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Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Book Description
We study the joint assortment planning and inventory management problem, where stock-out events elicit dynamic substitution effects, described by the Multinomial Logit (MNL) choice model. Special cases of this setting have extensively been studied in recent literature, notably the static assortment planning problem. Nevertheless, the general formulation is not known to admit efficient algorithms with analytical performance guarantees prior to this work, and most of its computational aspects are still wide open.In this paper, we devise the first provably-good approximation algorithm for dynamic assortment planning under the MNL model, attaining a constant-factor guarantee for a broad class of demand distributions, that satisfy the increasing failure rate property. Our algorithm relies on a combination of greedy procedures, where stocking decisions are restricted to specific classes of products and the objective function takes modified forms. We demonstrate that our approach substantially outperforms state-of-the-art heuristic methods in terms of performance and speed, leading to an average revenue gain of 4% to 12% in computational experiments. In the course of establishing our main result, we develop new algorithmic ideas that may be of independent interest. These include weaker notions of submodularity and monotonicity, shown sufficient to obtain constant-factor worst-case guarantees, despite using noisy estimates of the objective function.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 58
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Book Description
We study the joint assortment planning and inventory management problem, where stock-out events elicit dynamic substitution effects, described by the Multinomial Logit (MNL) choice model. Special cases of this setting have extensively been studied in recent literature, notably the static assortment planning problem. Nevertheless, the general formulation is not known to admit efficient algorithms with analytical performance guarantees prior to this work, and most of its computational aspects are still wide open.In this paper, we devise the first provably-good approximation algorithm for dynamic assortment planning under the MNL model, attaining a constant-factor guarantee for a broad class of demand distributions, that satisfy the increasing failure rate property. Our algorithm relies on a combination of greedy procedures, where stocking decisions are restricted to specific classes of products and the objective function takes modified forms. We demonstrate that our approach substantially outperforms state-of-the-art heuristic methods in terms of performance and speed, leading to an average revenue gain of 4% to 12% in computational experiments. In the course of establishing our main result, we develop new algorithmic ideas that may be of independent interest. These include weaker notions of submodularity and monotonicity, shown sufficient to obtain constant-factor worst-case guarantees, despite using noisy estimates of the objective function.
Author: Guillermo Gallego
Publisher: Springer
ISBN: 1493996061
Category : Business & Economics
Languages : en
Pages : 336
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Book Description
“There is no strategic investment that has a higher return than investing in good pricing, and the text by Gallego and Topaloghu provides the best technical treatment of pricing strategy and tactics available.” Preston McAfee, the J. Stanley Johnson Professor, California Institute of Technology and Chief Economist and Corp VP, Microsoft. “The book by Gallego and Topaloglu provides a fresh, up-to-date and in depth treatment of revenue management and pricing. It fills an important gap as it covers not only traditional revenue management topics also new and important topics such as revenue management under customer choice as well as pricing under competition and online learning. The book can be used for different audiences that range from advanced undergraduate students to masters and PhD students. It provides an in-depth treatment covering recent state of the art topics in an interesting and innovative way. I highly recommend it." Professor Georgia Perakis, the William F. Pounds Professor of Operations Research and Operations Management at the Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts. “This book is an important and timely addition to the pricing analytics literature by two authors who have made major contributions to the field. It covers traditional revenue management as well as assortment optimization and dynamic pricing. The comprehensive treatment of choice models in each application is particularly welcome. It is mathematically rigorous but accessible to students at the advanced undergraduate or graduate levels with a rich set of exercises at the end of each chapter. This book is highly recommended for Masters or PhD level courses on the topic and is a necessity for researchers with an interest in the field.” Robert L. Phillips, Director of Pricing Research at Amazon “At last, a serious and comprehensive treatment of modern revenue management and assortment optimization integrated with choice modeling. In this book, Gallego and Topaloglu provide the underlying model derivations together with a wide range of applications and examples; all of these facets will better equip students for handling real-world problems. For mathematically inclined researchers and practitioners, it will doubtless prove to be thought-provoking and an invaluable reference.” Richard Ratliff, Research Scientist at Sabre “This book, written by two of the leading researchers in the area, brings together in one place most of the recent research on revenue management and pricing analytics. New industries (ride sharing, cloud computing, restaurants) and new developments in the airline and hotel industries make this book very timely and relevant, and will serve as a critical reference for researchers.” Professor Kalyan Talluri, the Munjal Chair in Global Business and Operations, Imperial College, London, UK.
