoine Désir
Download or read book Robust Assortment Optimization Under the Markov Chain Model written by Antoine Désir and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assortment optimization arises widely in many practical applications such as retailing and online advertising. In this problem, the goal is to select a subset from a universe of substitutable products to offer customers in order to maximize the expected revenue. We study a robust assortment optimization problem under the Markov chain choice model. In this formulation, the parameters of the choice model are assumed to be uncertain and the goal is to maximize the worst-case expected revenue over all parameter values in an uncertainty set. Our main contribution is to prove a min-max duality result when the uncertainty set is row-wise. The result is surprising as the objective function does not satisfy the properties usually needed for known min-max results. Inspired by the duality result, we develop an efficient iterative algorithm for computing the optimal robust assortment under the Markov chain choice model. Moreover, our results yield operational insights into the effect of changing the uncertainty set on the optimal robust assortment. In particular, consistent with previous literature, we find that bigger uncertainty sets always lead to bigger assortments, and a firm should offer larger assortments to hedge against uncertainty.
Book Synopsis Assortment Optimization Under the Multivariate MNL Model by : Xin Chen
Download or read book Assortment Optimization Under the Multivariate MNL Model written by Xin Chen and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study an assortment optimization problem under a multi-purchase choice model in which customers choose a bundle of up to one product from each of two product categories. Different bundles have different utilities and the bundle price is the summation of the prices of products in it. For the uncapacitated setting where any set of products can be offered, we prove that this problem is strongly NP-hard. We show that an adjusted-revenue-ordered assortment provides a 1/2-approximation. Furthermore, we develop an approximation framework based on a linear programming relaxation of the problem and obtain a 0.74-approximation algorithm. This approximation ratio almost matches the integrality gap of the linear program, which is proven to be at most 0.75. For the capacitated setting, we prove that there does not exist a constant-factor approximation algorithm assuming the Exponential Time Hypothesis. The same hardness result holds for settings with general bundle prices or more than two categories. Finally, we conduct numerical experiments on randomly generated problem instances. The average approximation ratios of our algorithms are over 99%.
Book Synopsis Branch-and-Bound Algorithms for Assortment Optimization Under Weakly Rational Choice by : Clark Pixton
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.
Book Synopsis New Bounds for Assortment Optimization Under the Nested Logit Model by : Sumit Kunnumkal
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.
Book Synopsis Capacitated Assortment Optimization by : Antoine Désir
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.
Book Synopsis An Exact Method for Assortment Optimization Under the Nested Logit Model by : Laurent Alfandari
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.
Book Synopsis Assortment Optimization Under the Multinomial Logit Model with Utility-Based Rank Cutoffs by : Jacob Feldman
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.
Book Synopsis Capacitated Assortment and Price Optimization Under the Multinomial Logit Model by : Ruxian Wang
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.
Book Synopsis Assortment Optimization Under Multiple-Discrete Customer Choices by : Heng Zhang
Download or read book Assortment Optimization Under Multiple-Discrete Customer Choices written by Heng Zhang and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an assortment optimization problem where the customer may purchase multiple products and possibly more than one unit of each product purchased. We adopt the customer consumption model based on the Multiple-Discrete-Choice (MDC) model proposed by Huh and Li (2021). We identify conditions under which the profit-ordered sets are optimal. Without these conditions, we show that assortment optimization is NP-hard. Furthermore, we prove that a generalization of the profit-ordered sets achieves an approximation guarantee of 1/2. We also present an algorithm that computes an epsilon-optimal solution to the assortment problem in running time polynomial in 1/epsilon and the problem input size, once we impose the mild technical assumption that model parameters are bounded.
Book Synopsis Constrained Assortment Optimization Under the Mixed Logit Model with Design Options by : Knut Haase
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.
Book Synopsis When Advertising Meets Assortment Planning by : Chenhao Wang
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.
Book Synopsis Assortment Optimization and Pricing Under the Threshold-Based Choice Models by : Xu Tian
Download or read book Assortment Optimization and Pricing Under the Threshold-Based Choice Models written by Xu Tian and published by . This book was released on 2020 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we study revenue maximization assortment and pricing problems under threshold-based choice models, where a product is placed in a consumer's consideration set if its utility to the consumer exceeds the utility of an outside option by a specified threshold. We discuss two such models: the relative utility and absolute utility threshold-based choice models. For both models, the best revenue-ordered assortment and same-price policy can not achieve the optimal profit for the assortment problem or the pricing problem. Further, the revenue-maximizing assortment problem is NP-complete or NP-hard. However, we show that a performance guarantee relative to the optimal policy can be found for each model: for the relative utility model, by employing the best revenue-ordered assortment and same-price policy; for the absolute utility model, via a dynamic-program-based algorithm and a same-price policy. Finally, we show that our algorithms can be asymptotically optimal if the search cost of consumers is sufficiently small.
Book Synopsis Assortment Optimization Under Consider-Then-Choose Choice Models by : Ali Aouad
Download or read book Assortment Optimization Under Consider-Then-Choose Choice Models written by Ali Aouad and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider-then-choose models, borne out by empirical literature in marketing and psychology, explain that customers choose among alternatives in two phases, by first screening products to decide which alternatives to consider, before then ranking them. In this paper, we develop a dynamic programming framework to study the computational aspects of assortment optimization models posited on consider-then-choose premises. Although ranking-based choice models generally lead to computationally intractable assortment optimization problems, we are able to show that for many practical and empirically vetted assumptions on how customers consider and choose, the resulting dynamic program is efficient. Our approach unifies and subsumes several specialized settings analyzed in previous literature. Empirically, we demonstrate the versatility and predictive power of our modeling approach on a combination of synthetic and real industry datasets, where prediction errors are significantly reduced against common parametric choice models. In synthetic experiments, our algorithms lead to practical computation schemes that outperform a state-of-the-art integer programming solver in terms of running time, in several parameter regimes of interest.
Book Synopsis The Approximability of Assortment Optimization Under Ranking Preferences by : Ali Aouad
Download or read book The Approximability of Assortment Optimization Under Ranking Preferences written by Ali Aouad and published by . This book was released on 2018 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
