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Author: Yong Liang
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Languages : en
Pages : 0
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Book Description
We study an online joint assortment-inventory optimization problem, in which we assume that the choice behavior of each customer follows the Multinomial Logit (MNL) choice model, and the attraction parameters are unknown a priori. The retailer makes periodic assortment and inventory decisions to dynamically learn from the realized demands about the attraction parameters while maximizing the expected total profit over time. In this paper, we propose a novel algorithm that can effectively balance the exploration and exploitation in the online decision-making of assortment and inventory. Our algorithm builds on a new estimator for the MNL attraction parameters, a novel approach to incentivize exploration by adaptively tuning certain known and unknown parameters, and an optimization oracle to static single-cycle assortment-inventory planning problems with given parameters. We establish a regret upper bound for our algorithm and a lower bound for the online joint assortment-inventory optimization problem, suggesting that our algorithm achieves nearly optimal regret rate, provided that the static optimization oracle is exact. Then we incorporate more practical approximate static optimization oracles into our algorithm, and bound from above the impact of static optimization errors on the regret of our algorithm. At last, we perform numerical studies to demonstrate the effectiveness of our proposed algorithm.
Author: Yong Liang
Publisher:
ISBN:
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Languages : en
Pages : 0
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Book Description
We study an online joint assortment-inventory optimization problem, in which we assume that the choice behavior of each customer follows the Multinomial Logit (MNL) choice model, and the attraction parameters are unknown a priori. The retailer makes periodic assortment and inventory decisions to dynamically learn from the realized demands about the attraction parameters while maximizing the expected total profit over time. In this paper, we propose a novel algorithm that can effectively balance the exploration and exploitation in the online decision-making of assortment and inventory. Our algorithm builds on a new estimator for the MNL attraction parameters, a novel approach to incentivize exploration by adaptively tuning certain known and unknown parameters, and an optimization oracle to static single-cycle assortment-inventory planning problems with given parameters. We establish a regret upper bound for our algorithm and a lower bound for the online joint assortment-inventory optimization problem, suggesting that our algorithm achieves nearly optimal regret rate, provided that the static optimization oracle is exact. Then we incorporate more practical approximate static optimization oracles into our algorithm, and bound from above the impact of static optimization errors on the regret of our algorithm. At last, we perform numerical studies to demonstrate the effectiveness of our proposed algorithm.
Author: Omar El Housni
Publisher:
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Languages : en
Pages : 0
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We study a joint assortment and inventory optimization problem faced by an online retailer who needs to decide on both the assortment along with the inventories of a set of N substitutable products before the start of the selling season to maximize the expected profit. The problem raises both algorithmic and modeling challenges. One of the main challenges is to tractably model dynamic stock-out based substitution where a customer may substitute to the most preferred product that is available if their first choice is not offered or stocked-out. We first consider the joint assortment and inventory optimization problem for a Markov Chain choice model and present a near-optimal algorithm for the problem. Our results significantly improve over the results in Gallego and Kim (2020) where the regret can be linear in T (where T is the number of customers) in the worst case.We build upon their approach and give an algorithm with regret Õ( sqrt{NT}) with respect to an LP upper bound. Our algorithm achieves a good balance between expected revenue and inventory costs by identifying a subset of products that can pool demand from the universe of substitutable products without significantly cannibalizing the revenue in the presence of dynamic substitution behavior of customers. We also present a multi-step choice model that captures the complex choice process in an online retail setting characterized by a large universe of products and a heavy-tailed distribution of mean demands. Our model captures different steps of the choice process including search, formation of a consideration set and eventual purchase. We conduct computational experiments that show that our algorithm empirically outperforms previous approaches both on synthetic and realistic instances.