Author: Lijue Lu
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Single-period dynamic assortment planning involves the retailer's decision of selecting a set of products to offer and determining their initial inventory levels, considering stochastic demand and dynamic substitution. The objective is to maximize the expected revenue, subject to a capacity constraint on the total number of stocked products. This problem is notoriously difficult to solve, and existing literature offers effective heuristics. However, these heuristics are primarily designed for small-scale problems faced by brick-and-mortar retailers, where the capacity is generally limited due to shelf-space constraints. In contrast, online retailers often have much larger capacity levels, necessitating novel approaches. In this study, we introduce the first heuristic capable of handling large-scale dynamic assortment planning problems encountered by online retailers. Our approach is able to tackle scenarios with hundreds of thousands of customer arrivals, a capacity of thousands of units, and a wide range of product varieties. Moreover, our algorithm is relatively simple, making it more implementable in practice. To evaluate the effectiveness of our algorithm, we conduct extensive numerical experiments covering various customer types and scenarios. For small-scale problems (maximum of 200 customer arrivals), our approach achieves comparable revenue performance to the state-of-the-art approach while providing a significant speed advantage, being 30 times faster on average. As the problem size increases, the benefits of our algorithm become even more evident. For medium-sized problems (maximum of 1000 customer arrivals), our algorithm outperforms in both revenue and computational speed. While the state-of-the-art approach requires an average of 86 seconds, our algorithm produces superior revenues in just 0.3 seconds, on average. Real-world problems faced by online retailers may involve hundreds of thousands of customer arrivals, further highlighting the need for efficient and effective solutions. To illustrate the practical applicability of our approach, we apply it to a case study based on the online home goods retailer Wayfair. On average, our algorithm returns a solution in less than 80 seconds, while we had to stop the state-of-the-art algorithm after 24 hours. The revenue performance of our approach is on average 2.57 times better than that of the state-of-the-art approach in this case study.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
We study the dynamic assortment planning problem under the widely-utilized Multinomial Logit choice model (MNL). In this single-period assortment optimization and inventory management problem, the retailer jointly decides on an assortment, i.e., a subset of products to be offered, as well as on the inventory levels of these products, aiming to maximize the expected revenue subject to a capacity constraint on the total number of units stocked. The demand process is formed by a stochastic stream of arriving customers, who dynamically substitute between products according to the MNL model. This modeling approach has motivated a growing line of research on joint assortment and inventory optimization, initiated by the seminal papers of Bassok et al. (1999) and Mahajan and van Ryzin (2001). The currently best-known provably-good approximation in the dynamic setting considered, recently devised by Aouad et al. (2018b), leads to an expected revenue of at least 0.139 times the optimum under increasing-failure rate demand distributions, far from being satisfactory in practical revenue management applications. In this paper, we establish novel stochastic inequalities showing that, for any given inventory levels, the expected demand of each offered product is "stable" under basic algorithmic operations, such as scaling the MNL preference weights and shifting inventory across certain products. By exploiting this newly-gained understanding, we devise the first approximation scheme for dynamic assortment planning under the MNL model, allowing one to efficiently compute inventory levels that approach the optimal expected revenue within any degree of accuracy. Our approximation scheme is employed in extensive computational experiments to concurrently measure the performance of various algorithmic practices proposed in earlier literature. These experiments provide further insights regarding the value of dynamic substitution models, in comparison to simple inventory models that overlook stock-out effects, and shed light on their real-life deployability.
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: Chen, Xi
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
We study a family of stylized dynamic assortment planning problems, where for each arriving customer, the seller offers an assortment of substitutable products and customer makes the purchase among offered products according to a discrete choice model. This paper considers two popular choice models -- the multinominal logit model (MNL) and nested logit model. Since all the utility parameters of customers are unknown, the seller needs to simultaneously learn customers' choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or equivalently, to minimize the worst-case expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products N. However, when the number of products N is large as compared to the horizon length T, the accurate estimation of mean utilities is extremely difficult. To deal with the large N case that is natural in many online applications, we propose new policies which completely avoid estimating the utility parameter for each product; and thus our regret is independent of N. In particular, for MNL model, we develop a dynamic trisection search algorithm that achieves the optimal regret (up to a log-factor). For nested logit model, we propose a lower and upper confidence bound algorithm with an aggregated estimation. There are two major advantages of the proposed policies. First, the regret of all our policies has no dependence on N. Second, our policies are almost assumption free: there is no assumption on mean utility nor any "separability'' condition on the expected revenues for different assortments. We also provide numerical results to demonstrate the empirical performance of the proposed methods.
