Showrooming (webrooming) refers to a consumer inspecting a product at a brick-and-mortar/BM (online) retailer before purchasing it from a competing online (BM) retailer. Despite recent adoptions of price-matching and free-shipping policies, show/webrooming remains prevalent. We model different product value information that consumers can learn by visiting a BM retailer and researching an online retailer, and study consumers’ show/webrooming behavior in a unified model. We confirm that consumers can engage in show/webrooming for informational purposes, but webrooming may also be driven by a non-informational purpose. We find that show/webrooming may respectively benefit BM and online retailers; in particular there exist win-win-win outcomes where both retailers and the consumers benefit from show/webrooming. We propose in-store research assistance for BM retailers and customer demonstrator for online retailers and show that these operational strategies may improve the retailers’ competitiveness in the presence of show/webrooming. Our results are found to be robust in several model extensions.
{"title":"Showrooming, Webrooming, and Operational Strategies for Competitiveness","authors":"Chuanya Jiao, Bin Hu","doi":"10.2139/ssrn.3701788","DOIUrl":"https://doi.org/10.2139/ssrn.3701788","url":null,"abstract":"Showrooming (webrooming) refers to a consumer inspecting a product at a brick-and-mortar/BM (online) retailer before purchasing it from a competing online (BM) retailer. Despite recent adoptions of price-matching and free-shipping policies, show/webrooming remains prevalent. We model different product value information that consumers can learn by visiting a BM retailer and researching an online retailer, and study consumers’ show/webrooming behavior in a unified model. We confirm that consumers can engage in show/webrooming for informational purposes, but webrooming may also be driven by a non-informational purpose. We find that show/webrooming may respectively benefit BM and online retailers; in particular there exist win-win-win outcomes where both retailers and the consumers benefit from show/webrooming. We propose in-store research assistance for BM retailers and customer demonstrator for online retailers and show that these operational strategies may improve the retailers’ competitiveness in the presence of show/webrooming. Our results are found to be robust in several model extensions.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132043159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing further generalization of the generalized hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman. The GHE family is constructed by mixing a Generalized Inverse Gaussian (GIG) distribution with an elliptical distribution. We present an innovative theoretical framework where a closed form expression for the tail conditional expectation (TCE) is derived for this new family of distributions. We demonstrate that the GHE family is especially suitable for a heavy - tailed insurance losses data. Our theoretical TCE results are verified for two special cases, Laplace - GIG and Student-t - GIG mixtures. Both mixtures are shown to outperform the GH distribution providing excellent fit to univariate and multivariate insurance losses data. The TCE risk measure computed for the GHE family of distributions provides a more conservative estimator of risk in the extreme tail, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from extreme losses. Our multivariate analysis allows to quantify correlated risks by means of the GHE family: the TCE of the portfolio is decomposed into individual components, representing individual risks in the aggregate loss.
{"title":"A New Class of Generalised Hyper-Elliptical Distributions and Their Applications in Computing Conditional Tail Risk Measures","authors":"Katja Ignatieva, Z. Landsman","doi":"10.2139/ssrn.3757320","DOIUrl":"https://doi.org/10.2139/ssrn.3757320","url":null,"abstract":"This paper introduces a new family of Generalized Hyper-Elliptical (GHE) distributions providing further generalization of the generalized hyperbolic (GH) family of distributions, considered in Ignatieva and Landsman. The GHE family is constructed by mixing a Generalized Inverse Gaussian (GIG) distribution with an elliptical distribution. We present an innovative theoretical framework where a closed form expression for the tail conditional expectation (TCE) is derived for this new family of distributions. We demonstrate that the GHE family is especially suitable for a heavy - tailed insurance losses data. Our theoretical TCE results are verified for two special cases, Laplace - GIG and Student-t - GIG mixtures. Both mixtures are shown to outperform the GH distribution providing excellent fit to univariate and multivariate insurance losses data. The TCE risk measure computed for the GHE family of distributions provides a more conservative estimator of risk in the extreme tail, addressing the main challenge faced by financial companies on how to reliably quantify the risk arising from extreme losses. Our multivariate analysis allows to quantify correlated risks by means of the GHE family: the TCE of the portfolio is decomposed into individual components, representing individual risks in the aggregate loss.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121678552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Markov decision processes (MDPs) provide a powerful framework for analyzing dynamic decision making. However, their applications are significantly hindered by the difficulty of obtaining solutions. In this paper, we introduce reducible MDPs whose exact solution can be obtained by solving a simpler MDP, termed the coordinate MDP. The value function and an optimal policy of a reducible MDP are linear functions of those of the coordinate MDP. The coordinate MDP does not involve the multi-dimensional endogenous state. Thus, we achieve dimension reduction on the reducible MDP by solving the coordinate MDP.
