Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor

With rapidly increasing e-commerce sales, firms are leveraging the virtual pooling of online demands across customer locations in deciding the amount of inventory to be placed in each node in a fulfillment network. Such solutions require knowledge of the joint distribution of demands; however, in reality, only partial information about the joint distribution may be reliably estimated. We propose a distributionally robust multi-location newsvendor model for network inventory optimization where the worst-case expected cost is minimized over the set of demand distributions satisfying the known mean and covariance information. For the special case of two homogeneous customer locations with correlated demands, we show that a six-point distribution achieves the worst-case expected cost, and derive a closed-form expression for the optimal inventory decision. The general multi-location problem can be shown to be NP-hard. We develop a computationally tractable upper bound through the solution of a semidefinite program (SDP), which also yields heuristic inventory levels, for a special class of fulfillment cost structures, namely nested fulfillment structures. We also develop an algorithm to convert any general distance-based fulfillment cost structure into a nested fulfillment structure which tightly approximates the expected total fulfillment cost.https://deepblue.lib.umich.edu/bitstream/2027.42/146785/1/1389_Govindarajan.pd

Data-Driven Pricing for a New Product

Decisions regarding new products are often difficult to make, and mistakes can have grave consequences for a firm’s bottom line. Often, firms lack important information about a new product, such as its potential market size and the speed of its adoption by consumers. One of the most popular frameworks that has been used for modeling new product adoption is the Bass model. Although the Bass model and its many variants are used to study dynamic pricing of new products, the vast majority of these models require a priori knowledge of parameters that can only be estimated from historical data or guessed using institutional knowledge. In this paper, we study the interplay between pricing and learning for a monopolist whose objective is to maximize the expected revenue of a new product over a finite selling horizon. We extend the generalized Bass model to a stochastic setting by modeling adoption through a continuous-time Markov chain with which the adoption rate depends on the selling price and on the number of past sales. We study a pricing problem in which the parameters of this demand model are unknown, but the seller can utilize real-time demand data for learning the parameters. We propose two simple and computationally tractable pricing policies with O(ln m) regret, where m is the market size

Joint Inventory and Fulfillment Decisions for Omnichannel Retail Networks

With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration, ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration, ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.http://deepblue.lib.umich.edu/bitstream/2027.42/136157/1/1341_Govindarajan.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136157/4/1341_Govindarajan_Apr2017.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136157/6/1341_Govindarajan_Jan18.pdfDescription of 1341_Govindarajan_Apr2017.pdf : April 2017 revisionDescription of 1341_Govindarajan_Jan18.pdf : January 2018 revisio

Data-driven optimization and analytics for operations management applications

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2013.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (pages 163-166).In this thesis, we study data-driven decision making in operation management contexts, with a focus on both theoretical and practical aspects. The first part of the thesis analyzes the well-known newsvendor model but under the assumption that, even though demand is stochastic, its probability distribution is not part of the input. Instead, the only information available is a set of independent samples drawn from the demand distribution. We analyze the well-known sample average approximation (SAA) approach, and obtain new tight analytical bounds on the accuracy of the SAA solution. Unlike previous work, these bounds match the empirical performance of SAA observed in extensive computational experiments. Our analysis reveals that a distribution's weighted mean spread (WMS) impacts SAA accuracy. Furthermore, we are able to derive distribution parametric free bound on SAA accuracy for log-concave distributions through an innovative optimization-based analysis which minimizes WMS over the distribution family. In the second part of the thesis, we use spread information to introduce new families of demand distributions under the minimax regret framework. We propose order policies that require only a distribution's mean and spread information. These policies have several attractive properties. First, they take the form of simple closed-form expressions. Second, we can quantify an upper bound on the resulting regret. Third, under an environment of high profit margins, they are provably near-optimal under mild technical assumptions on the failure rate of the demand distribution. And finally, the information that they require is easy to estimate with data. We show in extensive numerical simulations that when profit margins are high, even if the information in our policy is estimated from (sometimes few) samples, they often manage to capture at least 99% of the optimal expected profit. The third part of the thesis describes both applied and analytical work in collaboration with a large multi-state gas utility. We address a major operational resource allocation problem in which some of the jobs are scheduled and known in advance, and some are unpredictable and have to be addressed as they appear. We employ a novel decomposition approach that solves the problem in two phases. The first is a job scheduling phase, where regular jobs are scheduled over a time horizon. The second is a crew assignment phase, which assigns jobs to maintenance crews under a stochastic number of future emergencies. We propose heuristics for both phases using linear programming relaxation and list scheduling. Using our models, we develop a decision support tool for the utility which is currently being piloted in one of the company's sites. Based on the utility's data, we project that the tool will result in 55% reduction in overtime hours.by Joline Ann Villaranda Uichanco.Ph. D