Author: Mohammed Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 256
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Finding optimal product offerings is a fundamental operational issue in modern retailing, exemplified by the development of recommendation systems and decision support tools. The challenge is that designing an accurate predictive choice model generally comes at the detriment of efficient algorithms, which can prescribe near-optimal decisions. This thesis attempts to resolve this disconnect in the context of assortment and inventory optimization, through theoretical and empirical investigation. First, we tightly characterize the complexity of general nonparametric assortment optimization problems. We reveal connections to maximum independent set and combinatorial pricing problems, allowing to derive strong inapproximability bounds. We devise simple algorithms that achieve essentially best-possible factors with respect to the price ratio, size of customers' consideration sets, etc. Second, we develop a novel tractable approach to choice modeling, in the vein of nonparametric models, by leveraging documented assumptions on the customers' consider-then-choose behavior. We show that the assortment optimization problem can be cast as a dynamic program, that exploits the properties of a bi-partite graph representation to perform a state space collapse. Surprisingly, this exact algorithm is provably and practically efficient under common consider-then-choose assumptions. On the estimation front, we show that a critical step of standard nonparametric estimation methods (rank aggregation) can be solved in polynomial time in settings of interest, contrary to general nonparametric models. Predictive experiments on a large purchase panel dataset show significant improvements against common benchmarks. Third, we turn our attention to joint assortment optimization and inventory management problems under dynamic customer choice substitution. Prior to our work, little was known about these optimization models, which are intractable using modern discrete optimization solvers. Using probabilistic analysis, we unravel hidden structural properties, such as weak notions of submodularity. Building on these findings, we develop efficient and yet conceptually-simple approximation algorithms for common parametric and nonparametric choice models. Among notable results, we provide best-possible approximations under general nonparametric choice models (up to lower-order terms), and develop the first constant-factor approximation under the popular Multinomial Logit model. In synthetic experiments vis-a-vis existing heuristics, our approach is an order of magnitude faster in several cases and increases revenue by 6% to 16%.
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: 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: Xue Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 62
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In this research, we consider an online assortment optimization problem, where a decision-maker needs to sequentially offer assortments to users instantaneously upon their arrivals and users select products from offered assortments according to the contextual multinomial logit choice model. We propose a computationally efficient Lasso-RP-MNL algorithm for the online assortment optimization problem under the cardinality constraint in high-dimensional settings. The Lasso-RP-MNL algorithm combines the Lasso and random projection as dimension reduction techniques to alleviate the computational complexity and improve the learning and estimation accuracy under high-dimensional data with limited samples. For each arriving user, the Lasso-RP-MNL algorithm constructs an upper-confidence bound for each individual product's attraction parameter, based on which the optimistic assortment can be identified by solving a reformulated linear programming problem. We demonstrate that for the feature dimension $d$ and the sample size dimension $T$, the expected cumulative regret under the Lasso-RP-MNL algorithm is upper bounded by $ tilde{ mathcal{O}}( sqrt{T} log d)$ asymptotically, where $ tilde{ mathcal{O}}$ suppresses the logarithmic dependence on $T$. Furthermore, we show that even when available samples are extremely limited, the Lasso-RP-MNL algorithm continues to perform well with a regret upper bound of $ tilde{ mathcal{O}}( T^{ frac{2}{3}} log d)$. Finally, through synthetic-data-based experiments and a high-dimensional XianYu assortment recommendation experiment, we show that the Lasso-RP-MNL algorithm is computationally efficient and outperforms other benchmarks in terms of the expected cumulative regret.
Author: Srikanth Jagabathula
Publisher:
ISBN:
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Languages : en
Pages : 51
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We consider the key operational problem of optimizing the mix of offered products to maximize revenues when product prices are exogenously set and product demand follows a general discrete choice model. The key challenge in making this decision is the computational difficulty of finding the best subset, which often requires exhaustive search. Existing approaches address the challenge by either deriving efficient algorithms for specific parametric structures or studying the performance of general-purpose heuristics. The former approach results in algorithms that lack portability to other structures; whereas the latter approach has resulted in algorithms with poor performance. We study a portable and easy-to-implement local search heuristic. We show that it efficiently finds the global optimum for the multinomial logit (MNL) model and derive performance guarantees for general choice structures. Empirically, it is better than prevailing heuristics when no efficient algorithms exist, and it is within 0.02% of optimality otherwise.