Extending the MDP framework to multiple players, we introduce reducible stochastic games. We show that these games reduce to simpler coordinate games that do not involve the multi-dimensional endogenous state. We specify sufficient conditions for the existence of a pure-strategy Markov perfect equilibrium in reducible stochastic games and derive closed-form expressions for the players' equilibrium values.
The reducible framework encompasses a variety of linear and nonlinear models and offers substantial simplification in analysis and computation. We provide guidelines for formulating problems as reducible models and illustrate ways to transform a model into the reducible framework. We demonstrate the applicability and modeling flexibility of reducible models in a wide range of contexts including capacity and inventory management and duopoly competition.
{"title":"Reducible Markov Decision Processes and Stochastic Games","authors":"Jie Ning","doi":"10.2139/ssrn.3225298","DOIUrl":"https://doi.org/10.2139/ssrn.3225298","url":null,"abstract":"Markov decision processes (MDPs) provide a powerful framework for analyzing dynamic decision making. However, their applications are significantly hindered by the difficulty of obtaining solutions. In this paper, we introduce reducible MDPs whose exact solution can be obtained by solving a simpler MDP, termed the coordinate MDP. The value function and an optimal policy of a reducible MDP are linear functions of those of the coordinate MDP. The coordinate MDP does not involve the multi-dimensional endogenous state. Thus, we achieve dimension reduction on the reducible MDP by solving the coordinate MDP.<br><br>Extending the MDP framework to multiple players, we introduce reducible stochastic games. We show that these games reduce to simpler coordinate games that do not involve the multi-dimensional endogenous state. We specify sufficient conditions for the existence of a pure-strategy Markov perfect equilibrium in reducible stochastic games and derive closed-form expressions for the players' equilibrium values.<br><br>The reducible framework encompasses a variety of linear and nonlinear models and offers substantial simplification in analysis and computation. We provide guidelines for formulating problems as reducible models and illustrate ways to transform a model into the reducible framework. We demonstrate the applicability and modeling flexibility of reducible models in a wide range of contexts including capacity and inventory management and duopoly competition. <br>","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132274986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Rakesh R. Mallipeddi, Subodha Kumar, C. Sriskandarajah, Yunxia Zhu
Explosive growth in the number of users on various social media platforms has transformed the way firms strategize their marketing activities. To take advantage of the vast size of social networks, firms have now turned their attention to influencer marketing wherein they employ independent influencers to promote their products on social media platforms. Despite the recent growth in influencer marketing, the problem of network seeding (i.e., identification of influencers to optimally post a firm’s message or advertisement) neither has been rigorously studied in the academic literature nor has been carefully addressed in practice. We develop a data-driven optimization framework to help a firm successfully conduct (i) short-horizon and (ii) long-horizon influencer marketing campaigns, for which two models are developed, respectively, to maximize the firm’s benefit. The models are based on the interactions with marketers, observation of firms’ message placements on social media, and model parameters estimated via empirical analysis performed on data from Twitter. Our empirical analysis discovers the effects of collective influence of multiple influencers and finds two important parameters to be included in the models, namely, multiple exposure effect and forgetting effect. For the short-horizon campaign, we develop an optimization model to select influencers and present structural properties for the model. Using these properties, we develop a mathematical programming based polynomial time procedure to provide near-optimal solutions. For the long-horizon problem, we develop an efficient solution procedure to simultaneously select influencers and schedule their message postings over a planning horizon. We demonstrate the superiority of our solution strategies for both short- and long-horizon problems against multiple benchmark methods used in practice. Finally, we present several managerially relevant insights for firms in the influencer marketing context. This paper was accepted by J. George Shanthikumar, big data analytics.