Data-driven revenue management

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007.Includes bibliographical references (p. 125-127).In this thesis, we consider the classical newsvendor model and various important extensions. We do not assume that the demand distribution is known, rather the only information available is a set of independent samples drawn from the demand distribution. In particular, the variants of the model we consider are: the classical profit-maximization newsvendor model, the risk-averse newsvendor model and the price-setting newsvendor model. If the explicit demand distribution is known, then the exact solutions to these models can be found either analytically or numerically via simulation methods. However, in most real-life settings, the demand distribution is not available, and usually there is only historical demand data from past periods. Thus, data-driven approaches are appealing in solving these problems. In this thesis, we evaluate the theoretical and empirical performance of nonparametric and parametric approaches for solving the variants of the newsvendor model assuming partial information on the distribution. For the classical profit-maximization newsvendor model and the risk-averse newsvendor model we describe general non-parametric approaches that do not make any prior assumption on the true demand distribution. We extend and significantly improve previous theoretical bounds on the number of samples required to guarantee with high probability that the data-driven approach provides a near-optimal solution. By near-optimal we mean that the approximate solution performs arbitrarily close to the optimal solution that is computed with respect to the true demand distributions.(cont.) For the price-setting newsvendor problem, we analyze a previously proposed simulation-based approach for a linear-additive demand model, and again derive bounds on the number of samples required to ensure that the simulation-based approach provides a near-optimal solution. We also perform computational experiments to analyze the empirical performance of these data-driven approaches.by Joline Ann Villaranda Uichanco.S.M

NUMERICAL ALGORITHMS FOR OPTIMAL CONSUMPTION AND INVESTMENT WITH TRANSACTION COSTS

Bachelor'sBACHELOR OF SCIENCE (HONOURS

AMBIGUOUS RISK MEASURES AND PIECEWISE LINEAR UTILITY MODELS IN PORTFOLIO MANAGEMENT

Master'sMASTER OF SCIENCE IN COMPUTATIONAL ENGINEERIN

The Data-Driven Newsvendor Problem: New Bounds and Insights

Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments. This bound reveals that the demand distribution’s weighted mean spread affects the accuracy of the SAA heuristic.National Science Foundation (U.S.) (Grant DMS-0732175)National Science Foundation (Grant CMMI-0846554)United States. Air Force Office of Scientific Research (Award FA9550-08-1-0369)United States. Air Force Office of Scientific Research (Award FA9550-11-1-0150)National Science Foundation (U.S.) (Grant CMMI- 0824674)National Science Foundation (U.S.) (Grant CMMI-0758061

Joint inventory and fulfillment decisions for omnichannel retail networks

An omnichannel retailer with a network of physical stores and online fulfillment centers facing two demands (online and in‐store) has to make important, interlinked decisions—how much inventory to keep at each location and where to fulfill each online order from, as online demand can be fulfilled from any location with available inventory. We consider inventory decisions at the start of the selling horizon for a seasonal product, with online fulfillment decisions made multiple times over the horizon. To address the intractability in considering inventory and fulfillment decisions together, we relax the problem using a hindsight‐optimal bound, for which the inventory decision can be made independent of the optimal fulfillment decisions, while still incorporating virtual pooling of online demands across locations. We develop a computationally fast and scalable inventory heuristic for the multilocation problem based on the two‐store analysis. The inventory heuristic directly informs dynamic fulfillment decisions that guide online demand fulfillment from stores. Using a numerical study based on a fictitious network embedded in the United States, we show that our heuristic significantly outperforms traditional strategies. The value of centralized inventory planning is highest when there is a moderate mix of online and in‐store demands leading to synergies between pooling within and across locations, and this value increases with the size of the network. The inventory‐aware fulfillment heuristic considerably outperforms myopic policies seen in practice, and is found to be near‐optimal under a wide range of problem parameters.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/169266/1/nav21969_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/169266/2/nav21969-sup-0001-supinfo.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/169266/3/nav21969.pd

Asymmetry and Ambiguity in Newsvendor Models

The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose to maximize the worst-case profit. Most models of this type assume that only the mean and the variance are known, but do not attempt to include asymmetry properties of the distribution. Other recent models address asymmetry by including skewness and kurtosis. However, closed-form expressions on the optimal bounds are difficult to find for such models. In this paper, we propose a framework under which the expectation of a piecewise linear objective function is optimized over a set of distributions with known asymmetry properties. This asymmetry is represented by the first two moments of multiple random variables that result from partitioning the original distribution. In the simplest case, this reduces to semivariance. The optimal bounds can be solved through a second-order cone programming (SOCP) problem. This framework can be applied to the risk-averse and risk-neutral newsvendor problems and option pricing. We provide a closed-form expression for the worst-case newsvendor profit with only mean, variance and semivariance information