Assortment Planning and Inventory Decisions under Stockout-Based Substitution PDF Download
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Author: Dorothee Honhon
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Languages : en
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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: 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: Jingwei Zhang
Publisher:
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Category :
Languages : en
Pages : 0
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We study the joint assortment and inventory planning problem with stockout-based substitution. In this problem, we pick the number of units to stock for the products at the beginning of the selling horizon. Each arriving customer makes a choice among the set of products with remaining on-hand inventories. Our goal is to pick the stocking quantities to maximize the total expected revenue from the sales net of the stocking cost. Using a fluid approximation for the problem, we give solutions with performance guarantees that significantly improve earlier results. Letting $T$ be the number of time periods in the selling horizon and $n$ be the number of products, when customers choose under a general choice model, we show that we can round the solution to the fluid approximation to obtain stocking quantities with an optimality gap of $O(n + sqrt{nT})$, improving earlier optimality gaps by a logarithmic factor. More importantly, when customers choose under the multinomial logit model, we develop a rounding scheme that uses the solution to the fluid approximation to generate stocking quantities with an optimality gap of $O( log T sqrt{T log T})$. The optimality gap that we give under the multinomial logit model is the first one that does not depend on the number of products. Such an optimality gap has important implications in the many-products regime. Earlier results cannot guarantee that the stocking quantities generated by the fluid approximation perform well when both the demand volume and number of products are large, which is a regime becoming more relevant for online retail applications with large product variety. In contrast, we can guarantee that the stocking quantities generated by our rounding scheme perform well when both the demand volume and number of products are large.
Author: Alys Jiaxin Liang
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Languages : en
Pages : 0
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We consider a deterministic (fluid) multi-period assortment and inventory planning problem under the Multinomial Logit (MNL) choice model with dynamic (stockout-based) substitution, customer returns with a general return time distribution, and a cumulative capacity (storage) constraint for all products. Specifically, there is a one-time inventory decision at the beginning of the selling horizon and a customer who makes a purchase in the current period is allowed to return the purchase at a future period. The returned item will be inspected and, if it passes the inspection, it will be restocked and becomes available again for sale in the next period. The objective of the firm is to identify the initial inventories of the products that maximize the total profit throughout the horizon. Due to the dynamics created by the dynamic substitution and customer returns, this is a technically challenging problem to solve. Unlike in the setting without returns where a product will no longer be available throughout the remaining periods after it stocks out, in the presence of returns, a product could again be available due to restocked returns and may even stock out again, and this cycle might continue for several times depending on the availability of other products. We focus on the fluid version of this problem and develop a linear program (LP)-based approach to exactly solve this problem. If the LP has a unique optimal solution, then this solution is also an optimal solution to our problem. If, however, the LP does not have a unique optimal solution, an arbitrary optimal solution of the LP may not be feasible for our problem. To deal with this scenario, we develop an algorithm using which, given any optimal LP solution, we can construct an alternative optimal LP solution that is also optimal for our problem. The algorithm uses both primal and dual LP solutions together with exploiting some key structural properties of the problem. We visualize our approach using illustrative examples.
Author: Omar El Housni
Publisher:
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Category :
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: Vishal Gaur
Publisher:
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Category :
Languages : en
Pages :
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We consider a single-period assortment planning and inventory management problem for aretailer, using a locational choice model to represent consumer demand. We first determinethe optimal variety, product location, and inventory decisions under static substitution, andshow that the optimal assortment consists of products equally spaced out such that there is nosubstitution among them regardless of the distribution of consumer preferences. The optimalsolution can be such that some customers prefer not to buy any product in the assortment, andsuch that the most popular product is not offered.We then obtain bounds on profit when customers dynamically substitute, using the staticsubstitution for the lower bound, and a retailer-controlled substitution for the upper bound.We thus define two heuristics to solve the problem under dynamic substitution, and numericallyevaluate their performance. This analysis shows the value of modeling dynamic substitution andidentifies conditions in which the static substitution solution serves as a good approximation.
Author: Joonkyum Lee
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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We demonstrate the value of utility-based choice models to estimate demand and plan inventory for new and used textbooks in the presence of consumer choice and stockout-based substitution at a university textbook retailer. Demand information is censored, the exact time of stockout is not observed, and the short selling season often does not allow for replenishment. Using data for 26,749 book titles from 2007 to 2011 and a simulation experiment calibrated on real data, we show that an attribute-based choice model generates accurate demand estimates (mean absolute percentage error less than 1%) even when nearly 90% of the textbooks in the fit sample experience stockout. This performance is driven by the heterogeneity of product attributes and is robust to the occurrence of product returns. We implement this model at the bookstore in a controlled field experiment and obtain over 10% increase in profit. The results show that accounting for asymmetric and stockout-based substitution in demand estimation and inventory planning enables us to make systematic corrections in inventory mix and inventory level compared to the existing process.