各种社交媒体平台上用户数量的爆炸式增长已经改变了企业制定营销活动战略的方式。为了利用社交网络的庞大规模，公司现在已经将注意力转向影响者营销，他们雇佣独立的影响者在社交媒体平台上推广他们的产品。尽管最近影响者营销有所增长，但网络播种(即识别影响者以最佳方式发布公司信息或广告)的问题既没有在学术文献中得到严格研究，也没有在实践中得到认真解决。我们开发了一个数据驱动的优化框架，以帮助公司成功地进行(i)短期和(ii)长期影响者营销活动，为此分别开发了两个模型，以最大化公司的利益。这些模型是基于与营销人员的互动，对公司在社交媒体上的信息放置的观察，以及通过对Twitter数据进行实证分析估计的模型参数。我们的实证分析发现了多个影响者的集体影响效应，并发现了两个需要纳入模型的重要参数，即多重暴露效应和遗忘效应。对于短期活动，我们开发了一个优化模型来选择影响者并为模型提供结构属性。利用这些性质，我们开发了一个基于数学规划的多项式时间过程来提供近最优解。对于长期问题，我们开发了一个有效的解决程序，同时选择影响者并在规划范围内安排他们的消息发布。针对实践中使用的多个基准方法，我们证明了我们的解决策略在短期和长期问题上的优越性。最后，我们为网红营销背景下的公司提出了几个管理相关的见解。本文被大数据分析J. George Shanthikumar接受。
{"title":"A Framework for Analyzing Influencer Marketing in Social Networks: Selection and Scheduling of Influencers","authors":"Rakesh R. Mallipeddi, Subodha Kumar, C. Sriskandarajah, Yunxia Zhu","doi":"10.2139/ssrn.3255198","DOIUrl":"https://doi.org/10.2139/ssrn.3255198","url":null,"abstract":"Explosive growth in the number of users on various social media platforms has transformed the way firms strategize their marketing activities. To take advantage of the vast size of social networks, firms have now turned their attention to influencer marketing wherein they employ independent influencers to promote their products on social media platforms. Despite the recent growth in influencer marketing, the problem of network seeding (i.e., identification of influencers to optimally post a firm’s message or advertisement) neither has been rigorously studied in the academic literature nor has been carefully addressed in practice. We develop a data-driven optimization framework to help a firm successfully conduct (i) short-horizon and (ii) long-horizon influencer marketing campaigns, for which two models are developed, respectively, to maximize the firm’s benefit. The models are based on the interactions with marketers, observation of firms’ message placements on social media, and model parameters estimated via empirical analysis performed on data from Twitter. Our empirical analysis discovers the effects of collective influence of multiple influencers and finds two important parameters to be included in the models, namely, multiple exposure effect and forgetting effect. For the short-horizon campaign, we develop an optimization model to select influencers and present structural properties for the model. Using these properties, we develop a mathematical programming based polynomial time procedure to provide near-optimal solutions. For the long-horizon problem, we develop an efficient solution procedure to simultaneously select influencers and schedule their message postings over a planning horizon. We demonstrate the superiority of our solution strategies for both short- and long-horizon problems against multiple benchmark methods used in practice. Finally, we present several managerially relevant insights for firms in the influencer marketing context. This paper was accepted by J. George Shanthikumar, big data analytics.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115479298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a carefully crafted dynamic programming approach for capacitated assortment optimization under the nested logit model in its utmost generality, potentially including partially captured nests and possibly synergistic products. Specifically, we show that the optimal revenue can be efficiently approached within any degree of accuracy through synthesizing ideas related to continuous-state dynamic programming, state space discretization, and sensitivity analysis of modified revenue functions. These developments allow us to devise the first fully polynomial-time approximation scheme in this context, thus resolving fundamental open questions posed in earlier literature.
