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

Essays on E-Commerce and Omnichannel Retail Operations

The advent of e-commerce has impacted the retail industry, as retail firms have innovated in response to customers increasingly preferring to purchase products online. This dissertation studies operational problems that accompany such retail innovations, and provides tractable heuristic solutions developed using stochastic and robust optimization methods. In particular, the first two chapters focus on the value of fulfillment flexibility - online orders can be fulfilled from any node in the firm's fulfillment network. The first chapter is devoted to omnichannel retailing, where e-commerce demand is integrated with the physical network of stores through ship-from-store fulfillment. For a retailer with a network of physical stores and fulfillment centers facing two demands (online and in-store), we consider the following interlinked decisions - how much inventory to keep at each location and where to fulfill each online order from. We show that the value of considering fulfillment flexibility in inventory planning is highest when there is a moderate mix of online and in-store demands, and develop computationally fast heuristics with promising asymptotic performance for large scale networks, which are shown to improve upon traditional strategies. The second chapter considers a pure play e-commerce fulfillment network, and studies the inventory placement decision. As e-commerce demands are volatile due to a variety of factors (price-matching, recommendation engines, etc.), we consider a distributionally robust setting, where the objective is to minimize the worst-case expected cost under given mean and covariance matrices of the underlying demand distribution. For this NP-hard problem, we develop computationally tractable heuristic in the form of a semi-definite program, with dimension quadratic in the size of the network. In the face of distribution uncertainty, we show that the robust heuristic outperforms inventory solutions that assume incorrect distributions. The final chapter offers a new take on a classic problem in retail - customer returns, which has grown to be an important issue in recent times with firms competing to provide lenient and convenient return policies to boost their e-commerce sales. However, several customers take advantage of such policies, which can lead to loss in revenue and increase in inventory costs. We study different return policies that a firm can employ depending on the information about customers' return behavior that is available to the firm. We derive the structure of the optimal return policies and show that personalizing return policies based on customers' historical data can significantly improve the firm's profits, but allows the firm to extract all customer surplus.PHDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153348/1/arav_1.pd

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

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