Author: Vineet Goyal
Publisher:
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Category :
Languages : en
Pages : 0
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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: Ying Cao (Ph. D.)
Publisher:
ISBN:
Category : Advertising
Languages : en
Pages :
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Book Description
This dissertation consists of three essays which study assortment planning and inventory management of substitutable products motivated by different practical problems. Chapter 2 considers the assortment planning problem for a retailer who faces customers that buy multiple differentiated products (n-pack) on a store visit. We develop two choice models: the probabilistic choice rule which captures the heterogeneous consumer population choice pattern and maximum choice rule which captures the homogeneous consumer population choice pattern. We find that, under probabilistic choice rule, the optimal assortment is such that it includes a certain number of the most and least popular products. In contrast, under maximum choice rule, the optimal assortment does not have a fixed structure except that it is guaranteed to include the most popular product. We develop an algorithm under maximum choice rule which is shown to have good performance. In addition, we derive the structure of optimal assortment under both choice rules when a retailer ignores key features of n-pack choice model including choice premium and basket shopping behavior. We also conduct a numerical study where we show that ignoring these key features can lead to significant profit loss for a retailer. Chapter 3 explores the assortment planning for a firm who faces a two-sided market. That is, the firm receives revenues from two distinct user groups: the customers, who pay for the products it sells and the advertisers who pay to advertise their brand to the customers. We obtain structural properties of the optimal assortment. We also consider the case where the firm is allowed to offer multiple products with the same attractiveness profile and price. In this case, we obtain conditions under which the optimal assortment is made out of distinct products. In addition, we show that ignoring the revenue from the customers or the advertisers, or focusing only on one segment when making product assortment decisions can lead to a significant revenue loss; specifically, we derive the theoretical bound on revenue loss in these situations. Chapter 4 studies the decision making of an inventory manager who needs to decide order quantities of multiple substitutable products in his store. As such, the decision maker typically checks the sales history of the products. When there is stock-out, the sales history provides inaccurate information because the lost sales are unobservable and the sales from substitution are indistinguishable from first-choice sales, which we refer to as the "doublecensoring effect". To study the impact of substitution rate and information amount on decision maker's performance, we design an experiment where subjects need to decide inventory levels for 2 substitutable products in consecutive 30 periods. The experimental data shows that subjects underestimate the demand for high demand product and overestimate the demand for low demand product. Moreover, the bias is worse when there is substitution in fully censored information treatment. Also, when subjects are provided with less information, they tend to order larger quantity in early periods in order to learn demand.
Author: J. Christian Lang
Publisher: Springer Science & Business Media
ISBN: 3642042473
Category : Business & Economics
Languages : en
Pages : 271
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Book Description
Quantitativeapproachesforsolvingproductionplanningandinventorymanagement problems in industry have gained growing importance in the past years. Due to the increasinguse of AdvancedPlanningSystems, a widespreadpracticalapplicationof the sophisticated optimization models and algorithms developed by the Production Management and Operations Research community now seem within reach. The possibility that productscan be replaced by certain substitute productsexists in various application areas of production planning and inventory management. Substitutions can be useful for a number of reasons, among others to circ- vent production and supply bottlenecks and disruptions, increase the service level, reduce setup costs and times, and lower inventories and thereby decrease ca- tal lockup. Considering the current trend in industry towards shorter product life cycles and greater product variety, the importance of substitutions appears likely to grow. Closely related to substitutions are ?exible bills-of-materials and recipes in multi-level production systems. However, so far, the aspect of substitutions has not attracted much attention in academic literature. Existing lot-sizing models matching complex requirements of industrial optimization problems (e.g., constrained capacities, sequence-dependent setups, multiple resources) such as the Capacitated Lot-Sizing Problem with Sequence-Dependent Setups (CLSD) and the General Lot-Sizing and Scheduling Problem for Multiple Production Stages (GLSPMS) do not feature in substitution options.
Author: Jing-Sheng J. Song
Publisher: Edward Elgar Publishing
ISBN: 180037710X
Category : Technology & Engineering
Languages : en
Pages : 565
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Book Description
This comprehensive Handbook provides an overview of state-of-the-art research on quantitative models for inventory management. Despite over half a century’s progress, inventory management remains a challenge, as evidenced by the recent Covid-19 pandemic. With an expanse of world-renowned inventory scholars from major international research universities, this Handbook explores key areas including mathematical modelling, the interplay of inventory decisions and other business decisions and the unique challenges posed to multiple industries.