{"title":"Approximation Schemes for Capacity-Constrained Assortment Optimization under the Nested Logit Model","authors":"D. Segev","doi":"10.2139/ssrn.3553264","DOIUrl":"https://doi.org/10.2139/ssrn.3553264","url":null,"abstract":"This paper proposes a carefully crafted dynamic programming approach for capacitated assortment optimization under the nested logit model in its utmost generality, potentially including partially captured nests and possibly synergistic products. Specifically, we show that the optimal revenue can be efficiently approached within any degree of accuracy through synthesizing ideas related to continuous-state dynamic programming, state space discretization, and sensitivity analysis of modified revenue functions. These developments allow us to devise the first fully polynomial-time approximation scheme in this context, thus resolving fundamental open questions posed in earlier literature.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134175251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.
{"title":"Extreme Points and Majorization: Economic Applications","authors":"Andreas Kleiner, B. Moldovanu, P. Strack","doi":"10.2139/ssrn.3551258","DOIUrl":"https://doi.org/10.2139/ssrn.3551258","url":null,"abstract":"We characterize the set of extreme points of monotonic functions that are either majorized by a given function \u0000 f or themselves majorize \u0000 f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function \u0000 f and inside the function is constant. Further consistency conditions need to be satisfied pinning down the value of an extreme point in each interval where it is constant. We apply these insights to a varied set of economic problems: equivalence and optimality of mechanisms for auctions and (matching) contests, Bayesian persuasion, optimal delegation, and decision making under uncertainty.\u0000","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129102530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An aid agency has CES preference aggregation over individual outcomes and allocates W units of discrete or bounded-continuous resources among N candidate recipients. Given observables and prior estimates, the expected needs without allocations and the marginal effects of allocations are heterogeneous across individuals. Despite combinatorial explosion with rising N, the optimal allocation function has closed-form solutions when marginal effects are nonincreasing. Solutions are characterized by resource-invariant optimal allocation queues that sequence the order in which individuals begin and stop to receive allocations. The welfare distance between optimal and alternative allocations is measured in percentage resource loss as resource equivalent variations.
{"title":"The Optimal Allocation of Resources among Heterogeneous Individuals","authors":"Fan Wang","doi":"10.2139/ssrn.3547706","DOIUrl":"https://doi.org/10.2139/ssrn.3547706","url":null,"abstract":"An aid agency has CES preference aggregation over individual outcomes and allocates W units of discrete or bounded-continuous resources among N candidate recipients. Given observables and prior estimates, the expected needs without allocations and the marginal effects of allocations are heterogeneous across individuals. Despite combinatorial explosion with rising N, the optimal allocation function has closed-form solutions when marginal effects are nonincreasing. Solutions are characterized by resource-invariant optimal allocation queues that sequence the order in which individuals begin and stop to receive allocations. The welfare distance between optimal and alternative allocations is measured in percentage resource loss as resource equivalent variations.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123208215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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.
{"title":"An Exact Method for Assortment Optimization under the Nested Logit Model","authors":"Laurent Alfandari, Alborz Hassanzadeh, I. Ljubić","doi":"10.2139/ssrn.3815699","DOIUrl":"https://doi.org/10.2139/ssrn.3815699","url":null,"abstract":"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.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"546 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116201370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Pak, Mark E. Ferguson, Olga Perdikaki, Su-Ming Wu
Promotional displays, such as end-of-aisle displays, provide a stimulus for discretionary and incremental sales at grocery stores, offering a powerful yet affordable tool to boost profit. In this study, we examine a store manager's choice of which stock-keeping units (SKUs) from a given category to assign to a promotional display space. While the academic literature and retail software solution providers offer a variety of optimization solutions for the assortment optimization problem, there is very little guidance for retailers on how to optimally determine when and what products to place on their promotional display space. Consequently, retailers often default to simple heuristics, which are typically suboptimal from a profit maximization standpoint, when making this decision. Thus, there is a need for a decision support tool to facilitate the product selection for promotional display space.
Using a grocery store sales transaction dataset, we demonstrate how to measure the incremental lift in sales of placing a particular SKU on promotional display space. Our optimization model includes the incremental lifts (from the estimation method) combined with the estimated base-sales rates and profit margins of each SKU so that the profit-maximizing SKU can be chosen for a promotional display space for each week of the year. Placing a SKU on promotional display can result in a significant lift in sales. For example, the estimated average display effect (i.e., sales lift) for the beer category across all SKUs and all weeks is 27%, which makes promotional display a very effective tool for stimulating incremental product sales. Overall, our methodology results in at least 1.6X improvement in incremental profit when compared to a common industry benchmark. We also test our methodology on two additional product categories and demonstrate that it performs equally well across product categories.