Author: Vineet Goyal
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
Assortment planning of substitutable products is a major operational issue that arises in many industries, such as retailing, airlines and consumer electronics. We consider a single-period joint assortment and inventory planning problem under dynamic substitution with stochastic demands, and provide complexity and algorithmic results as well as insightful structural characterizations of near-optimal solutions for important variants of the problem. First, we show that the assortment planning problem is NP-hard even for a very simple consumer choice model, where each customer is willing to buy only two products. In fact, we show that the problem is hard to approximate within a factor better than 1-1/e. Secondly, we show that for several interesting and practical choice models, one can devise a polynomial-time approximation scheme (PTAS), i.e., the problem can be solved efficiently to within any level of accuracy. To the best of our knowledge, this is the first efficient algorithm with provably near-optimal performance guarantees for assortment planning problems under dynamic substitution. Quite surprisingly, the algorithm we propose stocks only a constant number of different product types; this constant depends only on the desired accuracy level. This provides an important managerial insight that assortments with a relatively small number of product types can obtain almost all of the potential revenue. Furthermore, we show that our algorithm can be easily adapted for more general choice models, and present numerical experiments to show that it performs significantly better than other known approaches.
Author: Danny Segev
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The main contribution of this paper is to develop new techniques in approximate dynamic programming, along with the notions of rounded distributions and inventory filtering, to devise a quasi-PTAS for the capacitated assortment planning problem, originally studied by Goyal, Levi, and Segev (2009). Motivated by real-life applications, their nested preference lists model stands as one of very few settings, where near-optimal assortments and inventory levels can be computed efficiently. However, these findings crucially depend on certain distributional assumptions, leaving the general problem wide open in terms of approximability prior to this work. In addition to proposing the first rigorous approach for handling the nested preference lists model in its utmost generality, from a technical perspective, we augment the existing literature on dynamic programming with a number of promising ideas. These are novel algorithmic tools for efficiently keeping approximate distributions as part of the state description, while losing very little information and while accumulating only small approximation errors throughout the overall computation. From a conceptual perspective, at the cost of losing an eps-factor in optimality, we show how to dramatically improve on the truly exponential nature of standard dynamic programs, which seem essential for the purpose of computing optimal inventory levels.
Author: Dorothee Honhon
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We present an efficient dynamic programming algorithm to determine the optimal assortment and inventory levels in a single-period problem with stockout-based substitution. In our model, total customer demand is random and comprises of a fixed proportion of customers of different types. Customer preferences are modeled through the definition of these types. Each customer type corresponds to a specific preference ordering amongst products. A customer purchases the highest ranked product according to his type (if any) that is available at the time of his visit to the store (stockout-based substitution). We solve the optimal assortment problem using a dynamic programming formulation. We establish structural properties of the value function of the dynamic program that, in particular, help characterize multiple local maxima. We use the properties of the optima to construct a method for efficiently solving the problem in pseudopolynomial time. Our algorithm also gives a heuristic for the general case, i.e., when the proportion of customers of each type is random. In numerical tests, this heuristic performs better and faster than previously known methods, especially when the average demand and the degree of substitutability amongst products are high.
Author: Narendra Agrawal
Publisher: Springer
ISBN: 1489975624
Category : Business & Economics
Languages : en
Pages : 454
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Book Description
This new edition focuses on three crucial areas of retail supply chain management: (1) empirical studies of retail supply chain practices, (2) assortment and inventory planning and (3) integrating price optimization into retail supply chain decisions. The book has been fully updated, expanding on the distinguishing features of the original, while offering three new chapters on recent topics which reflect areas of great interest and relevance to the academic and professional communities alike - inventory management in the presence of data inaccuracies, retail workforce management, and fast fashion retail strategies. The innovations, lessons for practice, and new technological solutions for managing retail supply chains are important not just in retailing, but offer crucial insights and strategies for the ultimate effective management of supply chains in other industries as well. The retail industry has emerged as a fascinating choice for researchers in the field of supply chain management. It presents a vast array of stimulating challenges that have long provided the context of much of the research in the area of operations research and inventory management. However, in recent years, advances in computing capabilities and information technologies, hyper-competition in the retail industry, emergence of multiple retail formats and distribution channels, an ever increasing trend towards a globally dispersed retail network, and a better understanding of the importance of collaboration in the extended supply chain have led to a surge in academic research on topics in retail supply chain management. Many supply chain innovations (e.g., vendor managed inventory) were first conceived and successfully validated in this industry, and have since been adopted in others. Conversely, many retailers have been quick to adopt cutting edge practices that first originated in other industries. Retail Supply Chain Management: Quantitative Models and Empirical Studies, 2nd Ed. is an attempt to summarize the state of the art in this research, as well as offer a perspective on what new applications may lie ahead.
