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 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

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

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

Business analytics for flexible resource allocation under random emergencies

In this paper, we describe both applied and analytical work in collaboration with a large multistate gas utility. The project addressed a major operational resource allocation challenge that is typical to the industry. We study the resource allocation problem in which some of the tasks are scheduled and known in advance, and some are unpredictable and have to be addressed as they appear. The utility has maintenance crews that perform both standard jobs (each must be done before a specified deadline) as well as respond to emergency gas leaks (that occur randomly throughout the day and could disrupt the schedule and lead to significant overtime). The goal is to perform all the standard jobs by their respective deadlines, to address all emergency jobs in a timely manner, and to minimize maintenance crew overtime. We employ a novel decomposition approach that solves the problem in two phases. The first is a job scheduling phase, where standard jobs are scheduled over a time horizon. The second is a crew assignment phase, which solves a stochastic mixed integer program to assign jobs to maintenance crews under a stochastic number of future emergencies. For the first phase, we propose a heuristic based on the rounding of a linear programming relaxation formulation and prove an analytical worst-case performance guarantee. For the second phase, we propose an algorithm for assigning crews that is motivated by the structure of an optimal solution. We used our models and heuristics to develop a decision support tool that is being piloted in one of the utility's sites. Using the utility's data, we project that the tool will result in a 55% reduction in overtime hours.National Science Foundation (U.S.) (Grant CMMI-1162034)National Science Foundation (U.S.) (Grant CMMI-0824674)National Science Foundation (U.S.) (Grant CMMI-0758061