Our work provides an easy-to-implement, promotional display SKU-selection methodology that includes both an estimation and an optimization model. Our estimation model can handle an extensive and complex product assortment and accounts for important aspects of promotional activities such as the cannibalization of the inner aisle sales as well as halo effects. Our optimization model is flexible enough to consider practical aspects such as common business rules that restrict the selection of the same SKU over a consecutive set of weeks, display-related changeover costs and slotting fees offered by the manufacturers. Overall, our study underscores the importance of making effective promotional display decisions.
{"title":"Optimizing SKU Selection for Promotional Display Space at Grocery Retailers","authors":"O. Pak, Mark E. Ferguson, Olga Perdikaki, Su-Ming Wu","doi":"10.2139/ssrn.3506709","DOIUrl":"https://doi.org/10.2139/ssrn.3506709","url":null,"abstract":"Promotional displays, such as end-of-aisle displays, provide a stimulus for discretionary and incremental sales at grocery stores, offering a powerful yet affordable tool to boost profit. In this study, we examine a store manager's choice of which stock-keeping units (SKUs) from a given category to assign to a promotional display space. While the academic literature and retail software solution providers offer a variety of optimization solutions for the assortment optimization problem, there is very little guidance for retailers on how to optimally determine when and what products to place on their promotional display space. Consequently, retailers often default to simple heuristics, which are typically suboptimal from a profit maximization standpoint, when making this decision. Thus, there is a need for a decision support tool to facilitate the product selection for promotional display space.<br><br>Using a grocery store sales transaction dataset, we demonstrate how to measure the incremental lift in sales of placing a particular SKU on promotional display space. Our optimization model includes the incremental lifts (from the estimation method) combined with the estimated base-sales rates and profit margins of each SKU so that the profit-maximizing SKU can be chosen for a promotional display space for each week of the year. Placing a SKU on promotional display can result in a significant lift in sales. For example, the estimated average display effect (i.e., sales lift) for the beer category across all SKUs and all weeks is 27%, which makes promotional display a very effective tool for stimulating incremental product sales. Overall, our methodology results in at least 1.6X improvement in incremental profit when compared to a common industry benchmark. We also test our methodology on two additional product categories and demonstrate that it performs equally well across product categories.<br><br>Our work provides an easy-to-implement, promotional display SKU-selection methodology that includes both an estimation and an optimization model. Our estimation model can handle an extensive and complex product assortment and accounts for important aspects of promotional activities such as the cannibalization of the inner aisle sales as well as halo effects. Our optimization model is flexible enough to consider practical aspects such as common business rules that restrict the selection of the same SKU over a consecutive set of weeks, display-related changeover costs and slotting fees offered by the manufacturers. Overall, our study underscores the importance of making effective promotional display decisions.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128399229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We provide a simple proof of strong duality for the linear persuasion problem. The duality is established in Dworczak and Martini (2019) , under slightly stronger assumptions, using techniques from the literature on optimization with stochastic dominance constraints and several approximation arguments. We provide a short, alternative proof that is based on a direct argument to show the existence of optimal price functions, and on switching the roles of the primal and the dual to show that there is no duality gap.
{"title":"A Simple Proof of Strong Duality in the Linear Persuasion Problem","authors":"D. Dizdar, E. Kovác","doi":"10.2139/ssrn.3426166","DOIUrl":"https://doi.org/10.2139/ssrn.3426166","url":null,"abstract":"Abstract We provide a simple proof of strong duality for the linear persuasion problem. The duality is established in Dworczak and Martini (2019) , under slightly stronger assumptions, using techniques from the literature on optimization with stochastic dominance constraints and several approximation arguments. We provide a short, alternative proof that is based on a direct argument to show the existence of optimal price functions, and on switching the roles of the primal and the dual to show that there is no duality gap.","PeriodicalId":376757,"journal":{"name":"Decision-Making in Operations Research eJournal","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124744216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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