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Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
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.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 20
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Book Description
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.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Book Description
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.
Author: Jens Vygen
Publisher: Springer Nature
ISBN: 3031598350
Category :
Languages : en
Pages : 474
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Author: Jacob Feldman
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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: Xin Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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%.
Author: Laurent Alfandari
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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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: Xujin Chen
Publisher: Springer Nature
ISBN: 3030649466
Category : Computers
Languages : en
Pages : 476
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Book Description
This book constitutes the proceedings of the 16th International Conference on Web and Internet Economics, WINE 2020, held in Beijing, China, in December 2020. The 31 full papers presented together with 11 abstracts were carefully reviewed and selected from 136 submissions. The issues in theoretical computer science, artificial intelligence, operations research are of particular importance in the Web and the Internet that enable the interaction of large and diverse populations. The Conference on Web and Internet Economics (WINE) is an interdisciplinary forum for the exchange of ideas and results on incentives and computation arising from these various fields.
Author: Antoine Désir
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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: Chenhao Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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: Kameng Nip
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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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.