Author: Ali Aouad
Publisher:
ISBN:
Category :
Languages : en
Pages : 57
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Book Description
In this paper, we consider the yet-uncharted assortment optimization problem under the Exponomial choice model, where the objective is to determine the revenue maximizing set of products that should be offered to customers. Our main algorithmic contribution comes in the form of a fully polynomial-time approximation scheme (FPTAS), showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. This result is obtained through a synthesis of ideas related to approximate dynamic programming, that enable us to derive a compact discretization of the continuous state space by keeping track of several key statistics in "rounded" form throughout the overall computation. Consequently, we obtain the first provably-good algorithm for assortment optimization under the Exponomial choice model, which is complemented by a number of hardness results for natural extensions. We show in computational experiments that our solution method admits an efficient implementation, based on additional pruning criteria.Furthermore, we conduct empirical evaluations of the Exponomial choice model. We present a number of case studies using real-world data sets, spanning retail, online platforms, and transportation. We focus on a comparison with the popular Multinomial Logit choice model (MNL), which is largely dominant in the choice modeling practice, as both models share a simple parametric structure with desirable statistical and computational properties. We identify several settings where the Exponomial choice model has better predictive accuracy than MNL and leads to more profitable assortment decisions. We provide implementation guidelines and insights about the performance of the Exponomial choice model relative to MNL.
Author: Nita H. Shah
Publisher: Springer Nature
ISBN: 9811396981
Category : Business & Economics
Languages : en
Pages : 470
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Book Description
This book discusses inventory models for determining optimal ordering policies using various optimization techniques, genetic algorithms, and data mining concepts. It also provides sensitivity analyses for the models’ robustness. It presents a collection of mathematical models that deal with real industry scenarios. All mathematical model solutions are provided with the help of various optimization techniques to determine optimal ordering policy. The book offers a range of perspectives on the implementation of optimization techniques, inflation, trade credit financing, fuzzy systems, human error, learning in production, inspection, green supply chains, closed supply chains, reworks, game theory approaches, genetic algorithms, and data mining, as well as research on big data applications for inventory management and control. Starting from deterministic inventory models, the book moves towards advanced inventory models. The content is divided into eight major sections: inventory control and management – inventory models with trade credit financing for imperfect quality items; environmental impact on ordering policies; impact of learning on the supply chain models; EOQ models considering warehousing; optimal ordering policies with data mining and PSO techniques; supply chain models in fuzzy environments; optimal production models for multi-items and multi-retailers; and a marketing model to understand buying behaviour. Given its scope, the book offers a valuable resource for practitioners, instructors, students and researchers alike. It also offers essential insights to help retailers/managers improve business functions and make more accurate and realistic decisions.
Author: Chengzhang Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 51
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Book Description
We study the problem of jointly optimizing the price and order quantity for a perishable product, also known as the pricing-newsvendor problem. We consider the case with demand ambiguity where the demand is a function of the price and an uncertain factor, of which only the support information is known. We employ the minimax regret decision criterion to minimize the worst-case regret, which is defined as the difference between the optimal profit that could be obtained with perfect information and the realized profit using the decision made with ambiguous information. First, we characterize the optimal pricing and ordering decisions under the minimax regret criterion and compare their properties with those in the classical models that seek to maximize the expected profit. Specifically, we explore the impact of inventory risk by comparing the optimal price and the risk-free price, and study comparative statics with respect to the degree of demand ambiguity and the unit ordering cost. Second, we compare the minimax regret approach with two other approaches that are commonly used under demand ambiguity, namely the max-min robust approach and the regression-based data-driven approach. In the demand ambiguity setting, we show that the minimax regret approach avoids the high degree of conservativeness that is often incurred in the max-min approach. In the data-driven setting, we show via a numerical study that the minimax regret approach outperforms the classical regression-based approach when data is scarce, when the demand has high volatility, or when the demand model is misspecified.
